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Sample records for adjoint transport equation

  1. Nonlinear Acceleration of a Continuous Finite Element Discretization of the Self-Adjoint Angular Flux Form of the Transport Equation

    SciTech Connect

    Richard Sanchez; Cristian Rabiti; Yaqi Wang

    2013-11-01

    Nonlinear acceleration of a continuous finite element (CFE) discretization of the transport equation requires a modification of the transport solution in order to achieve local conservation, a condition used in nonlinear acceleration to define the stopping criterion. In this work we implement a coarse-mesh finite difference acceleration for a CFE discretization of the second-order self-adjoint angular flux (SAAF) form of the transport equation and use a postprocessing to enforce local conservation. Numerical results are given for one-group source calculations of one-dimensional slabs. We also give a novel formal derivation of the boundary conditions for the SAAF.

  2. Weak self-adjoint differential equations

    NASA Astrophysics Data System (ADS)

    Gandarias, M. L.

    2011-07-01

    The concepts of self-adjoint and quasi self-adjoint equations were introduced by Ibragimov (2006 J. Math. Anal. Appl. 318 742-57 2007 Arch. ALGA 4 55-60). In Ibragimov (2007 J. Math. Anal. Appl. 333 311-28), a general theorem on conservation laws was proved. In this paper, we generalize the concept of self-adjoint and quasi self-adjoint equations by introducing the definition of weak self-adjoint equations. We find a class of weak self-adjoint quasi-linear parabolic equations. The property of a differential equation to be weak self-adjoint is important for constructing conservation laws associated with symmetries of the differential equation.

  3. Finite Element Solution of the Self-Adjoint Angular Flux Equation for Coupled Electron-Photon Transport

    SciTech Connect

    Liscum-Powell, Jennifer L.; Prinja, Anil B.; Morel, Jim E.; Lorence, Leonard J Jr.

    2002-11-15

    A novel approach is proposed for charged particle transport calculations using a recently developed second-order, self-adjoint angular flux (SAAF) form of the Boltzmann transport equation with continuous slowing-down. A finite element discretization that is linear continuous in space and linear discontinuous (LD) in energy is described and implemented in a one-dimensional, planar geometry, multigroup, discrete ordinates code for charged particle transport. The cross-section generating code CEPXS is used to generate the electron and photon transport cross sections employed in this code. The discrete ordinates SAAF transport equation is solved using source iteration in conjunction with an inner iteration acceleration scheme and an outer iteration acceleration scheme. Outer iterations are required with the LD energy discretization scheme because the two angular flux unknowns within each group are coupled, which gives rise to effective upscattering. The inner iteration convergence is accelerated using diffusion synthetic acceleration, and the outer iteration convergence is accelerated using a diamond difference approximation to the LD energy discretization. Computational results are given that demonstrate the effectiveness of our convergence acceleration schemes and the accuracy of our discretized SAAF equation.

  4. The compressible adjoint equations in geodynamics: equations and numerical assessment

    NASA Astrophysics Data System (ADS)

    Ghelichkhan, Siavash; Bunge, Hans-Peter

    2016-04-01

    The adjoint method is a powerful means to obtain gradient information in a mantle convection model relative to past flow structure. While the adjoint equations in geodynamics have been derived for the conservation equations of mantle flow in their incompressible form, the applicability of this approximation to Earth is limited, because density increases by almost a factor of two from the surface to the Core Mantle Boundary. Here we introduce the compressible adjoint equations for the conservation equations in the anelastic-liquid approximation. Our derivation applies an operator formulation in Hilbert spaces, to connect to recent work in seismology (Fichtner et al (2006)) and geodynamics (Horbach et al (2014)), where the approach was used to derive the adjoint equations for the wave equation and incompressible mantle flow. We present numerical tests of the newly derived equations based on twin experiments, focusing on three simulations. A first, termed Compressible, assumes the compressible forward and adjoint equations, and represents the consistent means of including compressibility effects. A second, termed Mixed, applies the compressible forward equation, but ignores compressibility effects in the adjoint equations, where the incompressible equations are used instead. A third simulation, termed Incompressible, neglects compressibility effects entirely in the forward and adjoint equations relative to the reference twin. The compressible and mixed formulations successfully restore earlier mantle flow structure, while the incompressible formulation yields noticeable artifacts. Our results suggest the use of a compressible formulation, when applying the adjoint method to seismically derived mantle heterogeneity structure.

  5. FAST TRACK COMMUNICATION Quasi self-adjoint nonlinear wave equations

    NASA Astrophysics Data System (ADS)

    Ibragimov, N. H.; Torrisi, M.; Tracinà, R.

    2010-11-01

    In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e.g. for constructing conservation laws associated with symmetries of the differential equation.

  6. Adjoint Function: Physical Basis of Variational & Perturbation Theory in Transport

    2009-07-27

    Version 00 Dr. J.D. Lewins has now released the following legacy book for free distribution: Importance: The Adjoint Function: The Physical Basis of Variational and Perturbation Theory in Transport and Diffusion Problems, North-Holland Publishing Company - Amsterdam, 582 pages, 1966 Introduction: Continuous Systems and the Variational Principle 1. The Fundamental Variational Principle 2. The Importance Function 3. Adjoint Equations 4. Variational Methods 5. Perturbation and Iterative Methods 6. Non-Linear Theory

  7. A new mathematical adjoint for the modified SAAF-SN equations

    SciTech Connect

    Schunert, Sebastian; Wang, Yaqi; Martineau, Richard; DeHart, Mark D.

    2015-01-01

    We present a new adjoint FEM weak form, which can be directly used for evaluating the mathematical adjoint, suitable for perturbation calculations, of the self-adjoint angular flux SN equations (SAAF-SN) without construction and transposition of the underlying coefficient matrix. Stabilization schemes incorporated in the described SAAF-SN method make the mathematical adjoint distinct from the physical adjoint, i.e. the solution of the continuous adjoint equation with SAAF-SN . This weak form is implemented into RattleSnake, the MOOSE (Multiphysics Object-Oriented Simulation Environment) based transport solver. Numerical results verify the correctness of the implementation and show its utility both for fixed source and eigenvalue problems.

  8. Weak self-adjointness and conservation laws for a porous medium equation

    NASA Astrophysics Data System (ADS)

    Gandarias, M. L.

    2012-06-01

    The concepts of self-adjoint and quasi self-adjoint equations were introduced by Ibragimov (2006, 2007) [4,7]. In Ibragimov (2007) [6] a general theorem on conservation laws was proved. In Gandarias (2011) [3] we generalized the concept of self-adjoint and quasi self-adjoint equations by introducing the definition of weak self-adjoint equations. In this paper we find the subclasses of weak self-adjoint porous medium equations. By using the property of weak self-adjointness we construct some conservation laws associated with symmetries of the differential equation.

  9. Adjoint electron-photon transport Monte Carlo calculations with ITS

    SciTech Connect

    Lorence, L.J.; Kensek, R.P.; Halbleib, J.A.; Morel, J.E.

    1995-02-01

    A general adjoint coupled electron-photon Monte Carlo code for solving the Boltzmann-Fokker-Planck equation has recently been created. It is a modified version of ITS 3.0, a coupled electronphoton Monte Carlo code that has world-wide distribution. The applicability of the new code to radiation-interaction problems of the type found in space environments is demonstrated.

  10. Nonlinear self-adjointness and conservation laws for a porous medium equation with absorption

    NASA Astrophysics Data System (ADS)

    Gandarias, M. L.; Bruzón, M. S.

    2013-10-01

    We give conditions for a general porous medium equation to be nonlinear self-adjoint. By using the property of nonlinear self-adjointness we construct some conservation laws associated with classical and nonclassical generators of a porous medium equation with absorption.

  11. Nonlinear self-adjointness and conservation laws of Klein-Gordon-Fock equation with central symmetry

    NASA Astrophysics Data System (ADS)

    Abdulwahhab, Muhammad Alim

    2015-05-01

    The concept of nonlinear self-adjointness, introduced by Ibragimov, has significantly extends approaches to constructing conservation laws associated with symmetries since it incorporates the strict self-adjointness, the quasi self-adjointness as well as the usual linear self-adjointness. Using this concept, the nonlinear self-adjointness condition for the Klein-Gordon-Fock equation was established and subsequently used to construct simplified but infinitely many nontrivial and independent conserved vectors. The Noether's theorem was further applied to the Klein-Gordon-Fock equation to explore more distinct first integrals, result shows that conservation laws constructed through this approach are exactly the same as those obtained under strict self-adjointness of Ibragimov's method.

  12. Periodic differential equations with self-adjoint monodromy operator

    NASA Astrophysics Data System (ADS)

    Yudovich, V. I.

    2001-04-01

    A linear differential equation \\dot u=A(t)u with p-periodic (generally speaking, unbounded) operator coefficient in a Euclidean or a Hilbert space \\mathbb H is considered. It is proved under natural constraints that the monodromy operator U_p is self-adjoint and strictly positive if A^*(-t)=A(t) for all t\\in\\mathbb R.It is shown that Hamiltonian systems in the class under consideration are usually unstable and, if they are stable, then the operator U_p reduces to the identity and all solutions are p-periodic.For higher frequencies averaged equations are derived. Remarkably, high-frequency modulation may double the number of critical values.General results are applied to rotational flows with cylindrical components of the velocity a_r=a_z=0, a_\\theta=\\lambda c(t)r^\\beta, \\beta<-1, c(t) is an even p-periodic function, and also to several problems of free gravitational convection of fluids in periodic fields.

  13. Spatial and angular variation and discretization of the self-adjoint transport operator

    SciTech Connect

    Roberts, R.M.

    1996-03-11

    This mathematical treatise begins with a variational derivation of a second-order, self-adjoint form of the transport equation. Next, a space variational functional whose minimization solves the transport equation is derived. A one-dimensional example is given. Then, {ital S{sub N}} and {ital P{sub N}} discretized functionals are expressed. Next, the surface contributions to the functionals are discretized. Finally, the explicit forms of the {rvec D} and {rvec H} matrices are given for four different geometries: hexahedron, wedge, tetrahedron, and pyramid.

  14. Optimization of a neutron detector design using adjoint transport simulation

    SciTech Connect

    Yi, C.; Manalo, K.; Huang, M.; Chin, M.; Edgar, C.; Applegate, S.; Sjoden, G.

    2012-07-01

    A synthetic aperture approach has been developed and investigated for Special Nuclear Materials (SNM) detection in vehicles passing a checkpoint at highway speeds. SNM is postulated to be stored in a moving vehicle and detector assemblies are placed on the road-side or in chambers embedded below the road surface. Neutron and gamma spectral awareness is important for the detector assembly design besides high efficiencies, so that different SNMs can be detected and identified with various possible shielding settings. The detector assembly design is composed of a CsI gamma-ray detector block and five neutron detector blocks, with peak efficiencies targeting different energy ranges determined by adjoint simulations. In this study, formulations are derived using adjoint transport simulations to estimate detector efficiencies. The formulations is applied to investigate several neutron detector designs for Block IV, which has its peak efficiency in the thermal range, and Block V, designed to maximize the total neutron counts over the entire energy spectrum. Other Blocks detect different neutron energies. All five neutron detector blocks and the gamma-ray block are assembled in both MCNP and deterministic simulation models, with detector responses calculated to validate the fully assembled design using a 30-group library. The simulation results show that the 30-group library, collapsed from an 80-group library using an adjoint-weighting approach with the YGROUP code, significantly reduced the computational cost while maintaining accuracy. (authors)

  15. Development of CO2 inversion system based on the adjoint of the global coupled transport model

    NASA Astrophysics Data System (ADS)

    Belikov, Dmitry; Maksyutov, Shamil; Chevallier, Frederic; Kaminski, Thomas; Ganshin, Alexander; Blessing, Simon

    2014-05-01

    We present the development of an inverse modeling system employing an adjoint of the global coupled transport model consisting of the National Institute for Environmental Studies (NIES) Eulerian transport model (TM) and the Lagrangian plume diffusion model (LPDM) FLEXPART. NIES TM is a three-dimensional atmospheric transport model, which solves the continuity equation for a number of atmospheric tracers on a grid spanning the entire globe. Spatial discretization is based on a reduced latitude-longitude grid and a hybrid sigma-isentropic coordinate in the vertical. NIES TM uses a horizontal resolution of 2.5°×2.5°. However, to resolve synoptic-scale tracer distributions and to have the ability to optimize fluxes at resolutions of 0.5° and higher we coupled NIES TM with the Lagrangian model FLEXPART. The Lagrangian component of the forward and adjoint models uses precalculated responses of the observed concentration to the surface fluxes and 3-D concentrations field simulated with the FLEXPART model. NIES TM and FLEXPART are driven by JRA-25/JCDAS reanalysis dataset. Construction of the adjoint of the Lagrangian part is less complicated, as LPDMs calculate the sensitivity of measurements to the surrounding emissions field by tracking a large number of "particles" backwards in time. Developing of the adjoint to Eulerian part was performed with automatic differentiation tool the Transformation of Algorithms in Fortran (TAF) software (http://www.FastOpt.com). This method leads to the discrete adjoint of NIES TM. The main advantage of the discrete adjoint is that the resulting gradients of the numerical cost function are exact, even for nonlinear algorithms. The overall advantages of our method are that: 1. No code modification of Lagrangian model is required, making it applicable to combination of global NIES TM and any Lagrangian model; 2. Once run, the Lagrangian output can be applied to any chemically neutral gas; 3. High-resolution results can be obtained over

  16. Adjoint-based deviational Monte Carlo methods for phonon transport calculations

    NASA Astrophysics Data System (ADS)

    Péraud, Jean-Philippe M.; Hadjiconstantinou, Nicolas G.

    2015-06-01

    In the field of linear transport, adjoint formulations exploit linearity to derive powerful reciprocity relations between a variety of quantities of interest. In this paper, we develop an adjoint formulation of the linearized Boltzmann transport equation for phonon transport. We use this formulation for accelerating deviational Monte Carlo simulations of complex, multiscale problems. Benefits include significant computational savings via direct variance reduction, or by enabling formulations which allow more efficient use of computational resources, such as formulations which provide high resolution in a particular phase-space dimension (e.g., spectral). We show that the proposed adjoint-based methods are particularly well suited to problems involving a wide range of length scales (e.g., nanometers to hundreds of microns) and lead to computational methods that can calculate quantities of interest with a cost that is independent of the system characteristic length scale, thus removing the traditional stiffness of kinetic descriptions. Applications to problems of current interest, such as simulation of transient thermoreflectance experiments or spectrally resolved calculation of the effective thermal conductivity of nanostructured materials, are presented and discussed in detail.

  17. Automating adjoint wave-equation travel-time tomography using scientific workflow

    NASA Astrophysics Data System (ADS)

    Zhang, Xiaofeng; Chen, Po; Pullammanappallil, Satish

    2013-10-01

    Recent advances in commodity high-performance computing technology have dramatically reduced the computational cost for solving the seismic wave equation in complex earth structure models. As a consequence, wave-equation-based seismic tomography techniques are being actively developed and gradually adopted in routine subsurface seismic imaging practices. Wave-equation travel-time tomography is a seismic tomography technique that inverts cross-correlation travel-time misfits using full-wave Fréchet kernels computed by solving the wave equation. This technique can be implemented very efficiently using the adjoint method, in which the misfits are back-propagated from the receivers (i.e., seismometers) to produce the adjoint wave-field and the interaction between the adjoint wave-field and the forward wave-field from the seismic source gives the gradient of the objective function. Once the gradient is available, a gradient-based optimization algorithm can then be adopted to produce an optimal earth structure model that minimizes the objective function. This methodology is conceptually straightforward, but its implementation in practical situations is highly complex, error-prone and computationally demanding. In this study, we demonstrate the feasibility of automating wave-equation travel-time tomography based on the adjoint method using Kepler, an open-source software package for designing, managing and executing scientific workflows. The workflow technology allows us to abstract away much of the complexity involved in the implementation in a manner that is both robust and scalable. Our automated adjoint wave-equation travel-time tomography package has been successfully applied on a real active-source seismic dataset.

  18. An exact and consistent adjoint method for high-fidelity discretization of the compressible flow equations

    NASA Astrophysics Data System (ADS)

    Subramanian, Ramanathan Vishnampet Ganapathi

    Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvement. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs. Such methods have enabled sensitivity analysis and active control of turbulence at engineering flow conditions by providing gradient information at computational cost comparable to that of simulating the flow. They accelerate convergence of numerical design optimization algorithms, though this is predicated on the availability of an accurate gradient of the discretized flow equations. This is challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. We analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space--time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge--Kutta-like scheme

  19. Adjoint equations and analysis of complex systems: Application to virus infection modelling

    NASA Astrophysics Data System (ADS)

    Marchuk, G. I.; Shutyaev, V.; Bocharov, G.

    2005-12-01

    Recent development of applied mathematics is characterized by ever increasing attempts to apply the modelling and computational approaches across various areas of the life sciences. The need for a rigorous analysis of the complex system dynamics in immunology has been recognized since more than three decades ago. The aim of the present paper is to draw attention to the method of adjoint equations. The methodology enables to obtain information about physical processes and examine the sensitivity of complex dynamical systems. This provides a basis for a better understanding of the causal relationships between the immune system's performance and its parameters and helps to improve the experimental design in the solution of applied problems. We show how the adjoint equations can be used to explain the changes in hepatitis B virus infection dynamics between individual patients.

  20. Nonlinear self-adjointness and invariant solutions of a 2D Rossby wave equation

    NASA Astrophysics Data System (ADS)

    Cimpoiasu, Rodica; Constantinescu, Radu

    2014-02-01

    The paper investigates the nonlinear self-adjointness of the nonlinear inviscid barotropic nondivergent vorticity equation in a beta-plane. It is a particular form of Rossby equation which does not possess variational structure and it is studied using a recently method developed by Ibragimov. The conservation laws associated with the infinite-dimensional symmetry Lie algebra models are constructed and analyzed. Based on this Lie algebra, some classes of similarity invariant solutions with nonconstant linear and nonlinear shears are obtained. It is also shown how one of the conservation laws generates a particular wave solution of this equation.

  1. A Least-Squares Transport Equation Compatible with Voids

    SciTech Connect

    Hansen, Jon; Peterson, Jacob; Morel, Jim; Ragusa, Jean; Wang, Yaqi

    2014-12-01

    Standard second-order self-adjoint forms of the transport equation, such as the even-parity, odd-parity, and self-adjoint angular flux equation, cannot be used in voids. Perhaps more important, they experience numerical convergence difficulties in near-voids. Here we present a new form of a second-order self-adjoint transport equation that has an advantage relative to standard forms in that it can be used in voids or near-voids. Our equation is closely related to the standard least-squares form of the transport equation with both equations being applicable in a void and having a nonconservative analytic form. However, unlike the standard least-squares form of the transport equation, our least-squares equation is compatible with source iteration. It has been found that the standard least-squares form of the transport equation with a linear-continuous finite-element spatial discretization has difficulty in the thick diffusion limit. Here we extensively test the 1D slab-geometry version of our scheme with respect to void solutions, spatial convergence rate, and the intermediate and thick diffusion limits. We also define an effective diffusion synthetic acceleration scheme for our discretization. Our conclusion is that our least-squares Sn formulation represents an excellent alternative to existing second-order Sn transport formulations

  2. Neural Network Training by Integration of Adjoint Systems of Equations Forward in Time

    NASA Technical Reports Server (NTRS)

    Toomarian, Nikzad (Inventor); Barhen, Jacob (Inventor)

    1999-01-01

    A method and apparatus for supervised neural learning of time dependent trajectories exploits the concepts of adjoint operators to enable computation of the gradient of an objective functional with respect to the various parameters of the network architecture in a highly efficient manner. Specifically. it combines the advantage of dramatic reductions in computational complexity inherent in adjoint methods with the ability to solve two adjoint systems of equations together forward in time. Not only is a large amount of computation and storage saved. but the handling of real-time applications becomes also possible. The invention has been applied it to two examples of representative complexity which have recently been analyzed in the open literature and demonstrated that a circular trajectory can be learned in approximately 200 iterations compared to the 12000 reported in the literature. A figure eight trajectory was achieved in under 500 iterations compared to 20000 previously required. Tbc trajectories computed using our new method are much closer to the target trajectories than was reported in previous studies.

  3. Neural network training by integration of adjoint systems of equations forward in time

    NASA Technical Reports Server (NTRS)

    Toomarian, Nikzad (Inventor); Barhen, Jacob (Inventor)

    1992-01-01

    A method and apparatus for supervised neural learning of time dependent trajectories exploits the concepts of adjoint operators to enable computation of the gradient of an objective functional with respect to the various parameters of the network architecture in a highly efficient manner. Specifically, it combines the advantage of dramatic reductions in computational complexity inherent in adjoint methods with the ability to solve two adjoint systems of equations together forward in time. Not only is a large amount of computation and storage saved, but the handling of real-time applications becomes also possible. The invention has been applied it to two examples of representative complexity which have recently been analyzed in the open literature and demonstrated that a circular trajectory can be learned in approximately 200 iterations compared to the 12000 reported in the literature. A figure eight trajectory was achieved in under 500 iterations compared to 20000 previously required. The trajectories computed using our new method are much closer to the target trajectories than was reported in previous studies.

  4. A finite-volume Eulerian-Lagrangian localized adjoint method for solution of the advection-dispersion equation

    USGS Publications Warehouse

    Healy, R.W.; Russell, T.F.

    1993-01-01

    Test results demonstrate that the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) outperforms standard finite-difference methods for solute transport problems that are dominated by advection. FVELLAM systematically conserves mass globally with all types of boundary conditions. Integrated finite differences, instead of finite elements, are used to approximate the governing equation. This approach, in conjunction with a forward tracking scheme, greatly facilitates mass conservation. The mass storage integral is numerically evaluated at the current time level, and quadrature points are then tracked forward in time to the next level. Forward tracking permits straightforward treatment of inflow boundaries, thus avoiding the inherent problem in backtracking of characteristic lines intersecting inflow boundaries. FVELLAM extends previous results by obtaining mass conservation locally on Lagrangian space-time elements. -from Authors

  5. A new least-squares transport equation compatible with voids

    SciTech Connect

    Hansen, J. B.; Morel, J. E.

    2013-07-01

    We define a new least-squares transport equation that is applicable in voids, can be solved using source iteration with diffusion-synthetic acceleration, and requires only the solution of an independent set of second-order self-adjoint equations for each direction during each source iteration. We derive the equation, discretize it using the S{sub n} method in conjunction with a linear-continuous finite-element method in space, and computationally demonstrate various of its properties. (authors)

  6. Solution of the self-adjoint radiative transfer equation on hybrid computer systems

    NASA Astrophysics Data System (ADS)

    Gasilov, V. A.; Kuchugov, P. A.; Olkhovskaya, O. G.; Chetverushkin, B. N.

    2016-06-01

    A new technique for simulating three-dimensional radiative energy transfer for the use in the software designed for the predictive simulation of plasma with high energy density on parallel computers is proposed. A highly scalable algorithm that takes into account the angular dependence of the radiation intensity and is free of the ray effect is developed based on the solution of a second-order equation with a self-adjoint operator. A distinctive feature of this algorithm is a preliminary transformation of rotation to eliminate mixed derivatives with respect to the spatial variables, simplify the structure of the difference operator, and accelerate the convergence of the iterative solution of the equation. It is shown that the proposed method correctly reproduces the limiting cases—isotropic radiation and the directed radiation with a δ-shaped angular distribution.

  7. Sensitivity Analysis for Reactor Period Induced by Positive Reactivity Using One-point Adjoint Kinetic Equation

    NASA Astrophysics Data System (ADS)

    Chiba, G.; Tsuji, M.; Narabayashi, T.

    2014-04-01

    In order to better predict a kinetic behavior of a nuclear fission reactor, an improvement of the delayed neutron parameters is essential. The present paper specifies important nuclear data for a reactor kinetics: Fission yield and decay constant data of 86Ge, some bromine isotopes, 94Rb, 98mY and some iodine isotopes. Their importance is quantified as sensitivities with a help of the adjoint kinetic equation, and it is found that they are dependent on an inserted reactivity (or a reactor period). Moreover, dependence of sensitivities on nuclear data files is also quantified using the latest files. Even though the currently evaluated data are used, there are large differences among different data files from a view point of the delayed neutrons.

  8. Adjoint transport calculations for sensitivity analysis of the Hiroshima air-over-ground environment

    SciTech Connect

    Broadhead, B.L.; Cacuci, D.G.; Pace, J.V. III

    1984-01-01

    A major effort within the US Dose Reassessment Program is aimed at recalculating the transport of initial nuclear radiation in an air-over-ground environment. This paper is the first report of results from adjoint calculations in the Hiroshima air-over-ground environment. The calculations use a Hiroshima/Nagasaki multi-element ground, ENDF/B-V nuclear data, one-dimensional ANISN flux weighting for neutron and gamma cross sections, a source obtained by two-dimensional hydrodynamic and three-dimensional transport calculations, and best-estimate atmospheric conditions from Japanese sources. 7 references, 2 figures.

  9. A three-dimensional finite-volume Eulerian-Lagrangian Localized Adjoint Method (ELLAM) for solute-transport modeling

    USGS Publications Warehouse

    Heberton, C.I.; Russell, T.F.; Konikow, L.F.; Hornberger, G.Z.

    2000-01-01

    This report documents the U.S. Geological Survey Eulerian-Lagrangian Localized Adjoint Method (ELLAM) algorithm that solves an integral form of the solute-transport equation, incorporating an implicit-in-time difference approximation for the dispersive and sink terms. Like the algorithm in the original version of the U.S. Geological Survey MOC3D transport model, ELLAM uses a method of characteristics approach to solve the transport equation on the basis of the velocity field. The ELLAM algorithm, however, is based on an integral formulation of conservation of mass and uses appropriate numerical techniques to obtain global conservation of mass. The implicit procedure eliminates several stability criteria required for an explicit formulation. Consequently, ELLAM allows large transport time increments to be used. ELLAM can produce qualitatively good results using a small number of transport time steps. A description of the ELLAM numerical method, the data-input requirements and output options, and the results of simulator testing and evaluation are presented. The ELLAM algorithm was evaluated for the same set of problems used to test and evaluate Version 1 and Version 2 of MOC3D. These test results indicate that ELLAM offers a viable alternative to the explicit and implicit solvers in MOC3D. Its use is desirable when mass balance is imperative or a fast, qualitative model result is needed. Although accurate solutions can be generated using ELLAM, its efficiency relative to the two previously documented solution algorithms is problem dependent.

  10. Solution of the advection-dispersion equation by a finite-volume eulerian-lagrangian local adjoint method

    USGS Publications Warehouse

    Healy, R.W.; Russell, T.F.

    1992-01-01

    A finite-volume Eulerian-Lagrangian local adjoint method for solution of the advection-dispersion equation is developed and discussed. The method is mass conservative and can solve advection-dominated ground-water solute-transport problems accurately and efficiently. An integrated finite-difference approach is used in the method. A key component of the method is that the integral representing the mass-storage term is evaluated numerically at the current time level. Integration points, and the mass associated with these points, are then forward tracked up to the next time level. The number of integration points required to reach a specified level of accuracy is problem dependent and increases as the sharpness of the simulated solute front increases. Integration points are generally equally spaced within each grid cell. For problems involving variable coefficients it has been found to be advantageous to include additional integration points at strategic locations in each well. These locations are determined by backtracking. Forward tracking of boundary fluxes by the method alleviates problems that are encountered in the backtracking approaches of most characteristic methods. A test problem is used to illustrate that the new method offers substantial advantages over other numerical methods for a wide range of problems.

  11. A family of Eulerian-Lagrangian localized adjoint methods for multi-dimensional advection-reaction equations

    SciTech Connect

    Wang, H.; Man, S.; Ewing, R.E.; Qin, G.; Lyons, S.L.; Al-Lawatia, M.

    1999-06-10

    Many difficult problems arise in the numerical simulation of fluid flow processes within porous media in petroleum reservoir simulation and in subsurface contaminant transport and remediation. The authors develop a family of Eulerian-Lagrangian localized adjoint methods for the solution of the initial-boundary value problems for first-order advection-reaction equations on general multi-dimensional domains. Different tracking algorithms, including the Euler and Runge-Kutta algorithms, are used. The derived schemes, which are full mass conservative, naturally incorporate inflow boundary conditions into their formulations and do not need any artificial outflow boundary conditions. Moreover, they have regularly structured, well-conditioned, symmetric, and positive-definite coefficient matrices, which can be efficiently solved by the conjugate gradient method in an optimal order number of iterations without any preconditioning needed. Numerical results are presented to compare the performance of the ELLAM schemes with many well studied and widely used methods, including the upwind finite difference method, the Galerkin and the Petrov-Galerkin finite element methods with backward-Euler or Crank-Nicolson temporal discretization, the streamline diffusion finite element methods, the monotonic upstream-centered scheme for conservation laws (MUSCL), and the Minmod scheme.

  12. Optimization of the Direct Discrete Method Using the Solution of the Adjoint Equation and its Application in the Multi-Group Neutron Diffusion Equation

    SciTech Connect

    Ayyoubzadeh, Seyed Mohsen; Vosoughi, Naser

    2011-09-14

    Obtaining the set of algebraic equations that directly correspond to a physical phenomenon has been viable in the recent direct discrete method (DDM). Although this method may find its roots in physical and geometrical considerations, there are still some degrees of freedom that one may suspect optimize-able. Here we have used the information embedded in the corresponding adjoint equation to form a local functional, which in turn by its minimization, yield suitable dual mesh positioning.

  13. Variational data assimilation with a semi-Lagrangian semi-implicit global shallow-water equation model and its adjoint

    NASA Technical Reports Server (NTRS)

    Li, Y.; Navon, I. M.; Courtier, P.; Gauthier, P.

    1993-01-01

    An adjoint model is developed for variational data assimilation using the 2D semi-Lagrangian semi-implicit (SLSI) shallow-water equation global model of Bates et al. with special attention being paid to the linearization of the interpolation routines. It is demonstrated that with larger time steps the limit of the validity of the tangent linear model will be curtailed due to the interpolations, especially in regions where sharp gradients in the interpolated variables coupled with strong advective wind occur, a synoptic situation common in the high latitudes. This effect is particularly evident near the pole in the Northern Hemisphere during the winter season. Variational data assimilation experiments of 'identical twin' type with observations available only at the end of the assimilation period perform well with this adjoint model. It is confirmed that the computational efficiency of the semi-Lagrangian scheme is preserved during the minimization process, related to the variational data assimilation procedure.

  14. Adjoint-Based Design of Rotors using the Navier-Stokes Equations in a Noninertial Reference Frame

    NASA Technical Reports Server (NTRS)

    Nielsen, Eric J.; Lee-Rausch, Elizabeth M.; Jones, William T.

    2009-01-01

    Optimization of rotorcraft flowfields using an adjoint method generally requires a time-dependent implementation of the equations. The current study examines an intermediate approach in which a subset of rotor flowfields are cast as steady problems in a noninertial reference frame. This technique permits the use of an existing steady-state adjoint formulation with minor modifications to perform sensitivity analyses. The formulation is valid for isolated rigid rotors in hover or where the freestream velocity is aligned with the axis of rotation. Discrete consistency of the implementation is demonstrated using comparisons with a complex-variable technique, and a number of single- and multi-point optimizations for the rotorcraft figure of merit function are shown for varying blade collective angles. Design trends are shown to remain consistent as the grid is refined.

  15. Adjoint-Based Design of Rotors Using the Navier-Stokes Equations in a Noninertial Reference Frame

    NASA Technical Reports Server (NTRS)

    Nielsen, Eric J.; Lee-Rausch, Elizabeth M.; Jones, William T.

    2010-01-01

    Optimization of rotorcraft flowfields using an adjoint method generally requires a time-dependent implementation of the equations. The current study examines an intermediate approach in which a subset of rotor flowfields are cast as steady problems in a noninertial reference frame. This technique permits the use of an existing steady-state adjoint formulation with minor modifications to perform sensitivity analyses. The formulation is valid for isolated rigid rotors in hover or where the freestream velocity is aligned with the axis of rotation. Discrete consistency of the implementation is demonstrated by using comparisons with a complex-variable technique, and a number of single- and multipoint optimizations for the rotorcraft figure of merit function are shown for varying blade collective angles. Design trends are shown to remain consistent as the grid is refined.

  16. Calculation of the response of cylindrical targets to collimated beams of particles using one-dimensional adjoint transport techniques. [LMFBR

    SciTech Connect

    Dupree, S. A.

    1980-06-01

    The use of adjoint techniques to determine the interaction of externally incident collimated beams of particles with cylindrical targets is a convenient means of examining a class of problems important in radiation transport studies. The theory relevant to such applications is derived, and a simple example involving a fissioning target is discussed. Results from both discrete ordinates and Monte Carlo transport-code calculations are presented, and comparisons are made with results obtained from forward calculations. The accuracy of the discrete ordinates adjoint results depends on the order of angular quadrature used in the calculation. Reasonable accuracy by using EQN quadratures can be expected from order S/sub 16/ or higher.

  17. Nonlinear self-adjointness and conservation laws

    NASA Astrophysics Data System (ADS)

    Ibragimov, N. H.

    2011-10-01

    The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the strict self-adjointness (definition 1) and quasi-self-adjointness introduced earlier by the author. It is shown that the equations possessing nonlinear self-adjointness can be written equivalently in a strictly self-adjoint form by using appropriate multipliers. All linear equations possess the property of nonlinear self-adjointness, and hence can be rewritten in a nonlinear strictly self-adjoint form. For example, the heat equation ut - Δu = 0 becomes strictly self-adjoint after multiplying by u-1. Conservation laws associated with symmetries are given in an explicit form for all nonlinearly self-adjoint partial differential equations and systems.

  18. Nonlinear self-adjointness, conservation laws, and the construction of solutions of partial differential equations using conservation laws

    NASA Astrophysics Data System (ADS)

    Ibragimov, N. Kh; Avdonina, E. D.

    2013-10-01

    The method of nonlinear self-adjointness, which was recently developed by the first author, gives a generalization of Noether's theorem. This new method significantly extends approaches to constructing conservation laws associated with symmetries, since it does not require the existence of a Lagrangian. In particular, it can be applied to any linear equations and any nonlinear equations that possess at least one local conservation law. The present paper provides a brief survey of results on conservation laws which have been obtained by this method and published mostly in recent preprints of the authors, along with a method for constructing exact solutions of systems of partial differential equations with the use of conservation laws. In most cases the solutions obtained by the method of conservation laws cannot be found as invariant or partially invariant solutions. Bibliography: 23 titles.

  19. Analytical solution for the advection-dispersion transport equation in layered media

    Technology Transfer Automated Retrieval System (TEKTRAN)

    The advection-dispersion transport equation with first-order decay was solved analytically for multi-layered media using the classic integral transform technique (CITT). The solution procedure used an associated non-self-adjoint advection-diffusion eigenvalue problem that had the same form and coef...

  20. Transport equations for oscillating neutrinos

    NASA Astrophysics Data System (ADS)

    Zhang, Yunfan; Burrows, Adam

    2013-11-01

    We derive a suite of generalized Boltzmann equations, based on the density-matrix formalism, that incorporates the physics of neutrino oscillations for two- and three-flavor oscillations, matter refraction, and self-refraction. The resulting equations are straightforward extensions of the classical transport equations that nevertheless contain the full physics of quantum oscillation phenomena. In this way, our broadened formalism provides a bridge between the familiar neutrino transport algorithms employed by supernova modelers and the more quantum-heavy approaches frequently employed to illuminate the various neutrino oscillation effects. We also provide the corresponding angular-moment versions of this generalized equation set. Our goal is to make it easier for astrophysicists to address oscillation phenomena in a language with which they are familiar. The equations we derive are simple and practical, and are intended to facilitate progress concerning oscillation phenomena in the context of core-collapse supernova theory.

  1. Transport equations in tokamak plasmas

    SciTech Connect

    Callen, J. D.; Hegna, C. C.; Cole, A. J.

    2010-05-15

    Tokamak plasma transport equations are usually obtained by flux surface averaging the collisional Braginskii equations. However, tokamak plasmas are not in collisional regimes. Also, ad hoc terms are added for neoclassical effects on the parallel Ohm's law, fluctuation-induced transport, heating, current-drive and flow sources and sinks, small magnetic field nonaxisymmetries, magnetic field transients, etc. A set of self-consistent second order in gyroradius fluid-moment-based transport equations for nearly axisymmetric tokamak plasmas has been developed using a kinetic-based approach. The derivation uses neoclassical-based parallel viscous force closures, and includes all the effects noted above. Plasma processes on successive time scales and constraints they impose are considered sequentially: compressional Alfven waves (Grad-Shafranov equilibrium, ion radial force balance), sound waves (pressure constant along field lines, incompressible flows within a flux surface), and collisions (electrons, parallel Ohm's law; ions, damping of poloidal flow). Radial particle fluxes are driven by the many second order in gyroradius toroidal angular torques on a plasma species: seven ambipolar collision-based ones (classical, neoclassical, etc.) and eight nonambipolar ones (fluctuation-induced, polarization flows from toroidal rotation transients, etc.). The plasma toroidal rotation equation results from setting to zero the net radial current induced by the nonambipolar fluxes. The radial particle flux consists of the collision-based intrinsically ambipolar fluxes plus the nonambipolar fluxes evaluated at the ambipolarity-enforcing toroidal plasma rotation (radial electric field). The energy transport equations do not involve an ambipolar constraint and hence are more directly obtained. The 'mean field' effects of microturbulence on the parallel Ohm's law, poloidal ion flow, particle fluxes, and toroidal momentum and energy transport are all included self-consistently. The

  2. Transport equations in tokamak plasmasa)

    NASA Astrophysics Data System (ADS)

    Callen, J. D.; Hegna, C. C.; Cole, A. J.

    2010-05-01

    Tokamak plasma transport equations are usually obtained by flux surface averaging the collisional Braginskii equations. However, tokamak plasmas are not in collisional regimes. Also, ad hoc terms are added for neoclassical effects on the parallel Ohm's law, fluctuation-induced transport, heating, current-drive and flow sources and sinks, small magnetic field nonaxisymmetries, magnetic field transients, etc. A set of self-consistent second order in gyroradius fluid-moment-based transport equations for nearly axisymmetric tokamak plasmas has been developed using a kinetic-based approach. The derivation uses neoclassical-based parallel viscous force closures, and includes all the effects noted above. Plasma processes on successive time scales and constraints they impose are considered sequentially: compressional Alfvén waves (Grad-Shafranov equilibrium, ion radial force balance), sound waves (pressure constant along field lines, incompressible flows within a flux surface), and collisions (electrons, parallel Ohm's law; ions, damping of poloidal flow). Radial particle fluxes are driven by the many second order in gyroradius toroidal angular torques on a plasma species: seven ambipolar collision-based ones (classical, neoclassical, etc.) and eight nonambipolar ones (fluctuation-induced, polarization flows from toroidal rotation transients, etc.). The plasma toroidal rotation equation results from setting to zero the net radial current induced by the nonambipolar fluxes. The radial particle flux consists of the collision-based intrinsically ambipolar fluxes plus the nonambipolar fluxes evaluated at the ambipolarity-enforcing toroidal plasma rotation (radial electric field). The energy transport equations do not involve an ambipolar constraint and hence are more directly obtained. The "mean field" effects of microturbulence on the parallel Ohm's law, poloidal ion flow, particle fluxes, and toroidal momentum and energy transport are all included self-consistently. The

  3. Transport Equations In Tokamak Plasmas

    NASA Astrophysics Data System (ADS)

    Callen, J. D.

    2009-11-01

    Tokamak plasma transport equations are usually obtained by flux surface averaging the collisional Braginskii equations. However, tokamak plasmas are not in collisional regimes. Also, ad hoc terms are added for: neoclassical effects on the parallel Ohm's law (trapped particle effects on resistivity, bootstrap current); fluctuation-induced transport; heating, current-drive and flow sources and sinks; small B field non-axisymmetries; magnetic field transients etc. A set of self-consistent second order in gyroradius fluid-moment-based transport equations for nearly axisymmetric tokamak plasmas has been developed recently using a kinetic-based framework. The derivation uses neoclassical-based parallel viscous force closures, and includes all the effects noted above. Plasma processes on successive time scales (and constraints they impose) are considered sequentially: compressional Alfv'en waves (Grad-Shafranov equilibrium, ion radial force balance); sound waves (pressure constant along field lines, incompressible flows within a flux surface); and ion collisions (damping of poloidal flow). Radial particle fluxes are driven by the many second order in gyroradius toroidal angular torques on the plasma fluid: 7 ambipolar collision-based ones (classical, neoclassical, etc.) and 8 non-ambipolar ones (fluctuation-induced, polarization flows from toroidal rotation transients etc.). The plasma toroidal rotation equation [1] results from setting to zero the net radial current induced by the non-ambipolar fluxes. The radial particle flux consists of the collision-based intrinsically ambipolar fluxes plus the non-ambipolar fluxes evaluated at the ambipolarity-enforcing toroidal plasma rotation (radial electric field). The energy transport equations do not involve an ambipolar constraint and hence are more directly obtained. The resultant transport equations will be presented and contrasted with the usual ones. [4pt] [1] J.D. Callen, A.J. Cole, C.C. Hegna, ``Toroidal Rotation In

  4. Solution of the advection-dispersion equation in two dimensions by a finite-volume Eulerian-Lagrangian localized adjoint method

    USGS Publications Warehouse

    Healy, R.W.; Russell, T.F.

    1998-01-01

    We extend the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) for solution of the advection-dispersion equation to two dimensions. The method can conserve mass globally and is not limited by restrictions on the size of the grid Peclet or Courant number. Therefore, it is well suited for solution of advection-dominated ground-water solute transport problems. In test problem comparisons with standard finite differences, FVELLAM is able to attain accurate solutions on much coarser space and time grids. On fine grids, the accuracy of the two methods is comparable. A critical aspect of FVELLAM (and all other ELLAMs) is evaluation of the mass storage integral from the preceding time level. In FVELLAM this may be accomplished with either a forward or backtracking approach. The forward tracking approach conserves mass globally and is the preferred approach. The backtracking approach is less computationally intensive, but not globally mass conservative. Boundary terms are systematically represented as integrals in space and time which are evaluated by a common integration scheme in conjunction with forward tracking through time. Unlike the one-dimensional case, local mass conservation cannot be guaranteed, so slight oscillations in concentration can develop, particularly in the vicinity of inflow or outflow boundaries. Published by Elsevier Science Ltd.

  5. AN EULERIAN-LAGRANGIAN LOCALIZED ADJOINT METHOD FOR THE ADVECTION-DIFFUSION EQUATION

    EPA Science Inventory

    Many numerical methods use characteristic analysis to accommodate the advective component of transport. Such characteristic methods include Eulerian-Lagrangian methods (ELM), modified method of characteristics (MMOC), and operator splitting methods. A generalization of characteri...

  6. Adjoint of the global Eulerian-Lagrangian coupled atmospheric transport model (A-GELCA v1.0): development and validation

    NASA Astrophysics Data System (ADS)

    Belikov, Dmitry A.; Maksyutov, Shamil; Yaremchuk, Alexey; Ganshin, Alexander; Kaminski, Thomas; Blessing, Simon; Sasakawa, Motoki; Gomez-Pelaez, Angel J.; Starchenko, Alexander

    2016-02-01

    We present the development of the Adjoint of the Global Eulerian-Lagrangian Coupled Atmospheric (A-GELCA) model that consists of the National Institute for Environmental Studies (NIES) model as an Eulerian three-dimensional transport model (TM), and FLEXPART (FLEXible PARTicle dispersion model) as the Lagrangian Particle Dispersion Model (LPDM). The forward tangent linear and adjoint components of the Eulerian model were constructed directly from the original NIES TM code using an automatic differentiation tool known as TAF (Transformation of Algorithms in Fortran; http://www.FastOpt.com, with additional manual pre- and post-processing aimed at improving transparency and clarity of the code and optimizing the performance of the computing, including MPI (Message Passing Interface). The Lagrangian component did not require any code modification, as LPDMs are self-adjoint and track a significant number of particles backward in time in order to calculate the sensitivity of the observations to the neighboring emission areas. The constructed Eulerian adjoint was coupled with the Lagrangian component at a time boundary in the global domain. The simulations presented in this work were performed using the A-GELCA model in forward and adjoint modes. The forward simulation shows that the coupled model improves reproduction of the seasonal cycle and short-term variability of CO2. Mean bias and standard deviation for five of the six Siberian sites considered decrease roughly by 1 ppm when using the coupled model. The adjoint of the Eulerian model was shown, through several numerical tests, to be very accurate (within machine epsilon with mismatch around to ±6 e-14) compared to direct forward sensitivity calculations. The developed adjoint of the coupled model combines the flux conservation and stability of an Eulerian discrete adjoint formulation with the flexibility, accuracy, and high resolution of a Lagrangian backward trajectory formulation. A-GELCA will be incorporated

  7. Solving the transport equation with quadratic finite elements: Theory and applications

    SciTech Connect

    Ferguson, J.M.

    1997-12-31

    At the 4th Joint Conference on Computational Mathematics, the author presented a paper introducing a new quadratic finite element scheme (QFEM) for solving the transport equation. In the ensuing year the author has obtained considerable experience in the application of this method, including solution of eigenvalue problems, transmission problems, and solution of the adjoint form of the equation as well as the usual forward solution. He will present detailed results, and will also discuss other refinements of his transport codes, particularly for 3-dimensional problems on rectilinear and non-rectilinear grids.

  8. Top-Down Inversion of Aerosol Emissions through Adjoint Integration of Satellite Radiance and GEOS-Chem Chemical Transport Model

    NASA Astrophysics Data System (ADS)

    Xu, X.; Wang, J.; Henze, D. K.; Qu, W.; Kopacz, M.

    2012-12-01

    The knowledge of aerosol emissions from both natural and anthropogenic sources are needed to study the impacts of tropospheric aerosol on atmospheric composition, climate, and human health, but large uncertainties persist in quantifying the aerosol sources with the current bottom-up methods. This study presents a new top-down approach that spatially constrains the amount of aerosol emissions from satellite (MODIS) observed reflectance with the adjoint of a chemistry transport model (GEOS-Chem). We apply this technique with a one-month case study (April 2008) over the East Asia. The bottom-up estimated sulfate-nitrate-ammonium precursors, such as sulfur dioxide (SO2), ammonia (NH3), and nitrogen oxides (NOx), all from INTEX-B 2006 inventory, emissions of black carbon (BC), organic carbon (OC) from Bond-2007 inventory, and mineral dust simulated from DEAD dust mobilization scheme, are spatially optimized from the GEOS-Chem model and its adjoint constrained by the aerosol optical depth (AOD) that are derived from MODIS reflectance with the GEOS-Chem aerosol single scattering properties. The adjoint inverse modeling for the study period yields notable decreases in anthropogenic aerosol emissions over China: 436 Gg (33.5%) for SO2, 378 Gg (34.5%) for NH3, 319 (18.8%) for NOx, 10 Gg (9.1%) for BC, and 30 Gg (15.0%) for OC. The total amount of the mineral dust emission is reduced by 56.4% from the DEAD mobilization module which simulates dust production of 19020 Gg. Sub-regional adjustments are significant and directions of changes are spatially different. The model simulation with optimized aerosol emissions shows much better agreement with independent observations from sun-spectrophotometer observed AOD from AERONET, MISR (Multi-angle Imaging SpectroRadiometer) AOD, OMI (Ozone Monitoring Instrument) NO2 and SO2 columns, and surface aerosol concentrations measured over both anthropogenic pollution and dust source regions. Assuming the used bottom-up anthropogenic

  9. The gBL transport equations

    SciTech Connect

    Mynick, H.E.

    1989-05-01

    The transport equations arising from the ''generalized Balescu- Lenard'' (gBL) collision operator are obtained, and some of their properties examined. The equations contain neoclassical and turbulent transport as two special cases, having the same structure. The resultant theory offers potential explanation for a number of results not well understood, including the anomalous pinch, observed ratios of Q/GAMMAT on TFTR, and numerical reproduction of ASDEX profiles by a model for turbulent transport invoked without derivation, but by analogy to neoclassical theory. The general equations are specialized to consideration of a number of particular transport mechanisms of interest. 10 refs.

  10. Extraction of macroscopic and microscopic adjoint concepts using a lattice Boltzmann method and discrete adjoint approach.

    PubMed

    Hekmat, Mohamad Hamed; Mirzaei, Masoud

    2015-01-01

    In the present research, we tried to improve the performance of the lattice Boltzmann (LB) -based adjoint approach by utilizing the mesoscopic inherent of the LB method. In this regard, two macroscopic discrete adjoint (MADA) and microscopic discrete adjoint (MIDA) approaches are used to answer the following two challenging questions. Is it possible to extend the concept of the macroscopic and microscopic variables of the flow field to the corresponding adjoint ones? Further, similar to the conservative laws in the LB method, is it possible to find the comparable conservation equations in the adjoint approach? If so, then a definite framework, similar to that used in the flow solution by the LB method, can be employed in the flow sensitivity analysis by the MIDA approach. This achievement can decrease the implementation cost and coding efforts of the MIDA method in complicated sensitivity analysis problems. First, the MADA and MIDA equations are extracted based on the LB method using the duality viewpoint. Meanwhile, using an elementary case, inverse design of a two-dimensional unsteady Poiseuille flow in a periodic channel with constant body forces, the procedure of analytical evaluation of the adjoint variables is described. The numerical results show that similar correlations between the distribution functions can be seen between the corresponding adjoint ones. Besides, the results are promising, emphasizing the flow field adjoint variables can be evaluated via the adjoint distribution functions. Finally, the adjoint conservative laws are introduced. PMID:25679735

  11. Introduction to Adjoint Models

    NASA Technical Reports Server (NTRS)

    Errico, Ronald M.

    2015-01-01

    In this lecture, some fundamentals of adjoint models will be described. This includes a basic derivation of tangent linear and corresponding adjoint models from a parent nonlinear model, the interpretation of adjoint-derived sensitivity fields, a description of methods of automatic differentiation, and the use of adjoint models to solve various optimization problems, including singular vectors. Concluding remarks will attempt to correct common misconceptions about adjoint models and their utilization.

  12. The telegraph equation in charged particle transport

    NASA Technical Reports Server (NTRS)

    Gombosi, T. I.; Jokipii, J. R.; Kota, J.; Lorencz, K.; Williams, L. L.

    1993-01-01

    We present a new derivation of the telegraph equation which modifies its coefficients. First, an infinite order partial differential equation is obtained for the velocity space solid angle-averaged phase-space distribution of particles which underwent at least a few collisions. It is shown that, in the lowest order asymptotic expansion, this equation simplifies to the well-known diffusion equation. The second-order asymptotic expansion for isotropic small-angle scattering results in a modified telegraph equation with a signal propagation speed of v(5/11) exp 1/2 instead of the usual v/3 exp 1/2. Our derivation of a modified telegraph equation follows from an expansion of the Boltzmann equation in the relevant smallness parameters and not from a truncation of an eigenfunction expansion. This equation is consistent with causality. It is shown that, under steady state conditions in a convecting plasma, the telegraph equation may be regarded as a diffusion equation with a modified transport coefficient, which describes a combination of diffusion and cosmic-ray inertia.

  13. On inter-tidal transport equation

    USGS Publications Warehouse

    Cheng, Ralph T.; Feng, Shizuo; Pangen, Xi

    1989-01-01

    The transports of solutes, sediments, nutrients, and other tracers are fundamental to the interactive physical, chemical, and biological processes in estuaries. The characteristic time scales for most estuarine biological and chemical processes are on the order of several tidal cycles or longer. To address the long-term transport mechanism meaningfully, the formulation of an inter-tidal conservation equation is the main subject of this paper. The commonly used inter-tidal conservation equation takes the form of a convection-dispersion equation in which the convection is represented by the Eulerian residual current, and the dispersion terms are due to the introduction of a Fickian hypothesis, unfortunately, the physical significance of this equation is not clear, and the introduction of a Fickian hypothesis is at best an ad hoc approximation. Some recent research results on the Lagrangian residual current suggest that the long-term transport problem is more closely related to the Lagrangian residual current than to the Eulerian residual current. With the aid of additional insight of residual current, the inter-tidal transport equation has been reformulated in this paper using a small perturbation method for a weakly nonlinear tidal system. When tidal flows can be represented by an M2 system, the new intertidal transport equation also takes the form of a convective-dispersion equation without the introduction of a Fickian hypothesis. The convective velocity turns out to be the first order Lagrangian residual current (the sum of the Eulerian residual current and the Stokes’ drift), and the correlation terms take the form of convection with the Stokes’ drift as the convective velocity. The remaining dispersion terms are perturbations of lower order solution to higher order solutions due to shear effect and turbulent mixing.

  14. NESTLE: Few-group neutron diffusion equation solver utilizing the nodal expansion method for eigenvalue, adjoint, fixed-source steady-state and transient problems

    SciTech Connect

    Turinsky, P.J.; Al-Chalabi, R.M.K.; Engrand, P.; Sarsour, H.N.; Faure, F.X.; Guo, W.

    1994-06-01

    NESTLE is a FORTRAN77 code that solves the few-group neutron diffusion equation utilizing the Nodal Expansion Method (NEM). NESTLE can solve the eigenvalue (criticality); eigenvalue adjoint; external fixed-source steady-state; or external fixed-source. or eigenvalue initiated transient problems. The code name NESTLE originates from the multi-problem solution capability, abbreviating Nodal Eigenvalue, Steady-state, Transient, Le core Evaluator. The eigenvalue problem allows criticality searches to be completed, and the external fixed-source steady-state problem can search to achieve a specified power level. Transient problems model delayed neutrons via precursor groups. Several core properties can be input as time dependent. Two or four energy groups can be utilized, with all energy groups being thermal groups (i.e. upscatter exits) if desired. Core geometries modelled include Cartesian and Hexagonal. Three, two and one dimensional models can be utilized with various symmetries. The non-linear iterative strategy associated with the NEM method is employed. An advantage of the non-linear iterative strategy is that NSTLE can be utilized to solve either the nodal or Finite Difference Method representation of the few-group neutron diffusion equation.

  15. Aspheric surface testing by irradiance transport equation

    NASA Astrophysics Data System (ADS)

    Shomali, Ramin; Darudi, Ahmad; Nasiri, Sadollah; Asgharsharghi Bonab, Armir

    2010-10-01

    In this paper a method for aspheric surface testing is presented. The method is based on solving the Irradiance Transport Equation (ITE).The accuracy of ITE normally depends on the amount of the pick to valley of the phase distribution. This subject is investigated by a simulation procedure.

  16. Numerical solution of the electron transport equation

    NASA Astrophysics Data System (ADS)

    Woods, Mark

    The electron transport equation has been solved many times for a variety of reasons. The main difficulty in its numerical solution is that it is a very stiff boundary value problem. The most common numerical methods for solving boundary value problems are symmetric collocation methods and shooting methods. Both of these types of methods can only be applied to the electron transport equation if the boundary conditions are altered with unrealistic assumptions because they require too many points to be practical. Further, they result in oscillating and negative solutions, which are physically meaningless for the problem at hand. For these reasons, all numerical methods for this problem to date are a bit unusual because they were designed to try and avoid the problem of extreme stiffness. This dissertation shows that there is no need to introduce spurious boundary conditions or invent other numerical methods for the electron transport equation. Rather, there already exists methods for very stiff boundary value problems within the numerical analysis literature. We demonstrate one such method in which the fast and slow modes of the boundary value problem are essentially decoupled. This allows for an upwind finite difference method to be applied to each mode as is appropriate. This greatly reduces the number of points needed in the mesh, and we demonstrate how this eliminates the need to define new boundary conditions. This method is verified by showing that under certain restrictive assumptions, the electron transport equation has an exact solution that can be written as an integral. We show that the solution from the upwind method agrees with the quadrature evaluation of the exact solution. This serves to verify that the upwind method is properly solving the electron transport equation. Further, it is demonstrated that the output of the upwind method can be used to compute auroral light emissions.

  17. Adjoint sensitivity study on idealized explosive cyclogenesis

    NASA Astrophysics Data System (ADS)

    Chu, Kekuan; Zhang, Yi

    2016-06-01

    The adjoint sensitivity related to explosive cyclogenesis in a conditionally unstable atmosphere is investigated in this study. The PSU/NCAR limited-area, nonhydrostatic primitive equation numerical model MM5 and its adjoint system are employed for numerical simulation and adjoint computation, respectively. To ensure the explosive development of a baroclinic wave, the forecast model is initialized with an idealized condition including an idealized two-dimensional baroclinic jet with a balanced three-dimensional moderate-amplitude disturbance, derived from a potential vorticity inversion technique. Firstly, the validity period of the tangent linear model for this idealized baroclinic wave case is discussed, considering different initial moisture distributions and a dry condition. Secondly, the 48-h forecast surface pressure center and the vertical component of the relative vorticity of the cyclone are selected as the response functions for adjoint computation in a dry and moist environment, respectively. The preliminary results show that the validity of the tangent linear assumption for this idealized baroclinic wave case can extend to 48 h with intense moist convection, and the validity period can last even longer in the dry adjoint integration. Adjoint sensitivity analysis indicates that the rapid development of the idealized baroclinic wave is sensitive to the initial wind and temperature perturbations around the steering level in the upstream. Moreover, the moist adjoint sensitivity can capture a secondary high sensitivity center in the upper troposphere, which cannot be depicted in the dry adjoint run.

  18. Code System to Solve the Few-Group Neutron Diffusion Equation Utilizing the Nodal Expansion Method (NEM) for Eigenvalue, Adjoint, and Fixed-Source

    2004-04-21

    Version 04 NESTLE solves the few-group neutron diffusion equation utilizing the NEM. The NESTLE code can solve the eigenvalue (criticality), eigenvalue adjoint, external fixed-source steady-state, and external fixed-source or eigenvalue initiated transient problems. The eigenvalue problem allows criticality searches to be completed, and the external fixed-source steady-state problem can search to achieve a specified power level. Transient problems model delayed neutrons via precursor groups. Several core properties can be input as time dependent. Two- ormore » four-energy groups can be utilized, with all energy groups being thermal groups (i.e., upscatter exits) if desired. Core geometries modeled include Cartesian and hexagonal. Three-, two-, and one-dimensional models can be utilized with various symmetries. The thermal conditions predicted by the thermal-hydraulic model of the core are used to correct cross sections for temperature and density effects. Cross sections are parameterized by color, control rod state (i.e., in or out), and burnup, allowing fuel depletion to be modeled. Either a macroscopic or microscopic model may be employed.« less

  19. Pdf - Transport equations for chemically reacting flows

    NASA Technical Reports Server (NTRS)

    Kollmann, W.

    1989-01-01

    The closure problem for the transport equations for pdf and the characteristic functions of turbulent, chemically reacting flows is addressed. The properties of the linear and closed equations for the characteristic functional for Eulerian and Lagrangian variables are established, and the closure problem for the finite-dimensional case is discussed for pdf and characteristic functions. It is shown that the closure for the scalar dissipation term in the pdf equation developed by Dopazo (1979) and Kollmann et al. (1982) results in a single integral, in contrast to the pdf, where double integration is required. Some recent results using pdf methods obtained for turbulent flows with combustion, including effects of chemical nonequilibrium, are discussed.

  20. Maximal stochastic transport in the Lorenz equations

    NASA Astrophysics Data System (ADS)

    Agarwal, Sahil; Wettlaufer, John

    2015-11-01

    We calculate the stochastic upper bounds for the Lorenz equations using an extension of the background method. In analogy with Rayleigh-Benard convection the upper bounds are for heat transport versus Rayleigh number. As might be expected the stochastic upper bounds are larger than the deterministic counterpart of Souza and Doering (2015), but their variation with noise amplitude exhibits surprising behavior. Below the transition to chaotic dynamics the upper bounds increase monotonically with noise amplitude. However, in the chaotic regime this monotonicity is lost; at a particular Rayleigh number the bound may increase or decrease with noise amplitude. The origin of this behavior is the coupling between the noise and unstable periodic orbits. This is confirmed by examining the close returns plots of the full solutions to the stochastic equations. Finally, we note that these solutions demonstrate that the effect of noise is equivalent to the effect of chaos.

  1. Nonlinear self-adjointness through differential substitutions

    NASA Astrophysics Data System (ADS)

    Gandarias, M. L.

    2014-10-01

    It is known (Ibragimov, 2011; Galiakberova and Ibragimov, 2013) [14,18] that the property of nonlinear self-adjointness allows to associate conservation laws of the equations under study, with their symmetries. In this paper we show that, even when the equation is nonlinearly self-adjoint with a non differential substitution, finding the explicit form of the differential substitution can provide new conservation laws associated to its symmetries. By using the general theorem on conservation laws (Ibragimov, 2007) [11] and the property of nonlinear self-adjointness we find some new conservation laws for the modified Harry-Dym equation. By using a differential substitution we construct a conservation law for the Harry-Dym equation, which has not been derived before using Ibragimov method.

  2. Application of adjoint operators to neural learning

    NASA Technical Reports Server (NTRS)

    Barhen, J.; Toomarian, N.; Gulati, S.

    1990-01-01

    A technique for the efficient analytical computation of such parameters of the neural architecture as synaptic weights and neural gain is presented as a single solution of a set of adjoint equations. The learning model discussed concentrates on the adiabatic approximation only. A problem of interest is represented by a system of N coupled equations, and then adjoint operators are introduced. A neural network is formalized as an adaptive dynamical system whose temporal evolution is governed by a set of coupled nonlinear differential equations. An approach based on the minimization of a constrained neuromorphic energylike function is applied, and the complete learning dynamics are obtained as a result of the calculations.

  3. Nonlinear diffusion acceleration for the multigroup transport equation discretized with S{sub N} and continuous FEM with rattlesnake

    SciTech Connect

    Wang, Y.

    2013-07-01

    Nonlinear diffusion acceleration (NDA) can improve the performance of a neutron transport solver significantly especially for the multigroup eigenvalue problems. The high-order transport equation and the transport-corrected low-order diffusion equation form a nonlinear system in NDA, which can be solved via a Picard iteration. The consistency of the correction of the low-order equation is important to ensure the stabilization and effectiveness of the iteration. It also makes the low-order equation preserve the scalar flux of the high-order equation. In this paper, the consistent correction for a particular discretization scheme, self-adjoint angular flux (SAAF) formulation with discrete ordinates method (S{sub N}) and continuous finite element method (CFEM) is proposed for the multigroup neutron transport equation. Equations with the anisotropic scatterings and a void treatment are included. The Picard iteration with this scheme has been implemented and tested with RattleS{sub N}ake, a MOOSE-based application at INL. Convergence results are presented. (authors)

  4. Maximal stochastic transport in the Lorenz equations

    NASA Astrophysics Data System (ADS)

    Agarwal, Sahil; Wettlaufer, J. S.

    2016-01-01

    We calculate the stochastic upper bounds for the Lorenz equations using an extension of the background method. In analogy with Rayleigh-Bénard convection the upper bounds are for heat transport versus Rayleigh number. As might be expected, the stochastic upper bounds are larger than the deterministic counterpart of Souza and Doering [1], but their variation with noise amplitude exhibits interesting behavior. Below the transition to chaotic dynamics the upper bounds increase monotonically with noise amplitude. However, in the chaotic regime this monotonicity depends on the number of realizations in the ensemble; at a particular Rayleigh number the bound may increase or decrease with noise amplitude. The origin of this behavior is the coupling between the noise and unstable periodic orbits, the degree of which depends on the degree to which the ensemble represents the ergodic set. This is confirmed by examining the close returns plots of the full solutions to the stochastic equations and the numerical convergence of the noise correlations. The numerical convergence of both the ensemble and time averages of the noise correlations is sufficiently slow that it is the limiting aspect of the realization of these bounds. Finally, we note that the full solutions of the stochastic equations demonstrate that the effect of noise is equivalent to the effect of chaos.

  5. Asymptotic Analysis of Transport Equation in Annulus

    NASA Astrophysics Data System (ADS)

    Wu, Lei; Yang, Xiongfeng; Guo, Yan

    2016-09-01

    We consider the diffusive limit of a steady neutron transport equation with one-speed velocity in a two-dimensional annulus. A classical theorem in Bensoussan et al. (Publ Res Inst Math Sci 15:53-157, 1979) states that the solution can be approximated in L^{∞} by the sum of the interior solution and Knudsen layer derived from Milne problem. However, this result was disproved in Wu and Guo (Commun Math Phys 336:1473-1553, 2015) in a plate via a different boundary layer expansion with geometric correction. In this paper, we established the diffusive limit and provide a counterexample to Bensoussan et al. (1979) in non-convex domains.

  6. Model equations for high current transport

    SciTech Connect

    Lee, E.P.

    1985-06-01

    The use of distribution functions to model transverse beam dynamics is discussed. Emphasis is placed on envelope equations, moments, the Vlasov equation, and the Kapchinski-Vladimirskij distribution. 10 refs.

  7. Transport equations for multicomponent anisotropic space plasmas - A review

    NASA Technical Reports Server (NTRS)

    Barakat, A. R.; Schunk, R. W.

    1982-01-01

    An attempt is made to present a unified approach to the study of transport phenomena in multicomponent anisotropic space plasmas. In particular, a system of generalized transport equations is presented that can be applied to widely different plasma flow conditions. The generalized transport equations can describe subsonic and supersonic flows, collision-dominated and collisionless flows, plasma flows in rapidly changing magnetic field configurations, multicomponent plasma flows with large temperature differences between the interacting species, and plasma flows that contain anisotropic temperature distributions. In addition, if Maxwell's equations of electricity and magnetism are added to the system of transport equations, they can be used to model electrostatic shocks, double layers, and magnetic merging processes. These transport equations also contain terms which act to regulate both the heat flow and temperature anisotropy, processes which appear to be operating in the solar wind.

  8. Adjoint-Based Uncertainty Quantification with MCNP

    SciTech Connect

    Seifried, Jeffrey E.

    2011-09-01

    This work serves to quantify the instantaneous uncertainties in neutron transport simulations born from nuclear data and statistical counting uncertainties. Perturbation and adjoint theories are used to derive implicit sensitivity expressions. These expressions are transformed into forms that are convenient for construction with MCNP6, creating the ability to perform adjoint-based uncertainty quantification with MCNP6. These new tools are exercised on the depleted-uranium hybrid LIFE blanket, quantifying its sensitivities and uncertainties to important figures of merit. Overall, these uncertainty estimates are small (< 2%). Having quantified the sensitivities and uncertainties, physical understanding of the system is gained and some confidence in the simulation is acquired.

  9. Aerodynamic design optimization by using a continuous adjoint method

    NASA Astrophysics Data System (ADS)

    Luo, JiaQi; Xiong, JunTao; Liu, Feng

    2014-07-01

    This paper presents the fundamentals of a continuous adjoint method and the applications of this method to the aerodynamic design optimization of both external and internal flows. General formulation of the continuous adjoint equations and the corresponding boundary conditions are derived. With the adjoint method, the complete gradient information needed in the design optimization can be obtained by solving the governing flow equations and the corresponding adjoint equations only once for each cost function, regardless of the number of design parameters. An inverse design of airfoil is firstly performed to study the accuracy of the adjoint gradient and the effectiveness of the adjoint method as an inverse design method. Then the method is used to perform a series of single and multiple point design optimization problems involving the drag reduction of airfoil, wing, and wing-body configuration, and the aerodynamic performance improvement of turbine and compressor blade rows. The results demonstrate that the continuous adjoint method can efficiently and significantly improve the aerodynamic performance of the design in a shape optimization problem.

  10. Fully automatic adjoints: a robust and efficient mechanism for generating adjoint ocean models

    NASA Astrophysics Data System (ADS)

    Ham, D. A.; Farrell, P. E.; Funke, S. W.; Rognes, M. E.

    2012-04-01

    The problem of generating and maintaining adjoint models is sufficiently difficult that typically only the most advanced and well-resourced community ocean models achieve it. There are two current technologies which each suffer from their own limitations. Algorithmic differentiation, also called automatic differentiation, is employed by models such as the MITGCM [2] and the Alfred Wegener Institute model FESOM [3]. This technique is very difficult to apply to existing code, and requires a major initial investment to prepare the code for automatic adjoint generation. AD tools may also have difficulty with code employing modern software constructs such as derived data types. An alternative is to formulate the adjoint differential equation and to discretise this separately. This approach, known as the continuous adjoint and employed in ROMS [4], has the disadvantage that two different model code bases must be maintained and manually kept synchronised as the model develops. The discretisation of the continuous adjoint is not automatically consistent with that of the forward model, producing an additional source of error. The alternative presented here is to formulate the flow model in the high level language UFL (Unified Form Language) and to automatically generate the model using the software of the FEniCS project. In this approach it is the high level code specification which is differentiated, a task very similar to the formulation of the continuous adjoint [5]. However since the forward and adjoint models are generated automatically, the difficulty of maintaining them vanishes and the software engineering process is therefore robust. The scheduling and execution of the adjoint model, including the application of an appropriate checkpointing strategy is managed by libadjoint [1]. In contrast to the conventional algorithmic differentiation description of a model as a series of primitive mathematical operations, libadjoint employs a new abstraction of the simulation

  11. A rain splash transport equation assimilating field and laboratory measurements

    NASA Astrophysics Data System (ADS)

    Dunne, Thomas; Malmon, Daniel V.; Mudd, Simon M.

    2010-03-01

    Process-based models of hillslope evolution require transport equations relating sediment flux to its major controls. An equation for rain splash transport in the absence of overland flow was constructed by modifying an approach developed by Reeve (1982) and parameterizing it with measurements from single-drop laboratory experiments and simulated rainfall on a grassland in East Africa. The equation relates rain splash to hillslope gradient, the median raindrop diameter of a storm, and ground cover density; the effect of soil texture on detachability can be incorporated from other published results. The spatial and temporal applicability of such an equation for rain splash transport in the absence of overland flow on uncultivated hillslopes can be estimated from hydrological calculations. The predicted transport is lower than landscape-averaged geologic erosion rates from Kenya but is large enough to modify short, slowly eroding natural hillslopes as well as microtopographic interrill surfaces between which overland flow transports the mobilized sediment.

  12. Transport equations for partially ionized reactive plasma in magnetic field

    NASA Astrophysics Data System (ADS)

    Zhdanov, V. M.; Stepanenko, A. A.

    2016-06-01

    Transport equations for partially ionized reactive plasma in magnetic field taking into account the internal degrees of freedom and electronic excitation of plasma particles are derived. As a starting point of analysis the kinetic equation with a binary collision operator written in the Wang-Chang and Uhlenbeck form and with a reactive collision integral allowing for arbitrary chemical reactions is used. The linearized variant of Grad's moment method is applied to deduce the systems of moment equations for plasma and also full and reduced transport equations for plasma species nonequilibrium parameters.

  13. ADGEN: ADjoint GENerator for computer models

    SciTech Connect

    Worley, B.A.; Pin, F.G.; Horwedel, J.E.; Oblow, E.M.

    1989-05-01

    This paper presents the development of a FORTRAN compiler and an associated supporting software library called ADGEN. ADGEN reads FORTRAN models as input and produces and enhanced version of the input model. The enhanced version reproduces the original model calculations but also has the capability to calculate derivatives of model results of interest with respect to any and all of the model data and input parameters. The method for calculating the derivatives and sensitivities is the adjoint method. Partial derivatives are calculated analytically using computer calculus and saved as elements of an adjoint matrix on direct assess storage. The total derivatives are calculated by solving an appropriate adjoint equation. ADGEN is applied to a major computer model of interest to the Low-Level Waste Community, the PRESTO-II model. PRESTO-II sample problem results reveal that ADGEN correctly calculates derivatives of response of interest with respect to 300 parameters. The execution time to create the adjoint matrix is a factor of 45 times the execution time of the reference sample problem. Once this matrix is determined, the derivatives with respect to 3000 parameters are calculated in a factor of 6.8 that of the reference model for each response of interest. For a single 3000 for determining these derivatives by parameter perturbations. The automation of the implementation of the adjoint technique for calculating derivatives and sensitivities eliminates the costly and manpower-intensive task of direct hand-implementation by reprogramming and thus makes the powerful adjoint technique more amenable for use in sensitivity analysis of existing models. 20 refs., 1 fig., 5 tabs.

  14. Asymptotic analysis of the several competitive equations to solve the time-dependent neutron transport equation

    SciTech Connect

    Shin, U.; Miller, W.F. Jr. |; Morel, J.E.

    1994-10-01

    Using conventional diffusion limit analysis, we asymptotically compare three competitive time-dependent equations (the telegrapher`s equation, the time-dependent Simplified P{sub 2} (SP{sub 2}) equation, and the time-dependent Simplified Evcn-Parity (SEP) equation). The time-dependent SP{sub 2} equation contains higher order asymptotic approximations of the time-dependent transport equation than the other equations in a physical regime in which the time-dependent diffusion equation is the leading order approximation. In addition, we derive the multigroup modified time-dependent SP{sub 2} equation from the multigroup time-dependent transport equation by means of an asymptotic expansion in which the multigroup time-dependent diffusion equation is the leading, order approximation. Numerical comparisons of the timedependent diffusion, the telegrapher`s, the time-dependent SP{sub 2}, and S{sub 8} solutions in 2-D X-Y geometry show that, in most cases, the SP{sub 2} solutions contain most of the transport corrections for the diffusion approximation.

  15. Compressible turbulence transport equations for generalized second order closure

    SciTech Connect

    Cloutman, L D

    1999-05-01

    Progress on the theory of second order closure in turbulence models of various types requires knowledge of the transport equations for various turbulence correlations. This report documents a procedure that provides such equations for a wide variety of turbulence averages for compressible flows of a multicomponent fluid. Generalizing some work by Germano for incompressible flows, we introduce an appropriate extension of his generalized second order correlations and use a generalized mass-weighted averaging procedure to derive transport equations for the correlations. The averaging procedure includes all of the commonly used averages as special cases. The resulting equations provide an internally consistent starting point for future work in developing single-point statistical turbulence transport models for fluid flows. The form invariance of the in-compressible equations also holds for the compressible case, and we discuss some of the closure issues and frequently ignored complications of statistical turbulence models of compressible flows.

  16. Goal-based angular adaptivity applied to a wavelet-based discretisation of the neutral particle transport equation

    SciTech Connect

    Goffin, Mark A.; Buchan, Andrew G.; Dargaville, Steven; Pain, Christopher C.; Smith, Paul N.; Smedley-Stevenson, Richard P.

    2015-01-15

    A method for applying goal-based adaptive methods to the angular resolution of the neutral particle transport equation is presented. The methods are applied to an octahedral wavelet discretisation of the spherical angular domain which allows for anisotropic resolution. The angular resolution is adapted across both the spatial and energy dimensions. The spatial domain is discretised using an inner-element sub-grid scale finite element method. The goal-based adaptive methods optimise the angular discretisation to minimise the error in a specific functional of the solution. The goal-based error estimators require the solution of an adjoint system to determine the importance to the specified functional. The error estimators and the novel methods to calculate them are described. Several examples are presented to demonstrate the effectiveness of the methods. It is shown that the methods can significantly reduce the number of unknowns and computational time required to obtain a given error. The novelty of the work is the use of goal-based adaptive methods to obtain anisotropic resolution in the angular domain for solving the transport equation. -- Highlights: •Wavelet angular discretisation used to solve transport equation. •Adaptive method developed for the wavelet discretisation. •Anisotropic angular resolution demonstrated through the adaptive method. •Adaptive method provides improvements in computational efficiency.

  17. Adjoint affine fusion and tadpoles

    NASA Astrophysics Data System (ADS)

    Urichuk, Andrew; Walton, Mark A.

    2016-06-01

    We study affine fusion with the adjoint representation. For simple Lie algebras, elementary and universal formulas determine the decomposition of a tensor product of an integrable highest-weight representation with the adjoint representation. Using the (refined) affine depth rule, we prove that equally striking results apply to adjoint affine fusion. For diagonal fusion, a coefficient equals the number of nonzero Dynkin labels of the relevant affine highest weight, minus 1. A nice lattice-polytope interpretation follows and allows the straightforward calculation of the genus-1 1-point adjoint Verlinde dimension, the adjoint affine fusion tadpole. Explicit formulas, (piecewise) polynomial in the level, are written for the adjoint tadpoles of all classical Lie algebras. We show that off-diagonal adjoint affine fusion is obtained from the corresponding tensor product by simply dropping non-dominant representations.

  18. Relativistic transport equations for electromagnetic scalar, and pseudoscalar potentials

    SciTech Connect

    Shin, G.R.; Rafelski, J.

    1995-10-01

    The authors propose a particular form of relativistic transport equations arising from the classical limit of single-time Wigner function for Dirac particles evolving in the presence of scalar, pseudoscalar, and electromagnetic fields. These relativistic Vlasov-type equations for the particle and the antiparticle sector of the Fock space can be also obtained assuming the validity of the Liouville`s equation given a suitable classical Hamiltonian and the associated force. 11 refs.

  19. Onsager's-principle-consistent 13-moment transport equations.

    PubMed

    Singh, Narendra; Agrawal, Amit

    2016-06-01

    A new set of generalized transport equations is derived for higher-order moments which are generated in evolution equation for stress tensor and heat flux vector in 13-moment equations. The closure we employ satisfies Onsager's symmetry principle. In the derivation, we do not employ a phase density function based on Hermite polynomial series in terms of higher-order moments, unlike Grad's approach. The distribution function is rather chosen to satisfy collision invariance, and H-theorem and capture relatively strong deviations from equilibrium. The phase density function satisfies the linearized Boltzmann equation and provides the correct value of the Prandtl number for monatomic gas. The derived equations are compared with Grad's 13-moments equations for gas modeled as Maxwellian molecule. The merits of the proposed equations against Grad's and R13 equations are discussed. In particular, it is noted that the proposed equations contain higher-order terms compared to these equations but require a fewer number of boundary conditions as compared to the R13 equations. The Knudsen number envelope which can be covered to describe flows with these equations is therefore expected to be larger as compared to the earlier equations.

  20. Central role of the observable electric potential in transport equations.

    PubMed

    Garrido, J; Compañ, V; López, M L

    2001-07-01

    Nonequilibrium systems are usually studied in the framework of transport equations that involve the true electric potential (TEP), a nonobservable variable. Nevertheless another electric potential, the observable electric potential (OEP), may be defined to construct a useful set of transport equations. In this paper several basic characteristics of the OEP are deduced and emphasized: (i) the OEP distribution depends on thermodynamic state of the solution, (ii) the observable equations have a reference value for all other transport equations, (iii) the bridge that connects the OEP with a certain TEP is usually defined by the ion activity coefficient, (iv) the electric charge density is a nonobservable variable, and (v) the OEP formulation constitutes a natural model for studying the fluxes in membrane systems. PMID:11461346

  1. Central role of the observable electric potential in transport equations.

    PubMed

    Garrido, J; Compañ, V; López, M L

    2001-07-01

    Nonequilibrium systems are usually studied in the framework of transport equations that involve the true electric potential (TEP), a nonobservable variable. Nevertheless another electric potential, the observable electric potential (OEP), may be defined to construct a useful set of transport equations. In this paper several basic characteristics of the OEP are deduced and emphasized: (i) the OEP distribution depends on thermodynamic state of the solution, (ii) the observable equations have a reference value for all other transport equations, (iii) the bridge that connects the OEP with a certain TEP is usually defined by the ion activity coefficient, (iv) the electric charge density is a nonobservable variable, and (v) the OEP formulation constitutes a natural model for studying the fluxes in membrane systems.

  2. Transport equations with second-order differential collision operators

    SciTech Connect

    Cosner, C.; Lenhart, S.M.; Protopopescu, V.

    1988-07-01

    This paper discusses existence, uniqueness, and a priori estimates for time-dependent and time-independent transport equations with unbounded collision operators. These collision operators are described by second-order differential operators resulting from diffusion in the velocity space. The transport equations are degenerate parabolic-elliptic partial differential equations, that are treated by modifications of the Fichera-Oleinik-Radkevic Theory of second-order equations with nonnegative characteristic form. They consider weak solutions in spaces that are extensions of L/sup rho/ to include traces on certain parts of the boundary. This extension is necessary due to the nonclassical boundary conditions imposed by the transport problem, which requires a specific analysis of the behavior of our weak solutions.

  3. Kinetic theory of transport processes in partially ionized reactive plasma, I: General transport equations

    NASA Astrophysics Data System (ADS)

    Zhdanov, V. M.; Stepanenko, A. A.

    2016-03-01

    In this paper we derive the set of general transport equations for multicomponent partially ionized reactive plasma in the presence of electric and magnetic fields taking into account the internal degrees of freedom and electronic excitation of plasma particles. Our starting point is a generalized Boltzmann equation with the collision integral in the Wang-Chang and Uhlenbeck form and a reactive collision integral. We obtain a set of conservation equations for such plasma and employ a linearized variant of Grad's moment method to derive the system of moment (or transport) equations for the plasma species nonequilibrium parameters. Full and reduced transport equations, resulting from the linearized system of moment equations, are presented, which can be used to obtain transport relations and expressions for transport coefficients of electrons and heavy plasma particles (molecules, atoms and ions) in partially ionized reactive plasma.

  4. Diffusion Acceleration Schemes for Self-Adjoint Angular Flux Formulation with a Void Treatment

    SciTech Connect

    Yaqi Wang; Hongbin Zhang; Richard C. Martineau

    2014-02-01

    A Galerkin weak form for the monoenergetic neutron transport equation with a continuous finite element method and discrete ordinate method is developed based on self-adjoint angular flux formulation. This weak form is modified for treating void regions. A consistent diffusion scheme is developed with projection. Correction terms of the diffusion scheme are derived to reproduce the transport scalar flux. A source iteration that decouples the solution of all directions with both linear and nonlinear diffusion accelerations is developed and demonstrated. One-dimensional Fourier analysis is conducted to demonstrate the stability of the linear and nonlinear diffusion accelerations. Numerical results of these schemes are presented.

  5. Volume transport and generalized hydrodynamic equations for monatomic fluids.

    PubMed

    Eu, Byung Chan

    2008-10-01

    In this paper, the effects of volume transport on the generalized hydrodynamic equations for a pure simple fluid are examined from the standpoint of statistical mechanics and, in particular, kinetic theory of fluids. First, we derive the generalized hydrodynamic equations, namely, the constitutive equations for the stress tensor and heat flux for a single-component monatomic fluid, from the generalized Boltzmann equation in the presence of volume transport. Then their linear steady-state solutions are derived and examined with regard to the effects of volume transport on them. The generalized hydrodynamic equations and linear constitutive relations obtained for nonconserved variables make it possible to assess Brenner's proposition [Physica A 349, 11 (2005); Physica A 349, 60 (2005)] for volume transport and attendant mass and volume velocities as well as the effects of volume transport on the Newtonian law of viscosity, compression/dilatation (bulk viscosity) phenomena, and Fourier's law of heat conduction. On the basis of study made, it is concluded that the notion of volume transport is sufficiently significant to retain in irreversible thermodynamics of fluids and fluid mechanics.

  6. A new approach for developing adjoint models

    NASA Astrophysics Data System (ADS)

    Farrell, P. E.; Funke, S. W.

    2011-12-01

    Many data assimilation algorithms rely on the availability of gradients of misfit functionals, which can be efficiently computed with adjoint models. However, the development of an adjoint model for a complex geophysical code is generally very difficult. Algorithmic differentiation (AD, also called automatic differentiation) offers one strategy for simplifying this task: it takes the abstraction that a model is a sequence of primitive instructions, each of which may be differentiated in turn. While extremely successful, this low-level abstraction runs into time-consuming difficulties when applied to the whole codebase of a model, such as differentiating through linear solves, model I/O, calls to external libraries, language features that are unsupported by the AD tool, and the use of multiple programming languages. While these difficulties can be overcome, it requires a large amount of technical expertise and an intimate familiarity with both the AD tool and the model. An alternative to applying the AD tool to the whole codebase is to assemble the discrete adjoint equations and use these to compute the necessary gradients. With this approach, the AD tool must be applied to the nonlinear assembly operators, which are typically small, self-contained units of the codebase. The disadvantage of this approach is that the assembly of the discrete adjoint equations is still very difficult to perform correctly, especially for complex multiphysics models that perform temporal integration; as it stands, this approach is as difficult and time-consuming as applying AD to the whole model. In this work, we have developed a library which greatly simplifies and automates the alternate approach of assembling the discrete adjoint equations. We propose a complementary, higher-level abstraction to that of AD: that a model is a sequence of linear solves. The developer annotates model source code with library calls that build a 'tape' of the operators involved and their dependencies, and

  7. Transport equations for the inflationary trispectrum

    SciTech Connect

    Anderson, Gemma J.; Seery, David; Mulryne, David J. E-mail: D.Mulryne@qmul.ac.uk

    2012-10-01

    We use transport techniques to calculate the trispectrum produced in multiple-field inflationary models with canonical kinetic terms. Our method allows the time evolution of the local trispectrum parameters, τ{sub NL} and g{sub NL}, to be tracked throughout the inflationary phase. We illustrate our approach using examples. We give a simplified method to calculate the superhorizon part of the relation between field fluctuations on spatially flat hypersurfaces and the curvature perturbation on uniform density slices, ζ, and obtain its third-order part for the first time. We clarify how the 'backwards' formalism of Yokoyama et al. relates to our analysis and other recent work. We supply explicit formulae which enable each inflationary observable to be computed in any canonical model of interest, using a suitable first-order ODE solver.

  8. MCNP: Multigroup/adjoint capabilities

    SciTech Connect

    Wagner, J.C.; Redmond, E.L. II; Palmtag, S.P.; Hendricks, J.S.

    1994-04-01

    This report discusses various aspects related to the use and validity of the general purpose Monte Carlo code MCNP for multigroup/adjoint calculations. The increased desire to perform comparisons between Monte Carlo and deterministic codes, along with the ever-present desire to increase the efficiency of large MCNP calculations has produced a greater user demand for the multigroup/adjoint capabilities. To more fully utilize these capabilities, we review the applications of the Monte Carlo multigroup/adjoint method, describe how to generate multigroup cross sections for MCNP with the auxiliary CRSRD code, describe how to use the multigroup/adjoint capability in MCNP, and provide examples and results indicating the effectiveness and validity of the MCNP multigroup/adjoint treatment. This information should assist users in taking advantage of the MCNP multigroup/adjoint capabilities.

  9. Osmotic Transport across Cell Membranes in Nondilute Solutions: A New Nondilute Solute Transport Equation

    PubMed Central

    Elmoazzen, Heidi Y.; Elliott, Janet A.W.; McGann, Locksley E.

    2009-01-01

    The fundamental physical mechanisms of water and solute transport across cell membranes have long been studied in the field of cell membrane biophysics. Cryobiology is a discipline that requires an understanding of osmotic transport across cell membranes under nondilute solution conditions, yet many of the currently-used transport formalisms make limiting dilute solution assumptions. While dilute solution assumptions are often appropriate under physiological conditions, they are rarely appropriate in cryobiology. The first objective of this article is to review commonly-used transport equations, and the explicit and implicit assumptions made when using the two-parameter and the Kedem-Katchalsky formalisms. The second objective of this article is to describe a set of transport equations that do not make the previous dilute solution or near-equilibrium assumptions. Specifically, a new nondilute solute transport equation is presented. Such nondilute equations are applicable to many fields including cryobiology where dilute solution conditions are not often met. An illustrative example is provided. Utilizing suitable transport equations that fit for two permeability coefficients, fits were as good as with the previous three-parameter model (which includes the reflection coefficient, σ). There is less unexpected concentration dependence with the nondilute transport equations, suggesting that some of the unexpected concentration dependence of permeability is due to the use of inappropriate transport equations. PMID:19348741

  10. Theory of contributon transport

    SciTech Connect

    Painter, J.W.; Gerstl, S.A.W.; Pomraning, G.C.

    1980-10-01

    A general discussion of the physics of contributon transport is presented. To facilitate this discussion, a Boltzmann-like transport equation for contributons is obtained, and special contributon cross sections are defined. However, the main goal of this study is to identify contributon transport equations and investigate possible deterministic solution techniques. Four approaches to the deterministic solution of the contributon transport problem are investigated. These approaches are an attempt to exploit certain attractive properties of the contributon flux, psi = phi phi/sup +/, where phi and phi/sup +/ are the solutions to the forward and adjoint Boltzmann transport equations.

  11. Admitting the Inadmissible: Adjoint Formulation for Incomplete Cost Functionals in Aerodynamic Optimization

    NASA Technical Reports Server (NTRS)

    Arian, Eyal; Salas, Manuel D.

    1997-01-01

    We derive the adjoint equations for problems in aerodynamic optimization which are improperly considered as "inadmissible." For example, a cost functional which depends on the density, rather than on the pressure, is considered "inadmissible" for an optimization problem governed by the Euler equations. We show that for such problems additional terms should be included in the Lagrangian functional when deriving the adjoint equations. These terms are obtained from the restriction of the interior PDE to the control surface. Demonstrations of the explicit derivation of the adjoint equations for "inadmissible" cost functionals are given for the potential, Euler, and Navier-Stokes equations.

  12. Renormalized transport equations for the bistable potential model

    NASA Astrophysics Data System (ADS)

    Weidlich, Wolfgang; Grabert, Hermann

    1980-09-01

    Renormalized transport equations for general Fokker-Planck systems are derived and applied to the bistable potential model. The exact equation for the expectation value < x> t can be evaluated in both domains < D>∈ x ± and < x>∈ D 0 outside and between the potential minima, leading to drastic differences of the dynamics prevailing in D ± and D 0, respectively.

  13. Conservation Laws of a Family of Reaction-Diffusion-Convection Equations

    NASA Astrophysics Data System (ADS)

    Bruzón, M. S.; Gandarias, M. L.; de la Rosa, R.

    Ibragimov introduced the concept of nonlinear self-adjoint equations. This definition generalizes the concept of self-adjoint and quasi-self-adjoint equations. Gandarias defined the concept of weak self-adjoint. In this paper, we found a class of nonlinear self-adjoint nonlinear reaction-diffusion-convection equations which are neither self-adjoint nor quasi-self-adjoint nor weak self-adjoint. From a general theorem on conservation laws proved by Ibragimov we obtain conservation laws for these equations.

  14. Renormalization of transport equations in Fokker-Planck models

    NASA Astrophysics Data System (ADS)

    Grabert, Hermann; Weidlich, Wolfgang

    1980-06-01

    This paper is concerned with the derivation of nonlinear fluctuation-renormalized transport equations of a fluctuating thermodynamic system, on the assumption that the macroscopic variables defining a state undergo a Fokker-Planck process. It is shown that the renormalization effect may consist of two parts: a renormalization of the thermodynamic forces and a renormalization of the transport coefficients. Closed analytical expressions for the renormalized quantities in terms of the bare quantities appearing in the Fokker-Planck equation are derived. A scheme for the approximate evaluation of these expressions is given.

  15. Transport in molecular states language: Generalized quantum master equation approach

    NASA Astrophysics Data System (ADS)

    Esposito, Massimiliano; Galperin, Michael

    2009-05-01

    A simple scheme, capable of treating transport in molecular junctions in the language of many-body states, is presented. By introducing an ansatz in Liouville space, similar to the generalized Kadanoff-Baym approximation, a quantum master equation (QME)-like expression is derived starting from the exact equation of motion for Hubbard operators. Using an effective Liouville space propagation, a dressing similar to the standard diagrammatic one is proposed. The scheme is compared to the standard QME approach and its applicability to transport calculations is discussed.

  16. A rain splash transport equation assimilating field and laboratory measurements

    USGS Publications Warehouse

    Dunne, T.; Malmon, D.V.; Mudd, S.M.

    2010-01-01

    Process-based models of hillslope evolution require transport equations relating sediment flux to its major controls. An equation for rain splash transport in the absence of overland flow was constructed by modifying an approach developed by Reeve (1982) and parameterizing it with measurements from single-drop laboratory experiments and simulated rainfall on a grassland in East Africa. The equation relates rain splash to hillslope gradient, the median raindrop diameter of a storm, and ground cover density; the effect of soil texture on detachability can be incorporated from other published results. The spatial and temporal applicability of such an equation for rain splash transport in the absence of overland flow on uncultivated hillslopes can be estimated from hydrological calculations. The predicted transport is lower than landscape-averaged geologic erosion rates from Kenya but is large enough to modify short, slowly eroding natural hillslopes as well as microtopographic interrill surfaces between which overland flow transports the mobilized sediment. Copyright 2010 by the American Geophysical Union. Copyright 2010 by the American Geophysical Union.

  17. Properties of an affine transport equation and its holonomy

    NASA Astrophysics Data System (ADS)

    Vines, Justin; Nichols, David A.

    2016-10-01

    An affine transport equation was used recently to study properties of angular momentum and gravitational-wave memory effects in general relativity. In this paper, we investigate local properties of this transport equation in greater detail. Associated with this transport equation is a map between the tangent spaces at two points on a curve. This map consists of a homogeneous (linear) part given by the parallel transport map along the curve plus an inhomogeneous part, which is related to the development of a curve in a manifold into an affine tangent space. For closed curves, the affine transport equation defines a "generalized holonomy" that takes the form of an affine map on the tangent space. We explore the local properties of this generalized holonomy by using covariant bitensor methods to compute the generalized holonomy around geodesic polygon loops. We focus on triangles and "parallelogramoids" with sides formed from geodesic segments. For small loops, we recover the well-known result for the leading-order linear holonomy (˜ Riemann × area), and we derive the leading-order inhomogeneous part of the generalized holonomy (˜ Riemann × area^{3/2}). Our bitensor methods let us naturally compute higher-order corrections to these leading results. These corrections reveal the form of the finite-size effects that enter into the holonomy for larger loops; they could also provide quantitative errors on the leading-order results for finite loops.

  18. Multilevel methods for transport equations in diffusive regimes

    NASA Technical Reports Server (NTRS)

    Manteuffel, Thomas A.; Ressel, Klaus

    1993-01-01

    We consider the numerical solution of the single-group, steady state, isotropic transport equation. An analysis by means of the moment equations shows that a discrete ordinate S(sub N) discretization in direction (angle) with a least squares finite element discretization in space does not behave properly in the diffusion limit. A scaling of the S(sub N) equations is introduced so that the least squares discretization has the correct diffusion limit. For the resulting discrete system a full multigrid algorithm was developed.

  19. Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport

    SciTech Connect

    Wang, Chi-Jen

    2013-01-01

    In this thesis, we analyze both the spatiotemporal behavior of: (A) non-linear “reaction” models utilizing (discrete) reaction-diffusion equations; and (B) spatial transport problems on surfaces and in nanopores utilizing the relevant (continuum) diffusion or Fokker-Planck equations. Thus, there are some common themes in these studies, as they all involve partial differential equations or their discrete analogues which incorporate a description of diffusion-type processes. However, there are also some qualitative differences, as shall be discussed below.

  20. Transport equations for a general class of evolution equations with random perturbations

    NASA Astrophysics Data System (ADS)

    Guo, Maozheng; Wang, Xiao-Ping

    1999-10-01

    We derive transport equations from a general class of equations of form iut=H(X,D)u+V(X,D)u where H(X,D) and V(X,D) are pseudodifferential operators (Weyl operator) with symbols H(x,k) and V(x,k), where H(x,k) being polynomial in k and smooth in x,V(x,k) is a mean zero random function and is stationary in space variable. We also consider system of equations in the above form. Such equations cover many of the equations that arise in wave propagations, such as those considered in a paper by Ryzhik, Papanicolaou, and Keller [Wave Motion 24, 327-370 (1996)]. Our results generalize those by Ryzhik, Papanicolau, and Keller.

  1. Approximation of the transport equation by a weighted particle method

    SciTech Connect

    Mas-Gallic, S.; Poupaud, F.

    1988-08-01

    We study a particle method for numerically solving a model equation for the neutron transport. We present the method and develop the theoretical convergence analysis. We prove the stability and the convergence of the method in L/sup infinity/. Some computational test results are given.

  2. Correction of the wavefront using the irradiance transport equation

    NASA Astrophysics Data System (ADS)

    García, M.; Granados, F.; Cornejo, A.

    2008-07-01

    The correction of the wavefront in optical systems implies the use of wavefront sensors, software, and auxiliary optical systems. We propose evaluated the wavefront using the fact that the wavefront and its intensity are related in the mathematical expression the irradiance transport equation (ITE)

  3. A Posteriori Analysis for Hydrodynamic Simulations Using Adjoint Methodologies

    SciTech Connect

    Woodward, C S; Estep, D; Sandelin, J; Wang, H

    2009-02-26

    This report contains results of analysis done during an FY08 feasibility study investigating the use of adjoint methodologies for a posteriori error estimation for hydrodynamics simulations. We developed an approach to adjoint analysis for these systems through use of modified equations and viscosity solutions. Targeting first the 1D Burgers equation, we include a verification of the adjoint operator for the modified equation for the Lax-Friedrichs scheme, then derivations of an a posteriori error analysis for a finite difference scheme and a discontinuous Galerkin scheme applied to this problem. We include some numerical results showing the use of the error estimate. Lastly, we develop a computable a posteriori error estimate for the MAC scheme applied to stationary Navier-Stokes.

  4. Analysis of Transition-Sensitized Turbulent Transport Equations

    NASA Technical Reports Server (NTRS)

    Rumsey, Christopher L.; Thacker, William D.; Gatski, Thomas B.; Grosch, Chester E,

    2005-01-01

    The dynamics of an ensemble of linear disturbances in boundary-layer flows at various Reynolds numbers is studied through an analysis of the transport equations for the mean disturbance kinetic energy and energy dissipation rate. Effects of adverse and favorable pressure-gradients on the disturbance dynamics are also included in the analysis Unlike the fully turbulent regime where nonlinear phase scrambling of the fluctuations affects the flow field even in proximity to the wall, the early stage transition regime fluctuations studied here are influenced cross the boundary layer by the solid boundary. The dominating dynamics in the disturbance kinetic energy and dissipation rate equations are described. These results are then used to formulate transition-sensitized turbulent transport equations, which are solved in a two-step process and applied to zero-pressure-gradient flow over a flat plate. Computed results are in good agreement with experimental data.

  5. Monte Carlo simulation of high-field transport equations

    SciTech Connect

    Abdolsalami, F.

    1989-01-01

    The author has studied the importance of the intracollisional field effect in the quantum transport equation derived by Khan, Davies and Wilkins (Phys. Rev. B36, 2578(1987)) via Monte Carlo simulations. This transport equation is identical to the integral form of the Boltzmann transport equation except that the scattering-in rates contain the auxiliary function of energy width {radical}{vert bar}{alpha}{vert bar} instead of the sharp delta function of the semiclassical theory where {alpha} = {pi}{h bar}{sup 2} e/m* E {center dot} q. Here, E is the electric field, q is the phonon wave vector of m* is the effective mass. The transport equation studied corresponds to a single parabolic band of infinite width and is valid in the field dominated limit, i.e. {radical}{vert bar}{alpha}{vert bar} {much gt} h/{tau}{sub sc}, where {tau}{sup {minus}1} is the electron scattering-out rate. In his simulation, he takes the single parabolic band to be the central valley of GaAs with transition to higher valleys shut off. Electrons are assumed to scatter with polar optic and acoustic phonons with the scattering parameters chosen to simulate GaAs. The loss of intervalley scattering mechanism for high electric fields is compensated for by increasing each of the four scattering rates relative to the real values in GaAs by a factor {gamma}. The transport equation studied contains the auxilliary function which is not positive definite. Therefore, it can not represent a probability of scattering in a Monte Carlo simulation. The question whether or not intracollisional field effect is important can be resolved by replacing the nonpositive definite auxilliary function by a test positive definite function of width {radical}{vert bar}{alpha}{vert bar} and comparing the results of the Monte Carlo simulation of this quantum transport equation with those of the Boltzmann transport equation. If the results are identical, the intracollisional field effect is not important.

  6. A bedload transport equation for the Cerastoderma edule cockle

    NASA Astrophysics Data System (ADS)

    Anta, Jose; Peña, Enrique; Puertas, Jerónimo; Cea, Luis

    2013-02-01

    Hydrodynamics play an important role in the structure of many marine ecosystems of bivalves. After severe storm periods, large amounts of the Cerastoderma edule stocks were transported from the Lombos do Ulla shellfish bed (Spain). This paper presents the results of laboratory experiments carried out to analyze the bedload transport of this bivalve emulating the stormy shellfish bed conditions. Flow velocities were measured using particle image velocimetry and the double averaged methodology was applied to determine the main flow characteristics over different cockle patches. The flow structure exhibits properties of skimming and isolated flows depending on the density of bivalves. Bed shear stress was determined from the log-law and the cockles were geometrically characterized in order to derive specific bedload transport equations in a conventional deterministic sediment transport framework. The obtained formulas can be implemented in common numerical codes to further analyze mollusk stability, bedload transport and dispersal in their aquatic systems.

  7. Nonradiating sources with connections to the adjoint problem

    SciTech Connect

    Marengo, Edwin A.; Devaney, Anthony J.

    2004-09-01

    A general description of localized nonradiating (NR) sources whose generated fields are confined (nonzero only) within the source's support is developed that is applicable to any linear partial differential equation (PDE) including the usual PDEs of wave theory (e.g., the Helmholtz equation and the vector wave equation) as well as other PDEs arising in other disciplines. This description, which holds for both formally self-adjoint and non-self-adjoint linear partial differential operators (PDOs), is derived in the context of both the governing PDE and the corresponding adjoint PDE of the associated adjoint problem. It is shown that a necessary and sufficient condition for a source to be NR is that it obeys an orthogonality relation with respect to any solution in the source's support of the corresponding homogeneous adjoint PDE. For real linear PDOs, this description takes on a more relaxed form where, in addition to the previous necessary and sufficient condition, the obeying of a complementary orthogonality relation with respect to any solution in the source's support of the homogeneous form of the same governing PDE is also both necessary and sufficient for the source to be NR.

  8. Numerical Study of Fractional Ensemble Average Transport Equations

    NASA Astrophysics Data System (ADS)

    Kim, S.; Park, Y.; Gyeong, C. B.; Lee, O.

    2014-12-01

    In this presentation, a newly developed theory is applied to the case of stationary and non-stationary stochastic advective flow field, and a numerical solution method is presented for the resulting fractional Fokker-Planck equation (fFPE), which describes the evolution of the probability density function (PDF) of contaminant concentration. The derived fFPE is evaluated for three different form: 1) purely advective form, 2) second-order moment form and 3) second-order cumulant form. The Monte Carlo analysis of the fractional governing equation is then performed in a stochastic flow field, generated by a fractional Brownian motion for the stationary and non-stationary stochastic advection, in order to provide a benchmark for the results obtained from the fFPEs. When compared to the Monte Carlo simulation based PDFs and their ensemble average, the second-order cumulant form gives a good fit in terms of the shape and mode of the PDF of the contaminant concentration. Therefore, it is quite promising that the non-Fickian transport behavior can be modeled by the derived fractional ensemble average transport equations either by means of the long memory in the underlying stochastic flow, or by means of the time-space non-stationarity of the underlying stochastic flow, or by means of the time and space fractional derivatives of the transport equations. This subject is supported by Korea Ministry of Environment as "The Eco Innovation Project : Non-point source pollution control research group"

  9. Study on adjoint-based optimization method for multi-stage turbomachinery

    NASA Astrophysics Data System (ADS)

    Li, Weiwei; Tian, Yong; Yi, Weilin; Ji, Lucheng; Shao, Weiwei; Xiao, Yunhan

    2011-10-01

    Adjoint-based optimization method is a hotspot in turbomachinery. First, this paper presents principles of adjoint method from Lagrange multiplier viewpoint. Second, combining a continuous route with thin layer RANS equations, we formulate adjoint equations and anti-physical boundary conditions. Due to the multi-stage environment in turbomachinery, an adjoint interrow mixing method is introduced. Numerical techniques of solving flow equations and adjoint equations are almost the same, and once they are converged respectively, the gradients of an objective function to design variables can be calculated using complex method efficiently. Third, integrating a shape perturbation parameterization and a simple steepest descent method, a frame of adjoint-based aerodynamic shape optimization for multi-stage turbomachinery is constructed. At last, an inverse design of an annular cascade is employed to validate the above approach, and adjoint field of an Aachen 1.5 stage turbine demonstrates the conservation and areflexia of the adjoint interrow mixing method. Then a direct redesign of a 1+1 counter-rotating turbine aiming to increase efficiency and apply constraints to mass flow rate and pressure ratio is taken.

  10. Conservations laws for a porous medium equation through nonclassical generators

    NASA Astrophysics Data System (ADS)

    Gandarias, M. L.

    2014-02-01

    In Ibragimov (2007) [13] a general theorem on conservation laws was proved. In Gandarias (2011) and Ibragimov (2011) [7,15] the concepts of self-adjoint and quasi self-adjoint equations were generalized and the definitions of weak self-adjoint equations and nonlinearly self-adjoint equations were introduced. In this paper, we find the subclasses of nonlinearly self-adjoint porous medium equations. By using the property of nonlinear self-adjointness, we construct some conservation laws associated with classical and nonclassical generators of the differential equation.

  11. Global Adjoint Tomography

    NASA Astrophysics Data System (ADS)

    Bozdag, Ebru; Lefebvre, Matthieu; Lei, Wenjie; Peter, Daniel; Smith, James; Komatitsch, Dimitri; Tromp, Jeroen

    2015-04-01

    We will present our initial results of global adjoint tomography based on 3D seismic wave simulations which is one of the most challenging examples in seismology in terms of intense computational requirements and vast amount of high-quality seismic data that can potentially be assimilated in inversions. Using a spectral-element method, we incorporate full 3D wave propagation in seismic tomography by running synthetic seismograms and adjoint simulations to compute exact sensitivity kernels in realistic 3D background models. We run our global simulations on the Oak Ridge National Laboratory's Cray XK7 "Titan" system taking advantage of the GPU version of the SPECFEM3D_GLOBE package. We have started iterations with initially selected 253 earthquakes within the magnitude range of 5.5 < Mw < 7.0 and numerical simulations having resolution down to ~27 s to invert for a transversely isotropic crust and mantle model using a non-linear conjugate gradient algorithm. The measurements are currently based on frequency-dependent traveltime misfits. We use both minor- and major-arc body and surface waves by running 200 min simulations where inversions are performed with more than 2.6 million measurements. Our initial results after 12 iterations already indicate several prominent features such as enhanced slab (e.g., Hellenic, Japan, Bismarck, Sandwich), plume/hotspot (e.g., the Pacific superplume, Caroline, Yellowstone, Hawaii) images, etc. To improve the resolution and ray coverage, particularly in the lower mantle, our aim is to increase the resolution of numerical simulations first going down to ~17 s and then to ~9 s to incorporate high-frequency body waves in inversions. While keeping track of the progress and illumination of features in our models with a limited data set, we work towards to assimilate all available data in inversions from all seismic networks and earthquakes in the global CMT catalogue.

  12. Sonic Boom Mitigation Through Aircraft Design and Adjoint Methodology

    NASA Technical Reports Server (NTRS)

    Rallabhandi, Siriam K.; Diskin, Boris; Nielsen, Eric J.

    2012-01-01

    This paper presents a novel approach to design of the supersonic aircraft outer mold line (OML) by optimizing the A-weighted loudness of sonic boom signature predicted on the ground. The optimization process uses the sensitivity information obtained by coupling the discrete adjoint formulations for the augmented Burgers Equation and Computational Fluid Dynamics (CFD) equations. This coupled formulation links the loudness of the ground boom signature to the aircraft geometry thus allowing efficient shape optimization for the purpose of minimizing the impact of loudness. The accuracy of the adjoint-based sensitivities is verified against sensitivities obtained using an independent complex-variable approach. The adjoint based optimization methodology is applied to a configuration previously optimized using alternative state of the art optimization methods and produces additional loudness reduction. The results of the optimizations are reported and discussed.

  13. Learning a trajectory using adjoint functions and teacher forcing

    NASA Technical Reports Server (NTRS)

    Toomarian, Nikzad B.; Barhen, Jacob

    1992-01-01

    A new methodology for faster supervised temporal learning in nonlinear neural networks is presented which builds upon the concept of adjoint operators to allow fast computation of the gradients of an error functional with respect to all parameters of the neural architecture, and exploits the concept of teacher forcing to incorporate information on the desired output into the activation dynamics. The importance of the initial or final time conditions for the adjoint equations is discussed. A new algorithm is presented in which the adjoint equations are solved simultaneously (i.e., forward in time) with the activation dynamics of the neural network. We also indicate how teacher forcing can be modulated in time as learning proceeds. The results obtained show that the learning time is reduced by one to two orders of magnitude with respect to previously published results, while trajectory tracking is significantly improved. The proposed methodology makes hardware implementation of temporal learning attractive for real-time applications.

  14. A transport equation for reaction rate in turbulent flows

    NASA Astrophysics Data System (ADS)

    Sabelnikov, V. A.; Lipatnikov, A. N.; Chakraborty, N.; Nishiki, S.; Hasegawa, T.

    2016-08-01

    New transport equations for chemical reaction rate and its mean value in turbulent flows have been derived and analyzed. Local perturbations of the reaction zone by turbulent eddies are shown to play a pivotal role even for weakly turbulent flows. The mean-reaction-rate transport equation is shown to involve two unclosed dominant terms and a joint closure relation for the sum of these two terms is developed. Obtained analytical results and, in particular, the closure relation are supported by processing two widely recognized sets of data obtained from earlier direct numerical simulations of statistically planar 1D premixed flames associated with both weak large-scale and intense small-scale turbulence.

  15. Transport equations for subdiffusion with nonlinear particle interaction.

    PubMed

    Straka, P; Fedotov, S

    2015-02-01

    We show how the nonlinear interaction effects 'volume filling' and 'adhesion' can be incorporated into the fractional subdiffusive transport of cells and individual organisms. To this end, we use microscopic random walk models with anomalous trapping and systematically derive generic non-Markovian and nonlinear governing equations for the mean concentrations of the subdiffusive cells or organisms. We uncover an interesting interaction between the nonlinearities and the non-Markovian nature of the transport. In the subdiffusive case, this interaction manifests itself in a nontrivial combination of nonlinear terms with fractional derivatives. In the long time limit, however, these equations simplify to a form without fractional operators. This provides an easy method for the study of aggregation phenomena. In particular, this enables us to show that volume filling can prevent "anomalous aggregation," which occurs in subdiffusive systems with a spatially varying anomalous exponent.

  16. Adjoint simulation of stream depletion due to aquifer pumping.

    PubMed

    Neupauer, Roseanna M; Griebling, Scott A

    2012-01-01

    If an aquifer is hydraulically connected to an adjacent stream, a pumping well operating in the aquifer will draw some water from aquifer storage and some water from the stream, causing stream depletion. Several analytical, semi-analytical, and numerical approaches have been developed to estimate stream depletion due to pumping. These approaches are effective if the well location is known. If a new well is to be installed, it may be desirable to install the well at a location where stream depletion is minimal. If several possible locations are considered for the location of a new well, stream depletion would have to be estimated for all possible well locations, which can be computationally inefficient. The adjoint approach for estimating stream depletion is a more efficient alternative because with one simulation of the adjoint model, stream depletion can be estimated for pumping at a well at any location. We derive the adjoint equations for a coupled system with a confined aquifer, an overlying unconfined aquifer, and a river that is hydraulically connected to the unconfined aquifer. We assume that the stage in the river is known, and is independent of the stream depletion, consistent with the assumptions of the MODFLOW river package. We describe how the adjoint equations can be solved using MODFLOW. In an illustrative example, we show that for this scenario, the adjoint approach is as accurate as standard forward numerical simulation methods, and requires substantially less computational effort.

  17. Mesh-free adjoint methods for nonlinear filters

    NASA Astrophysics Data System (ADS)

    Daum, Fred

    2005-09-01

    We apply a new industrial strength numerical approximation, called the "mesh-free adjoint method", to solve the nonlinear filtering problem. This algorithm exploits the smoothness of the problem, unlike particle filters, and hence we expect that mesh-free adjoints are superior to particle filters for many practical applications. The nonlinear filter problem is equivalent to solving the Fokker-Planck equation in real time. The key idea is to use a good adaptive non-uniform quantization of state space to approximate the solution of the Fokker-Planck equation. In particular, the adjoint method computes the location of the nodes in state space to minimize errors in the final answer. This use of an adjoint is analogous to optimal control algorithms, but it is more interesting. The adjoint method is also analogous to importance sampling in particle filters, but it is better for four reasons: (1) it exploits the smoothness of the problem; (2) it explicitly minimizes the errors in the relevant functional; (3) it explicitly models the dynamics in state space; and (4) it can be used to compute a corrected value for the desired functional using the residuals. We will attempt to make this paper accessible to normal engineers who do not have PDEs for breakfast.

  18. Inverse problems for homogeneous transport equations: II. The multidimensional case

    NASA Astrophysics Data System (ADS)

    Bal, Guillaume

    2000-08-01

    A companion paper by Bal (Bal G 2000 Inverse Problems 16 997) and this paper are parts I and II of a series dealing with the reconstruction from boundary measurements of the scattering operator of homogeneous linear transport equations. This part II deals with the case of convex bounded domains in dimensions higher than one. We distinguish the analysis of smooth boundaries from that of boundaries with discontinuities such as corners. We propose a reconstruction in the case of degenerate symmetric scattering operators and show the well-posedness of the inverse problem. The proof of well-posedness is based on a decomposition of angular moments of the transport solution into unbounded and bounded components. This decomposition allows us to show the linear independence of a sufficiently large number of angular moments of the transport solution that are used to construct an invertible system for the scattering coefficients to be reconstructed.

  19. Towards Global Adjoint Tomography

    NASA Astrophysics Data System (ADS)

    Bozdag, E.; Zhu, H.; Peter, D. B.; Tromp, J.

    2012-12-01

    Seismic tomography is at a stage where we can harness entire seismograms using the opportunities offered by advances in numerical wave propagation solvers and high-performance computing. Adjoint methods provide an efficient way for incorporating full nonlinearity of wave propagation and 3D Fréchet kernels in iterative seismic inversions which have so far given promising results at continental and regional scales. Our goal is to take adjoint tomography forward to image the entire planet. Using an iterative conjugate gradient scheme, we initially set the aim to obtain a global crustal and mantle model with confined transverse isotropy in the upper mantle. We have started with around 255 global CMT events having moment magnitudes between 5.8 and 7, and used GSN stations as well as some local networks such as USArray, European stations etc. Prior to the structure inversion, we reinvert global CMT solutions by computing Green functions in our 3D reference model to take into account effects of crustal variations on source parameters. Using the advantages of numerical simulations, our strategy is to invert crustal and mantle structure together to avoid any bias introduced into upper-mantle images due to "crustal corrections", which are commonly used in classical tomography. 3D simulations dramatically increase the usable amount of data so that, with the current earthquake-station setup, we perform each iteration with more than two million measurements. Multi-resolution smoothing based on ray density is applied to the gradient to better deal with the imperfect source-station distribution on the globe and extract more information underneath regions with dense ray coverage and vice versa. Similar to frequency domain approach, we reduce nonlinearities by starting from long periods and gradually increase the frequency content of data after successive model updates. To simplify the problem, we primarily focus on the elastic structure and therefore our measurements are based on

  20. Optimal Transport, Convection, Magnetic Relaxation and Generalized Boussinesq Equations

    NASA Astrophysics Data System (ADS)

    Brenier, Yann

    2009-10-01

    We establish a connection between optimal transport theory (see Villani in Topics in optimal transportation. Graduate studies in mathematics, vol. 58, AMS, Providence, 2003, for instance) and classical convection theory for geophysical flows (Pedlosky, in Geophysical fluid dynamics, Springer, New York, 1979). Our starting point is the model designed few years ago by Angenent, Haker, and Tannenbaum (SIAM J. Math. Anal. 35:61-97, 2003) to solve some optimal transport problems. This model can be seen as a generalization of the Darcy-Boussinesq equations, which is a degenerate version of the Navier-Stokes-Boussinesq (NSB) equations. In a unified framework, we relate different variants of the NSB equations (in particular what we call the generalized hydrostatic-Boussinesq equations) to various models involving optimal transport (and the related Monge-Ampère equation, Brenier in Commun. Pure Appl. Math. 64:375-417, 1991; Caffarelli in Commun. Pure Appl. Math. 45:1141-1151, 1992). This includes the 2D semi-geostrophic equations (Hoskins in Annual review of fluid mechanics, vol. 14, pp. 131-151, Palo Alto, 1982; Cullen et al. in SIAM J. Appl. Math. 51:20-31, 1991, Arch. Ration. Mech. Anal. 185:341-363, 2007; Benamou and Brenier in SIAM J. Appl. Math. 58:1450-1461, 1998; Loeper in SIAM J. Math. Anal. 38:795-823, 2006) and some fully nonlinear versions of the so-called high-field limit of the Vlasov-Poisson system (Nieto et al. in Arch. Ration. Mech. Anal. 158:29-59, 2001) and of the Keller-Segel for Chemotaxis (Keller and Segel in J. Theor. Biol. 30:225-234, 1971; Jäger and Luckhaus in Trans. Am. Math. Soc. 329:819-824, 1992; Chalub et al. in Mon. Math. 142:123-141, 2004). Mathematically speaking, we establish some existence theorems for local smooth, global smooth or global weak solutions of the different models. We also justify that the inertia terms can be rigorously neglected under appropriate scaling assumptions in the generalized Navier-Stokes-Boussinesq equations

  1. Implicitly causality enforced solution of multidimensional transient photon transport equation.

    PubMed

    Handapangoda, Chintha C; Premaratne, Malin

    2009-12-21

    A novel method for solving the multidimensional transient photon transport equation for laser pulse propagation in biological tissue is presented. A Laguerre expansion is used to represent the time dependency of the incident short pulse. Owing to the intrinsic causal nature of Laguerre functions, our technique automatically always preserve the causality constrains of the transient signal. This expansion of the radiance using a Laguerre basis transforms the transient photon transport equation to the steady state version. The resulting equations are solved using the discrete ordinates method, using a finite volume approach. Therefore, our method enables one to handle general anisotropic, inhomogeneous media using a single formulation but with an added degree of flexibility owing to the ability to invoke higher-order approximations of discrete ordinate quadrature sets. Therefore, compared with existing strategies, this method offers the advantage of representing the intensity with a high accuracy thus minimizing numerical dispersion and false propagation errors. The application of the method to one, two and three dimensional geometries is provided. PMID:20052050

  2. Renormalization group methods for the Reynolds stress transport equations

    NASA Technical Reports Server (NTRS)

    Rubinstein, R.

    1992-01-01

    The Yakhot-Orszag renormalization group is used to analyze the pressure gradient-velocity correlation and return to isotropy terms in the Reynolds stress transport equations. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a rapid pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constants are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of deriving higher order nonlinear models by approximating the sums more accurately. The Yakhot-Orszag renormalization group provides a systematic procedure for deriving turbulence models. Typical applications have included theoretical derivation of the universal constants of isotropic turbulence theory, such as the Kolmogorov constant, and derivation of two equation models, again with theoretically computed constants and low Reynolds number forms of the equations. Recent work has applied this formalism to Reynolds stress modeling, previously in the form of a nonlinear eddy viscosity representation of the Reynolds stresses, which can be used to model the simplest normal stress effects. The present work attempts to apply the Yakhot-Orszag formalism to Reynolds stress transport modeling.

  3. Is Onsager symmetry relevant in the transport equations for magnetically confined plasmas

    SciTech Connect

    Balescu, R. )

    1991-03-01

    A global, algebraic view of the transport processes in a magnetically confined plasma is developed. Both the neoclassical (banana) and the anomalous transport matrices are represented in a factorized form, thus separating the roles of the dynamics and of the geometric constraints. The self-adjointness of the collision operator (the sole condition for classical Onsager symmetry) is shown to be a necessary, but not sufficient condition for this symmetry in confined plasmas. The latter results for the banana transport matrix from a delicate relationship between dynamic and geometric components. This structure is not present in the anomalous transport matrix, and the Onsager symmetry is broken in this case. It is stressed that the symmetry breaking does not violate any general principles.

  4. Quantum-mechanical transport equation for atomic systems.

    NASA Technical Reports Server (NTRS)

    Berman, P. R.

    1972-01-01

    A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position R and moving with classical velocity v. It is quantum mechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.

  5. Vorticity Preserving Flux Corrected Transport Scheme for the Acoustic Equations

    SciTech Connect

    Lung, Tyler B.; Roe, Phil; Morgan, Nathaniel R.

    2012-08-15

    Long term research goals are to develop an improved cell-centered Lagrangian Hydro algorithm with the following qualities: 1. Utilizes Flux Corrected Transport (FCT) to achieve second order accuracy with multidimensional physics; 2. Does not rely on the one-dimensional Riemann problem; and 3. Implements a form of vorticity control. Short term research goals are to devise and implement a 2D vorticity preserving FCT solver for the acoustic equations on an Eulerian mesh: 1. Develop a flux limiting mechanism for systems of governing equations with symmetric wave speeds; 2. Verify the vorticity preserving properties of the scheme; and 3. Compare the performance of the scheme to traditional MUSCL-Hancock and other algorithms.

  6. The discrete adjoint approach to aerodynamic shape optimization

    NASA Astrophysics Data System (ADS)

    Nadarajah, Siva Kumaran

    A viscous discrete adjoint approach to automatic aerodynamic shape optimization is developed, and the merits of the viscous discrete and continuous adjoint approaches are discussed. The viscous discrete and continuous adjoint gradients for inverse design and drag minimization cost functions are compared with finite-difference and complex-step gradients. The optimization of airfoils in two-dimensional flow for inverse design and drag minimization is illustrated. Both the discrete and continuous adjoint methods are used to formulate two new design problems. First, the time-dependent optimal design problem is established, and both the time accurate discrete and continuous adjoint equations are derived. An application to the reduction of the time-averaged drag coefficient while maintaining time-averaged lift and thickness distribution of a pitching airfoil in transonic flow is demonstrated. Second, the remote inverse design problem is formulated. The optimization of a three-dimensional biconvex wing in supersonic flow verifies the feasibility to reduce the near field pressure peak. Coupled drag minimization and remote inverse design cases produce wings with a lower drag and a reduced near field peak pressure signature.

  7. The fast neutron fluence and the activation detector activity calculations using the effective source method and the adjoint function

    SciTech Connect

    Hep, J.; Konecna, A.; Krysl, V.; Smutny, V.

    2011-07-01

    This paper describes the application of effective source in forward calculations and the adjoint method to the solution of fast neutron fluence and activation detector activities in the reactor pressure vessel (RPV) and RPV cavity of a VVER-440 reactor. Its objective is the demonstration of both methods on a practical task. The effective source method applies the Boltzmann transport operator to time integrated source data in order to obtain neutron fluence and detector activities. By weighting the source data by time dependent decay of the detector activity, the result of the calculation is the detector activity. Alternatively, if the weighting is uniform with respect to time, the result is the fluence. The approach works because of the inherent linearity of radiation transport in non-multiplying time-invariant media. Integrated in this way, the source data are referred to as the effective source. The effective source in the forward calculations method thereby enables the analyst to replace numerous intensive transport calculations with a single transport calculation in which the time dependence and magnitude of the source are correctly represented. In this work, the effective source method has been expanded slightly in the following way: neutron source data were performed with few group method calculation using the active core calculation code MOBY-DICK. The follow-up neutron transport calculation was performed using the neutron transport code TORT to perform multigroup calculations. For comparison, an alternative method of calculation has been used based upon adjoint functions of the Boltzmann transport equation. Calculation of the three-dimensional (3-D) adjoint function for each required computational outcome has been obtained using the deterministic code TORT and the cross section library BGL440. Adjoint functions appropriate to the required fast neutron flux density and neutron reaction rates have been calculated for several significant points within the RPV

  8. Tsunami waveform inversion by adjoint methods

    NASA Astrophysics Data System (ADS)

    Pires, Carlos; Miranda, Pedro M. A.

    2001-09-01

    An adjoint method for tsunami waveform inversion is proposed, as an alternative to the technique based on Green's functions of the linear long wave model. The method has the advantage of being able to use the nonlinear shallow water equations, or other appropriate equation sets, and to optimize an initial state given as a linear or nonlinear function of any set of free parameters. This last facility is used to perform explicit optimization of the focal fault parameters, characterizing the initial sea surface displacement of tsunamigenic earthquakes. The proposed methodology is validated with experiments using synthetic data, showing the possibility of recovering all relevant details of a tsunami source from tide gauge observations, providing that the adjoint method is constrained in an appropriate manner. It is found, as in other methods, that the inversion skill of tsunami sources increases with the azimuthal and temporal coverage of assimilated tide gauge stations; furthermore, it is shown that the eigenvalue analysis of the Hessian matrix of the cost function provides a consistent and useful methodology to choose the subset of independent parameters that can be inverted with a given dataset of observations and to evaluate the error of the inversion process. The method is also applied to real tide gauge series, from the tsunami of the February 28, 1969, Gorringe Bank earthquake, suggesting some reasonable changes to the assumed focal parameters of that event. It is suggested that the method proposed may be able to deal with transient tsunami sources such as those generated by submarine landslides.

  9. Modeling tracer transport in randomly heterogeneous porous media by nonlocal moment equations: Anomalous transport

    NASA Astrophysics Data System (ADS)

    Morales-Casique, E.; Lezama-Campos, J. L.; Guadagnini, A.; Neuman, S. P.

    2013-05-01

    Modeling tracer transport in geologic porous media suffers from the corrupt characterization of the spatial distribution of hydrogeologic properties of the system and the incomplete knowledge of processes governing transport at multiple scales. Representations of transport dynamics based on a Fickian model of the kind considered in the advection-dispersion equation (ADE) fail to capture (a) the temporal variation associated with the rate of spreading of a tracer, and (b) the distribution of early and late arrival times which are often observed in field and/or laboratory scenarios and are considered as the signature of anomalous transport. Elsewhere we have presented exact stochastic moment equations to model tracer transport in randomly heterogeneous aquifers. We have also developed a closure scheme which enables one to provide numerical solutions of such moment equations at different orders of approximations. The resulting (ensemble) average and variance of concentration fields were found to display a good agreement against Monte Carlo - based simulation results for mildly heterogeneous (or well-conditioned strongly heterogeneous) media. Here we explore the ability of the moment equations approach to describe the distribution of early arrival times and late time tailing effects which can be observed in Monte-Carlo based breakthrough curves (BTCs) of the (ensemble) mean concentration. We show that BTCs of mean resident concentration calculated at a fixed space location through higher-order approximations of moment equations display long tailing features of the kind which is typically associated with anomalous transport behavior and are not represented by an ADE model with constant dispersive parameter, such as the zero-order approximation.

  10. Double-Difference Adjoint Tomography

    NASA Astrophysics Data System (ADS)

    Yuan, Yanhua O.; Simons, Frederik J.; Tromp, Jeroen

    2016-04-01

    We introduce a double-difference method for the inversion of seismic wavespeed structure by adjoint tomography. Differences between seismic observations and model-based predictions at individual stations may arise from factors other than structural heterogeneity, such as errors in the assumed source-time function, inaccurate timings, and systematic uncertainties. To alleviate the corresponding nonuniqueness in the inverse problem, we construct differential measurements between stations, thereby largely canceling out the source signature and systematic errors. We minimize the discrepancy between observations and simulations in terms of differential measurements made on station pairs. We show how to implement the double-difference concept in adjoint tomography, both theoretically and in practice. We compare the sensitivities of absolute and differential measurements. The former provide absolute information on structure along the ray paths between stations and sources, whereas the latter explain relative (and thus higher-resolution) structural variations in areas close to the stations. Whereas in conventional tomography, a measurement made on a single earthquake-station pair provides very limited structural information, in double-difference tomography, one earthquake can actually resolve significant details of the structure. The double-difference methodology can be incorporated into the usual adjoint tomography workflow by simply pairing up all conventional measurements; the computational cost of the necessary adjoint simulations is largely unaffected. Rather than adding to the computational burden, the inversion of double-difference measurements merely modifies the construction of the adjoint sources for data assimilation.

  11. Adjoint ITS calculations using the CEPXS electron-photon cross sections

    SciTech Connect

    Lorence, L.J.; Kensek, R.P.; Halbleib, J.A.

    1995-12-31

    Continuous-energy Monte Carlo Codes are not generally suited for adjoint coupled electron-photon transport. Line radiation (e.g., fluorescence) is especially difficult to implement in adjoint mode with continuous-energy codes. The only published work on adjoint electron Monte Carlo transport is Jordan. The adjoint capability of his NOVICE code is expedited by a multigroup approximation. More recently, a Boltzmann-Fokker-Planck (BFP) Monte Carlo technique has been developed for adjoint electron transport. As in NOVICE, particle transport with BFP Monte Carlo is neither entirely continuous energy nor entirely multigroup. The BFP method has been tested in the multigroup version of MCNP and is being integrated into the ITS code package. Multigroup data produced by the CEPXS cross-section-generating code is needed to operate the BFP codes in adjoint electron-photon mode. In this paper, we present adjoint electron-photon transport results obtained with a new version of CEPXS and a new multigroup version of ITS.

  12. Modeling of Flow Transition Using an Intermittency Transport Equation

    NASA Technical Reports Server (NTRS)

    Suzen, Y. B.; Huang, P. G.

    1999-01-01

    A new transport equation for intermittency factor is proposed to model transitional flows. The intermittent behavior of the transitional flows is incorporated into the computations by modifying the eddy viscosity, mu(sub t), obtainable from a turbulence model, with the intermittency factor, gamma: mu(sub t, sup *) = gamma.mu(sub t). In this paper, Menter's SST model (Menter, 1994) is employed to compute mu(sub t) and other turbulent quantities. The proposed intermittency transport equation can be considered as a blending of two models - Steelant and Dick (1996) and Cho and Chung (1992). The former was proposed for near-wall flows and was designed to reproduce the streamwise variation of the intermittency factor in the transition zone following Dhawan and Narasimha correlation (Dhawan and Narasimha, 1958) and the latter was proposed for free shear flows and was used to provide a realistic cross-stream variation of the intermittency profile. The new model was used to predict the T3 series experiments assembled by Savill (1993a, 1993b) including flows with different freestream turbulence intensities and two pressure-gradient cases. For all test cases good agreements between the computed results and the experimental data are observed.

  13. Transport equations of electrodiffusion processes in the laboratory reference frame.

    PubMed

    Garrido, Javier

    2006-02-23

    The transport equations of electrodiffusion processes use three reference frames for defining the fluxes: Fick's reference in diffusion, solvent-fixed reference in transference numbers, and laboratory fluxes in electric conductivity. The convenience of using only one reference frame is analyzed here from the point of view of the thermodynamics of irreversible processes. A relation between the fluxes of ions and solvent and the electric current density is deduced first from a mass and volume balance. This is then used to show that (i) the laboratory and Fick's diffusion coefficients are identical and (ii) the transference numbers of both the solvent and the ion in the laboratory reference frame are related. Finally, four experimental methods for the measurement of ion transference numbers are analyzed critically. New expressions for evaluating transference numbers for the moving boundary method and the chronopotentiometry technique are deduced. It is concluded that the ion transport equation in the laboratory reference frame plays a key role in the description of electrodiffusion processes. PMID:16494340

  14. Transport equations of electrodiffusion processes in the laboratory reference frame.

    PubMed

    Garrido, Javier

    2006-02-23

    The transport equations of electrodiffusion processes use three reference frames for defining the fluxes: Fick's reference in diffusion, solvent-fixed reference in transference numbers, and laboratory fluxes in electric conductivity. The convenience of using only one reference frame is analyzed here from the point of view of the thermodynamics of irreversible processes. A relation between the fluxes of ions and solvent and the electric current density is deduced first from a mass and volume balance. This is then used to show that (i) the laboratory and Fick's diffusion coefficients are identical and (ii) the transference numbers of both the solvent and the ion in the laboratory reference frame are related. Finally, four experimental methods for the measurement of ion transference numbers are analyzed critically. New expressions for evaluating transference numbers for the moving boundary method and the chronopotentiometry technique are deduced. It is concluded that the ion transport equation in the laboratory reference frame plays a key role in the description of electrodiffusion processes.

  15. A New 2D-Transport, 1D-Diffusion Approximation of the Boltzmann Transport equation

    SciTech Connect

    Larsen, Edward

    2013-06-17

    The work performed in this project consisted of the derivation, implementation, and testing of a new, computationally advantageous approximation to the 3D Boltz- mann transport equation. The solution of the Boltzmann equation is the neutron flux in nuclear reactor cores and shields, but solving this equation is difficult and costly. The new “2D/1D” approximation takes advantage of a special geometric feature of typical 3D reactors to approximate the neutron transport physics in a specific (ax- ial) direction, but not in the other two (radial) directions. The resulting equation is much less expensive to solve computationally, and its solutions are expected to be sufficiently accurate for many practical problems. In this project we formulated the new equation, discretized it using standard methods, developed a stable itera- tion scheme for solving the equation, implemented the new numerical scheme in the MPACT code, and tested the method on several realistic problems. All the hoped- for features of this new approximation were seen. For large, difficult problems, the resulting 2D/1D solution is highly accurate, and is calculated about 100 times faster than a 3D discrete ordinates simulation.

  16. Probability density adjoint for sensitivity analysis of the Mean of Chaos

    SciTech Connect

    Blonigan, Patrick J. Wang, Qiqi

    2014-08-01

    Sensitivity analysis, especially adjoint based sensitivity analysis, is a powerful tool for engineering design which allows for the efficient computation of sensitivities with respect to many parameters. However, these methods break down when used to compute sensitivities of long-time averaged quantities in chaotic dynamical systems. This paper presents a new method for sensitivity analysis of ergodic chaotic dynamical systems, the density adjoint method. The method involves solving the governing equations for the system's invariant measure and its adjoint on the system's attractor manifold rather than in phase-space. This new approach is derived for and demonstrated on one-dimensional chaotic maps and the three-dimensional Lorenz system. It is found that the density adjoint computes very finely detailed adjoint distributions and accurate sensitivities, but suffers from large computational costs.

  17. Transport Code for Regular Triangular Geometry

    1993-06-09

    DIAMANT2 solves the two-dimensional static multigroup neutron transport equation in planar regular triangular geometry. Both regular and adjoint, inhomogeneous and homogeneous problems subject to vacuum, reflective or input specified boundary flux conditions are solved. Anisotropy is allowed for the scattering source. Volume and surface sources are allowed for inhomogeneous problems.

  18. Neglected transport equations: extended Rankine-Hugoniot conditions and J -integrals for fracture

    NASA Astrophysics Data System (ADS)

    Davey, K.; Darvizeh, R.

    2016-03-01

    Transport equations in integral form are well established for analysis in continuum fluid dynamics but less so for solid mechanics. Four classical continuum mechanics transport equations exist, which describe the transport of mass, momentum, energy and entropy and thus describe the behaviour of density, velocity, temperature and disorder, respectively. However, one transport equation absent from the list is particularly pertinent to solid mechanics and that is a transport equation for movement, from which displacement is described. This paper introduces the fifth transport equation along with a transport equation for mechanical energy and explores some of the corollaries resulting from the existence of these equations. The general applicability of transport equations to discontinuous physics is discussed with particular focus on fracture mechanics. It is well established that bulk properties can be determined from transport equations by application of a control volume methodology. A control volume can be selected to be moving, stationary, mass tracking, part of, or enclosing the whole system domain. The flexibility of transport equations arises from their ability to tolerate discontinuities. It is insightful thus to explore the benefits derived from the displacement and mechanical energy transport equations, which are shown to be beneficial for capturing the physics of fracture arising from a displacement discontinuity. Extended forms of the Rankine-Hugoniot conditions for fracture are established along with extended forms of J -integrals.

  19. Neglected transport equations: extended Rankine-Hugoniot conditions and J -integrals for fracture

    NASA Astrophysics Data System (ADS)

    Davey, K.; Darvizeh, R.

    2016-09-01

    Transport equations in integral form are well established for analysis in continuum fluid dynamics but less so for solid mechanics. Four classical continuum mechanics transport equations exist, which describe the transport of mass, momentum, energy and entropy and thus describe the behaviour of density, velocity, temperature and disorder, respectively. However, one transport equation absent from the list is particularly pertinent to solid mechanics and that is a transport equation for movement, from which displacement is described. This paper introduces the fifth transport equation along with a transport equation for mechanical energy and explores some of the corollaries resulting from the existence of these equations. The general applicability of transport equations to discontinuous physics is discussed with particular focus on fracture mechanics. It is well established that bulk properties can be determined from transport equations by application of a control volume methodology. A control volume can be selected to be moving, stationary, mass tracking, part of, or enclosing the whole system domain. The flexibility of transport equations arises from their ability to tolerate discontinuities. It is insightful thus to explore the benefits derived from the displacement and mechanical energy transport equations, which are shown to be beneficial for capturing the physics of fracture arising from a displacement discontinuity. Extended forms of the Rankine-Hugoniot conditions for fracture are established along with extended forms of J -integrals.

  20. Local-in-Time Adjoint-Based Method for Optimal Control/Design Optimization of Unsteady Compressible Flows

    NASA Technical Reports Server (NTRS)

    Yamaleev, N. K.; Diskin, B.; Nielsen, E. J.

    2009-01-01

    .We study local-in-time adjoint-based methods for minimization of ow matching functionals subject to the 2-D unsteady compressible Euler equations. The key idea of the local-in-time method is to construct a very accurate approximation of the global-in-time adjoint equations and the corresponding sensitivity derivative by using only local information available on each time subinterval. In contrast to conventional time-dependent adjoint-based optimization methods which require backward-in-time integration of the adjoint equations over the entire time interval, the local-in-time method solves local adjoint equations sequentially over each time subinterval. Since each subinterval contains relatively few time steps, the storage cost of the local-in-time method is much lower than that of the global adjoint formulation, thus making the time-dependent optimization feasible for practical applications. The paper presents a detailed comparison of the local- and global-in-time adjoint-based methods for minimization of a tracking functional governed by the Euler equations describing the ow around a circular bump. Our numerical results show that the local-in-time method converges to the same optimal solution obtained with the global counterpart, while drastically reducing the memory cost as compared to the global-in-time adjoint formulation.

  1. Attribution of primary formaldehyde and sulfur dioxide at Texas City during SHARP/formaldehyde and olefins from large industrial releases (FLAIR) using an adjoint chemistry transport model

    NASA Astrophysics Data System (ADS)

    Olaguer, Eduardo P.; Herndon, Scott C.; Buzcu-Guven, Birnur; Kolb, Charles E.; Brown, Michael J.; Cuclis, Alex E.

    2013-10-01

    adjoint version of the Houston Advanced Research Center (HARC) neighborhood air quality model with 200 m horizontal resolution, coupled offline to the Quick Urban & Industrial Complex (QUIC-URB) fast response urban wind model, was used to perform 4-D variational (4Dvar) inverse modeling of an industrial release of formaldehyde (HCHO) and sulfur dioxide (SO2) in Texas City, Texas during the 2009 Study of Houston Atmospheric Radical Precursors (SHARP). The source attribution was based on real-time observations by the Aerodyne mobile laboratory and a high resolution 3-D digital model of the emitting petrochemical complex and surrounding urban canopy. The inverse model estimate of total primary HCHO emitted during the incident agrees very closely with independent remote sensing estimates based on both Imaging and Multi-Axis Differential Optical Absorption Spectroscopy (DOAS). Whereas a previous analysis of Imaging DOAS data attributed the HCHO release to a Fluidized Catalytic Cracking Unit (FCCU), the HARC model attributed most of the HCHO event emissions to both the FCCU and desulfurization processes. Fugitives contributed significantly to primary HCHO, as did combustion processes, whereas the latter accounted for most SO2 event emissions. The inferred HCHO-to-SO2 molar emission ratio was similar to that computed directly from ambient air measurements during the release. The model-estimated HCHO-to-CO molar emission ratio for combustion units with significant inferred emissions ranged from 2% to somewhat less than 7%, consistent with other observationally-based estimates obtained during SHARP. A model sensitivity study demonstrated that the inclusion of urban morphology has a significant, but not critical, impact on the source attribution.

  2. Nodal collocation approximation for the multidimensional PL equations applied to transport source problems

    SciTech Connect

    Verdu, G.; Capilla, M.; Talavera, C. F.; Ginestar, D.

    2012-07-01

    PL equations are classical high order approximations to the transport equations which are based on the expansion of the angular dependence of the angular neutron flux and the nuclear cross sections in terms of spherical harmonics. A nodal collocation method is used to discretize the PL equations associated with a neutron source transport problem. The performance of the method is tested solving two 1D problems with analytical solution for the transport equation and a classical 2D problem. (authors)

  3. Supersonic biplane design via adjoint method

    NASA Astrophysics Data System (ADS)

    Hu, Rui

    In developing the next generation supersonic transport airplane, two major challenges must be resolved. The fuel efficiency must be significantly improved, and the sonic boom propagating to the ground must be dramatically reduced. Both of these objectives can be achieved by reducing the shockwaves formed in supersonic flight. The Busemann biplane is famous for using favorable shockwave interaction to achieve nearly shock-free supersonic flight at its design Mach number. Its performance at off-design Mach numbers, however, can be very poor. This dissertation studies the performance of supersonic biplane airfoils at design and off-design conditions. The choked flow and flow-hysteresis phenomena of these biplanes are studied. These effects are due to finite thickness of the airfoils and non-uniqueness of the solution to the Euler equations, creating over an order of magnitude more wave drag than that predicted by supersonic thin airfoil theory. As a result, the off-design performance is the major barrier to the practical use of supersonic biplanes. The main contribution of this work is to drastically improve the off-design performance of supersonic biplanes by using an adjoint based aerodynamic optimization technique. The Busemann biplane is used as the baseline design, and its shape is altered to achieve optimal wave drags in series of Mach numbers ranging from 1.1 to 1.7, during both acceleration and deceleration conditions. The optimized biplane airfoils dramatically reduces the effects of the choked flow and flow-hysteresis phenomena, while maintaining a certain degree of favorable shockwave interaction effects at the design Mach number. Compared to a diamond shaped single airfoil of the same total thickness, the wave drag of our optimized biplane is lower at almost all Mach numbers, and is significantly lower at the design Mach number. In addition, by performing a Navier-Stokes solution for the optimized airfoil, it is verified that the optimized biplane improves

  4. Rayleigh streaming simulation using the vorticity transport equation

    NASA Astrophysics Data System (ADS)

    Sastrapradja, Debbie

    One part of understanding thermoacoustic devices involves studying a physical phenomenon called acoustic streaming, a steady fluid flow induced by oscillating acoustic waves. Current numerical calculation of acoustic streaming can involve major computing time and resources. In order to develop a quicker model, the vorticity transport equation (VTE) is used. The goal of using the VTE is to obtain a relatively fast solution with minimal computational resources, which in this case is a single PC. The intent of this method is that it is used in the early design stage of thermoacoustic devices where preliminary (although less detailed) fast results are desired. It is also preferred that the computing power be minimized as not to tie up other resources for the optimized design of thermoacoustic devices. The most well known type of acoustic streaming, Rayleigh streaming, is simulated using the VTE method. A clustered grid is utilized to capture the boundary layer effect on the acoustic streaming. The governing equations used are the VTE, Poisson's equation, and an equation that relates the stream function with the velocity. The outline of the method of calculation involves (i) generating a clustered grid and ensuring there are enough points in the boundary layer, (ii) transforming the clustered grid into the uniform computational grid, (iii) transforming the governing equations to account for the clustering, (iv) calculating the vorticity and the stream function at each grid point using a Direct Method, and (v) calculating the acoustic streaming velocity using the stream function. Steps (iv) through (v) are repeated until the solution converges. It is demonstrated that the VTE method to calculate Rayleigh streaming works well. There are two cases being simulated in the research, a parallel plate case and a cylindrical tube case. The numerical results agree with the analytical results for both cases, although there are some discrepancies in the cylindrical tube case. At

  5. Renormalization group analysis of the Reynolds stress transport equation

    NASA Technical Reports Server (NTRS)

    Rubinstein, R.; Barton, J. M.

    1992-01-01

    The pressure velocity correlation and return to isotropy term in the Reynolds stress transport equation are analyzed using the Yakhot-Orszag renormalization group. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a fast pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constant are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of driving higher order nonlinear models by approximating the sums more accurately.

  6. Riccati equation for simulation of leads in quantum transport

    NASA Astrophysics Data System (ADS)

    Bravi, M.; Farchioni, R.; Grosso, G.; Pastori Parravicini, G.

    2014-10-01

    We present a theoretical procedure with numerical demonstration of a workable and efficient method to evaluate the surface Green's function of semi-infinite leads connected to a device. Such a problem always occurs in quantum transport calculations but also in the study of surfaces and heterojunctions. We show here that these semi-infinite leads can be properly described by real-energy Green's functions obtained analytically by a smart solution of the Riccati matrix equation. The performance of our method is demonstrated in the case of a multichain two-dimensional electron-gas system, composed of a central ribbon connected to two semi-infinite leads, pierced by two opposite magnetic fields.

  7. A simple Boltzmann transport equation for ballistic to diffusive transient heat transport

    SciTech Connect

    Maassen, Jesse Lundstrom, Mark

    2015-04-07

    Developing simplified, but accurate, theoretical approaches to treat heat transport on all length and time scales is needed to further enable scientific insight and technology innovation. Using a simplified form of the Boltzmann transport equation (BTE), originally developed for electron transport, we demonstrate how ballistic phonon effects and finite-velocity propagation are easily and naturally captured. We show how this approach compares well to the phonon BTE, and readily handles a full phonon dispersion and energy-dependent mean-free-path. This study of transient heat transport shows (i) how fundamental temperature jumps at the contacts depend simply on the ballistic thermal resistance, (ii) that phonon transport at early times approach the ballistic limit in samples of any length, and (iii) perceived reductions in heat conduction, when ballistic effects are present, originate from reductions in temperature gradient. Importantly, this framework can be recast exactly as the Cattaneo and hyperbolic heat equations, and we discuss how the key to capturing ballistic heat effects is to use the correct physical boundary conditions.

  8. Transport equations for linear surface waves with random underlying flows

    NASA Astrophysics Data System (ADS)

    Bal, Guillaume; Chou, Tom

    1999-11-01

    We define the Wigner distribution and use it to develop equations for linear surface capillary-gravity wave propagation in the transport regime. The energy density a(r, k) contained in waves propagating with wavevector k at field point r is given by dota(r,k) + nabla_k[U_⊥(r,z=0) \\cdotk + Ω(k)]\\cdotnabla_ra [13pt] \\: hspace1in - (nabla_r\\cdotU_⊥)a - nabla_r(k\\cdotU_⊥)\\cdotnabla_ka = Σ(δU^2) where U_⊥(r, z=0) is a slowly varying surface current, and Ω(k) = √(k^3+k)tanh kh is the free capillary-gravity dispersion relation. Note that nabla_r\\cdotU_⊥(r,z=0) neq 0, and that the surface currents exchange energy density with the propagating waves. When an additional weak random current √\\varepsilon δU(r/\\varepsilon) varying on the scale of k-1 is included, we find an additional scattering term Σ(δU^2) as a function of correlations in δU. Our results can be applied to the study of surface wave energy transport over a turbulent ocean.

  9. Double-difference Adjoint Tomography

    NASA Astrophysics Data System (ADS)

    Yuan, Y. O.; Simons, F. J.; Tromp, J.

    2015-12-01

    We introduce the "double-difference" method, hugely popular in source inversion, in adjoint tomography. Differences between seismic observations and simulations may be explained in terms of many factors besides structural heterogeneity, e.g., errors in the source-time function, inaccurate timing, and systematic uncertainties. To alleviate nonuniqueness in the inverse problem, we make a differential measurement between stations, which largely cancels out the source signature and systematic errors. We seek to minimize the difference between differential measurements of observations and simulations at distinct stations. We show how to implement the double-difference concept in adjoint tomography, both theoretically and in practice. In contrast to conventional inversions aiming to maximize absolute agreement between observations and simulations, by differencing pairs of measurements at distinct locations, we obtain gradients of the new differential misfit function with respect to structural perturbations which are relatively insensitive to an incorrect source signature or timing errors. Furthermore, we analyze sensitivities of absolute and differential measurements. The former provide absolute information on structure along the ray paths between stations and sources, whereas the latter explain relative (and thus high-resolution) structural variations in areas close to the stations. In conventional tomography, one earthquake provides very limited structural resolution, as reflected in a misfit gradient consisting of "streaks" between the stations and the source. In double-difference tomography, one earthquake can actually resolve significant details of the structure, i.e., the double-differences provide a hugely powerful constraint on structural variations. Algorithmically, we incorporate the double-difference concept into the conventional adjoint tomography workflow by simply pairing up all regular measurements. Thus, the computational cost of the related adjoint

  10. Generalized parallel heat transport equations in collisional to weakly collisional plasmas

    NASA Astrophysics Data System (ADS)

    Zawaideh, Emad; Kim, N. S.; Najmabadi, Farrokh

    1988-11-01

    A new set of two-fluid heat-transport equations for heat conduction in collisional to weakly collisional plasmas was derived on the basis of gyrokinetic equations in flux coordinates. In these equations, no restrictions on the anisotropy of the ion distribution function or the collisionality are imposed. In the highly collisional limit, these equations reduce to the classical heat conduction equation of Spitzer and Haerm (1953), while in the weakly collisional limit, they describe a saturated heat flux. Numerical examples comparing these equations with conventional heat transport equations are presented.

  11. Discrete Adjoint-Based Design Optimization of Unsteady Turbulent Flows on Dynamic Unstructured Grids

    NASA Technical Reports Server (NTRS)

    Nielsen, Eric J.; Diskin, Boris; Yamaleev, Nail K.

    2009-01-01

    An adjoint-based methodology for design optimization of unsteady turbulent flows on dynamic unstructured grids is described. The implementation relies on an existing unsteady three-dimensional unstructured grid solver capable of dynamic mesh simulations and discrete adjoint capabilities previously developed for steady flows. The discrete equations for the primal and adjoint systems are presented for the backward-difference family of time-integration schemes on both static and dynamic grids. The consistency of sensitivity derivatives is established via comparisons with complex-variable computations. The current work is believed to be the first verified implementation of an adjoint-based optimization methodology for the true time-dependent formulation of the Navier-Stokes equations in a practical computational code. Large-scale shape optimizations are demonstrated for turbulent flows over a tiltrotor geometry and a simulated aeroelastic motion of a fighter jet.

  12. An adjoint method for the calculation of remote sensitivities in supersonic flow

    NASA Astrophysics Data System (ADS)

    Nadarajah, Siva K.; Jameson, Antony; Alonso, Juan

    2006-02-01

    This paper presents an adjoint method for the calculation of remote sensitivities in supersonic flow. The goal is to develop a set of discrete adjoint equations and their corresponding boundary conditions in order to quantify the influence of geometry modifications on the pressure distribution at an arbitrary location within the domain of interest. First, this paper presents the complete formulation and discretization of the discrete adjoint equations. The special treatment of the adjoint boundary condition to obtain remote sensitivities or sensitivities of pressure distributions at points remotely located from the wing surface are discussed. Secondly, we present results that demonstrate the application of the theory to a three-dimensional remote inverse design problem using a low sweep biconvex wing and a highly swept blunt leading edge wing. Lastly, we present results that establish the added benefit of using an objective function that contains the sum of the remote inverse and drag minimization cost functions.

  13. Multigroup Three-Dimensional Direct Integration Method Radiation Transport Analysis Code System.

    1987-09-18

    Version 00 TRISTAN solves the three-dimensional, fixed-source, Boltzmann transport equation for neutrons or gamma rays in rectangular geometry. The code can solve an adjoint problem as well as a usual transport problem. TRISTAN is a suitable tool to analyze radiation shielding problems such as streaming and deep penetration problems.

  14. Accurate adjoint design sensitivities for nano metal optics.

    PubMed

    Hansen, Paul; Hesselink, Lambertus

    2015-09-01

    We present a method for obtaining accurate numerical design sensitivities for metal-optical nanostructures. Adjoint design sensitivity analysis, long used in fluid mechanics and mechanical engineering for both optimization and structural analysis, is beginning to be used for nano-optics design, but it fails for sharp-cornered metal structures because the numerical error in electromagnetic simulations of metal structures is highest at sharp corners. These locations feature strong field enhancement and contribute strongly to design sensitivities. By using high-accuracy FEM calculations and rounding sharp features to a finite radius of curvature we obtain highly-accurate design sensitivities for 3D metal devices. To provide a bridge to the existing literature on adjoint methods in other fields, we derive the sensitivity equations for Maxwell's equations in the PDE framework widely used in fluid mechanics. PMID:26368483

  15. Adjoint-Based Methods for Estimating CO2 Sources and Sinks from Atmospheric Concentration Data

    NASA Technical Reports Server (NTRS)

    Andrews, Arlyn E.

    2003-01-01

    Work to develop adjoint-based methods for estimating CO2 sources and sinks from atmospheric concentration data was initiated in preparation for last year's summer institute on Carbon Data Assimilation (CDAS) at the National Center for Atmospheric Research in Boulder, CO. The workshop exercises used the GSFC Parameterized Chemistry and Transport Model and its adjoint. Since the workshop, a number of simulations have been run to evaluate the performance of the model adjoint. Results from these simulations will be presented, along with an outline of challenges associated with incorporating a variety of disparate data sources, from sparse, but highly precise, surface in situ observations to less accurate, global future satellite observations.

  16. Self-adjointness of deformed unbounded operators

    SciTech Connect

    Much, Albert

    2015-09-15

    We consider deformations of unbounded operators by using the novel construction tool of warped convolutions. By using the Kato-Rellich theorem, we show that unbounded self-adjoint deformed operators are self-adjoint if they satisfy a certain condition. This condition proves itself to be necessary for the oscillatory integral to be well-defined. Moreover, different proofs are given for self-adjointness of deformed unbounded operators in the context of quantum mechanics and quantum field theory.

  17. Adjoint-Based Algorithms for Adaptation and Design Optimizations on Unstructured Grids

    NASA Technical Reports Server (NTRS)

    Nielsen, Eric J.

    2006-01-01

    Schemes based on discrete adjoint algorithms present several exciting opportunities for significantly advancing the current state of the art in computational fluid dynamics. Such methods provide an extremely efficient means for obtaining discretely consistent sensitivity information for hundreds of design variables, opening the door to rigorous, automated design optimization of complex aerospace configuration using the Navier-Stokes equation. Moreover, the discrete adjoint formulation provides a mathematically rigorous foundation for mesh adaptation and systematic reduction of spatial discretization error. Error estimates are also an inherent by-product of an adjoint-based approach, valuable information that is virtually non-existent in today's large-scale CFD simulations. An overview of the adjoint-based algorithm work at NASA Langley Research Center is presented, with examples demonstrating the potential impact on complex computational problems related to design optimization as well as mesh adaptation.

  18. On the derivation of vector radiative transfer equation for polarized radiative transport in graded index media

    NASA Astrophysics Data System (ADS)

    Zhao, J. M.; Tan, J. Y.; Liu, L. H.

    2012-02-01

    Light transport in graded index media follows a curved trajectory determined by Fermat's principle. Besides the effect of variation of the refractive index on the transport of radiative intensity, the curved ray trajectory will induce geometrical effects on the transport of polarization ellipse. This paper presents a complete derivation of vector radiative transfer equation for polarized radiation transport in absorption, emission and scattering graded index media. The derivation is based on the analysis of the conserved quantities for polarized light transport along curved trajectory and a novel approach. The obtained transfer equation can be considered as a generalization of the classic vector radiative transfer equation that is only valid for uniform refractive index media. Several variant forms of the transport equation are also presented, which include the form for Stokes parameters defined with a fixed reference and the Eulerian forms in the ray coordinate and in several common orthogonal coordinate systems.

  19. Unsteady Adjoint Approach for Design Optimization of Flapping Airfoils

    NASA Technical Reports Server (NTRS)

    Lee, Byung Joon; Liou, Meng-Sing

    2012-01-01

    This paper describes the work for optimizing the propulsive efficiency of flapping airfoils, i.e., improving the thrust under constraining aerodynamic work during the flapping flights by changing their shape and trajectory of motion with the unsteady discrete adjoint approach. For unsteady problems, it is essential to properly resolving time scales of motion under consideration and it must be compatible with the objective sought after. We include both the instantaneous and time-averaged (periodic) formulations in this study. For the design optimization with shape parameters or motion parameters, the time-averaged objective function is found to be more useful, while the instantaneous one is more suitable for flow control. The instantaneous objective function is operationally straightforward. On the other hand, the time-averaged objective function requires additional steps in the adjoint approach; the unsteady discrete adjoint equations for a periodic flow must be reformulated and the corresponding system of equations solved iteratively. We compare the design results from shape and trajectory optimizations and investigate the physical relevance of design variables to the flapping motion at on- and off-design conditions.

  20. Three-Dimensional Turbulent RANS Adjoint-Based Error Correction

    NASA Technical Reports Server (NTRS)

    Park, Michael A.

    2003-01-01

    Engineering problems commonly require functional outputs of computational fluid dynamics (CFD) simulations with specified accuracy. These simulations are performed with limited computational resources. Computable error estimates offer the possibility of quantifying accuracy on a given mesh and predicting a fine grid functional on a coarser mesh. Such an estimate can be computed by solving the flow equations and the associated adjoint problem for the functional of interest. An adjoint-based error correction procedure is demonstrated for transonic inviscid and subsonic laminar and turbulent flow. A mesh adaptation procedure is formulated to target uncertainty in the corrected functional and terminate when error remaining in the calculation is less than a user-specified error tolerance. This adaptation scheme is shown to yield anisotropic meshes with corrected functionals that are more accurate for a given number of grid points then isotropic adapted and uniformly refined grids.

  1. Forward-backward transport theories of ion-solid interactions: Variational approach

    NASA Astrophysics Data System (ADS)

    Prinja, Anil K.

    1989-05-01

    The relationship between the popular so-called backward or Lindhard-type transport equations for linear energetic cascades and the direct or forward Boltzmann equation description is rigorously examined for an arbitrary atomic species mix. A variational principle is systematically derived that characterizes the forward model with generalized boundary conditions (internal reflection at a free surface) and is extremized to yield self-consistently the adjoint equations and boundary conditions as components of the corresponding Euler-Lagrange system. The adjoint function is treated purely as a mathematical artifact, which follows naturally from the variational principle. Dubious physical arguments to assign adjoint boundary conditions are thereby avoided. A truly backward description is derived from the adjoint formalism, which under the assumption of space and time homogeneity, reduces to the familiar Lindhard form. The Lindhard-type equations are seen to be neither backward nor forward equations but assume a hybrid form. In contrast, the forward and truly backward (or adjoint) models are exact and of general validity. They are complementary approaches and thus describe a duality that is mediated by the variational principle.

  2. Analytical solution for one-dimensional advection-dispersion transport equation with distance-dependent coefficients

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Mathematical models describing contaminant transport in heterogeneous porous media are often formulated as an advection-dispersion transport equation with distance-dependent transport coefficients. In this work, a general analytical solution is presented for the linear, one-dimensional advection-di...

  3. Mapping pan-Arctic methane emissions at high spatial resolution using an adjoint atmospheric transport and inversion method and process-based wetland and lake biogeochemical models

    NASA Astrophysics Data System (ADS)

    Tan, Z.; Zhuang, Q.; Henze, D. K.; Frankenberg, C.; Dlugokencky, E.; Sweeney, C.; Turner, A. J.

    2015-11-01

    Understanding methane emissions from the Arctic, a fast warming carbon reservoir, is important for projecting changes in the global methane cycle under future climate scenarios. Here we optimize Arctic methane emissions with a nested-grid high-resolution inverse model by assimilating both high-precision surface measurements and column-average SCIAMACHY satellite retrievals of methane mole fraction. For the first time, methane emissions from lakes are integrated into an atmospheric transport and inversion estimate, together with prior wetland emissions estimated by six different biogeochemical models. We find that, the global methane emissions during July 2004-June 2005 ranged from 496.4 to 511.5 Tg yr-1, with wetland methane emissions ranging from 130.0 to 203.3 Tg yr-1. The Arctic methane emissions during July 2004-June 2005 were in the range of 14.6-30.4 Tg yr-1, with wetland and lake emissions ranging from 8.8 to 20.4 Tg yr-1 and from 5.4 to 7.9 Tg yr-1 respectively. Canadian and Siberian lakes contributed most of the estimated lake emissions. Due to insufficient measurements in the region, Arctic methane emissions are less constrained in northern Russia than in Alaska, northern Canada and Scandinavia. Comparison of different inversions indicates that the distribution of global and Arctic methane emissions is sensitive to prior wetland emissions. Evaluation with independent datasets shows that the global and Arctic inversions improve estimates of methane mixing ratios in boundary layer and free troposphere. The high-resolution inversions provide more details about the spatial distribution of methane emissions in the Arctic.

  4. Adjoint Error Estimation for Linear Advection

    SciTech Connect

    Connors, J M; Banks, J W; Hittinger, J A; Woodward, C S

    2011-03-30

    An a posteriori error formula is described when a statistical measurement of the solution to a hyperbolic conservation law in 1D is estimated by finite volume approximations. This is accomplished using adjoint error estimation. In contrast to previously studied methods, the adjoint problem is divorced from the finite volume method used to approximate the forward solution variables. An exact error formula and computable error estimate are derived based on an abstractly defined approximation of the adjoint solution. This framework allows the error to be computed to an arbitrary accuracy given a sufficiently well resolved approximation of the adjoint solution. The accuracy of the computable error estimate provably satisfies an a priori error bound for sufficiently smooth solutions of the forward and adjoint problems. The theory does not currently account for discontinuities. Computational examples are provided that show support of the theory for smooth solutions. The application to problems with discontinuities is also investigated computationally.

  5. Time-Dependent Ginzburg-Landau Equation and Boltzmann Transport Equation for Charge-Density-Wave Conductors

    NASA Astrophysics Data System (ADS)

    Takane, Yositake; Hayashi, Masahiko; Ebisawa, Hiromichi

    2016-08-01

    The time-dependent Ginzburg-Landau equation and the Boltzmann transport equation for charge-density-wave (CDW) conductors are derived from a microscopic one-dimensional model by applying the Keldysh Green's function approach under a quasiclassical approximation. The effects of an external electric field and impurity pinning of the CDW are fully taken into account without relying on a phenomenological argument. These equations simultaneously describe the spatiotemporal dynamics of both the CDW and quasiparticles; thus, they serve as a starting point to develop a general framework to analyze various nonequilibrium phenomena, such as current conversion between the CDW condensate and quasiparticles, in realistic CDW conductors. It is shown that, in typical situations, the equations correctly describe the nonlinear behavior of electric conductivity in a simpler manner.

  6. Consistent Adjoint Driven Importance Sampling using Space, Energy and Angle

    SciTech Connect

    Peplow, Douglas E.; Mosher, Scott W; Evans, Thomas M

    2012-08-01

    For challenging radiation transport problems, hybrid methods combine the accuracy of Monte Carlo methods with the global information present in deterministic methods. One of the most successful hybrid methods is CADIS Consistent Adjoint Driven Importance Sampling. This method uses a deterministic adjoint solution to construct a biased source distribution and consistent weight windows to optimize a specific tally in a Monte Carlo calculation. The method has been implemented into transport codes using just the spatial and energy information from the deterministic adjoint and has been used in many applications to compute tallies with much higher figures-of-merit than analog calculations. CADIS also outperforms user-supplied importance values, which usually take long periods of user time to develop. This work extends CADIS to develop weight windows that are a function of the position, energy, and direction of the Monte Carlo particle. Two types of consistent source biasing are presented: one method that biases the source in space and energy while preserving the original directional distribution and one method that biases the source in space, energy, and direction. Seven simple example problems are presented which compare the use of the standard space/energy CADIS with the new space/energy/angle treatments.

  7. The kinetics of selective biological transport. II. Equations for induced uphill transport of sugars in human erythrocytes.

    PubMed

    Miller, D M

    1965-07-01

    Equations describing the movement of sugars during induced uphill transport were derived on the assumption of a simple carrier transport mechanism and subjected to experimental verification. Since there was good agreement between the experimental points and the theoretical curves, no changes in the original postulates were required.

  8. A practical discrete-adjoint method for high-fidelity compressible turbulence simulations

    NASA Astrophysics Data System (ADS)

    Vishnampet, Ramanathan; Bodony, Daniel J.; Freund, Jonathan B.

    2015-03-01

    Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvements. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs, though this is predicated on the availability of a sufficiently accurate solution of the forward and adjoint systems. These are challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. Here, we analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space-time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge-Kutta-like scheme, though it would be just first-order accurate if used outside the adjoint formulation for time integration, with finite-difference spatial operators for the adjoint system. Its computational cost only modestly exceeds that of the flow equations. We confirm that its

  9. A practical discrete-adjoint method for high-fidelity compressible turbulence simulations

    SciTech Connect

    Vishnampet, Ramanathan; Bodony, Daniel J.; Freund, Jonathan B.

    2015-03-15

    Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvements. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs, though this is predicated on the availability of a sufficiently accurate solution of the forward and adjoint systems. These are challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. Here, we analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space–time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge–Kutta-like scheme, though it would be just first-order accurate if used outside the adjoint formulation for time integration, with finite-difference spatial operators for the adjoint system. Its computational cost only modestly exceeds that of the flow equations. We confirm that

  10. Adjoint-field errors in high fidelity compressible turbulence simulations for sound control

    NASA Astrophysics Data System (ADS)

    Vishnampet, Ramanathan; Bodony, Daniel; Freund, Jonathan

    2013-11-01

    A consistent discrete adjoint for high-fidelity discretization of the three-dimensional Navier-Stokes equations is used to quantify the error in the sensitivity gradient predicted by the continuous adjoint method, and examine the aeroacoustic flow-control problem for free-shear-flow turbulence. A particular quadrature scheme for approximating the cost functional makes our discrete adjoint formulation for a fourth-order Runge-Kutta scheme with high-order finite differences practical and efficient. The continuous adjoint-based sensitivity gradient is shown to to be inconsistent due to discretization truncation errors, grid stretching and filtering near boundaries. These errors cannot be eliminated by increasing the spatial or temporal resolution since chaotic interactions lead them to become O (1) at the time of control actuation. Although this is a known behavior for chaotic systems, its effect on noise control is much harder to anticipate, especially given the different resolution needs of different parts of the turbulence and acoustic spectra. A comparison of energy spectra of the adjoint pressure fields shows significant error in the continuous adjoint at all wavenumbers, even though they are well-resolved. The effect of this error on the noise control mechanism is analyzed.

  11. A Generalized Adjoint Approach for Quantifying Reflector Assembly Discontinuity Factor Uncertainties

    SciTech Connect

    Yankov, Artem; Collins, Benjamin; Jessee, Matthew Anderson; Downar, Thomas

    2012-01-01

    Sensitivity-based uncertainty analysis of assembly discontinuity factors (ADFs) can be readily performed using adjoint methods for infinite lattice models. However, there is currently no adjoint-based methodology to obtain uncertainties for ADFs along an interface between a fuel and reflector region. To accommodate leakage effects in a reflector region, a 1D approximation is usually made in order to obtain the homogeneous interface flux required to calculate the ADF. Within this 1D framework an adjoint-based method is proposed that is capable of efficiently calculating ADF uncertainties. In the proposed method the sandwich rule is utilized to relate the covariance of the input parameters of 1D diffusion theory in the reflector region to the covariance of the interface ADFs. The input parameters covariance matrix can be readily obtained using sampling-based codes such as XSUSA or adjoint-based codes such as TSUNAMI. The sensitivity matrix is constructed using a fixed-source adjoint approach for inputs characterizing the reflector region. An analytic approach is then used to determine the sensitivity of the ADFs to fuel parameters using the neutron balance equation. A stochastic approach is used to validate the proposed adjoint-based method.

  12. Generalized adjoint consistent treatment of wall boundary conditions for compressible flows

    NASA Astrophysics Data System (ADS)

    Hartmann, Ralf; Leicht, Tobias

    2015-11-01

    In this article, we revisit the adjoint consistency analysis of Discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations with application to the Reynolds-averaged Navier-Stokes and k- ω turbulence equations. Here, particular emphasis is laid on the discretization of wall boundary conditions. While previously only one specific combination of discretizations of wall boundary conditions and of aerodynamic force coefficients has been shown to give an adjoint consistent discretization, in this article we generalize this analysis and provide a discretization of the force coefficients for any consistent discretization of wall boundary conditions. Furthermore, we demonstrate that a related evaluation of the cp- and cf-distributions is required. The freedom gained in choosing the discretization of boundary conditions without loosing adjoint consistency is used to devise a new adjoint consistent discretization including numerical fluxes on the wall boundary which is more robust than the adjoint consistent discretization known up to now. While this work is presented in the framework of Discontinuous Galerkin discretizations, the insight gained is also applicable to (and thus valuable for) other discretization schemes. In particular, the discretization of integral quantities, like the drag, lift and moment coefficients, as well as the discretization of local quantities at the wall like surface pressure and skin friction should follow as closely as possible the discretization of the flow equations and boundary conditions at the wall boundary.

  13. Transport equation for plasmas in a stationary-homogeneous turbulence

    NASA Astrophysics Data System (ADS)

    Wang, Shaojie

    2016-02-01

    For a plasma in a stationary homogeneous turbulence, the Fokker-Planck equation is derived from the nonlinear Vlasov equation by introducing the entropy principle. The ensemble average in evaluating the kinetic diffusion tensor, whose symmetry has been proved, can be computed in a straightforward way when the fluctuating particle trajectories are provided. As an application, it has been shown that a mean parallel electric filed can drive a particle flux through the Stokes-Einstein relation, independent of the details of the fluctuations.

  14. Simple jumping process with memory: Transport equation and diffusion

    NASA Astrophysics Data System (ADS)

    Kamińska, A.; Srokowski, T.

    2004-06-01

    We present a stochastic jumping process, defined in terms of jump-size probability density and jumping rate, which is a generalization of the well-known kangaroo process. The definition takes into account two process values: after and before the jump. Therefore, the process is able to preserve memory about its previous values. It possesses a simple stationary limit. Its master equation is interpreted as the kinetic equation with variable collision rate. The process can be easily applied to model systems which relax to distributions other than Maxwellian. The case of a constant jumping rate corresponds to the diffusion process, either normal or ballistic.

  15. AN EXACT PEAK CAPTURING AND OSCILLATION-FREE SCHEME TO SOLVE ADVECTION-DISPERSION TRANSPORT EQUATIONS

    EPA Science Inventory

    An exact peak capturing and essentially oscillation-free (EPCOF) algorithm, consisting of advection-dispersion decoupling, backward method of characteristics, forward node tracking, and adaptive local grid refinement, is developed to solve transport equations. This algorithm repr...

  16. Eigen decomposition solution to the one-dimensional time-dependent photon transport equation.

    PubMed

    Handapangoda, Chintha C; Pathirana, Pubudu N; Premaratne, Malin

    2011-02-14

    The time-dependent one-dimensional photon transport (radiative transfer) equation is widely used to model light propagation through turbid media with a slab geometry, in a vast number of disciplines. Several numerical and semi-analytical techniques are available to accurately solve this equation. In this work we propose a novel efficient solution technique based on eigen decomposition of the vectorized version of the photon transport equation. Using clever transformations, the four variable integro-differential equation is reduced to a set of first order ordinary differential equations using a combination of a spectral method and the discrete ordinates method. An eigen decomposition approach is then utilized to obtain the closed-form solution of this reduced set of ordinary differential equations. PMID:21369115

  17. Numerical evaluation of the intensity transport equation for well-known wavefronts and intensity distributions

    NASA Astrophysics Data System (ADS)

    Campos-García, Manuel; Granados-Agustín, Fermín.; Cornejo-Rodríguez, Alejandro; Estrada-Molina, Amilcar; Avendaño-Alejo, Maximino; Moreno-Oliva, Víctor Iván.

    2013-11-01

    In order to obtain a clearer interpretation of the Intensity Transport Equation (ITE), in this work, we propose an algorithm to solve it for some particular wavefronts and its corresponding intensity distributions. By simulating intensity distributions in some planes, the ITE is turns into a Poisson equation with Neumann boundary conditions. The Poisson equation is solved by means of the iterative algorithm SOR (Simultaneous Over-Relaxation).

  18. Utilisation de sources et d'adjoints dragon pour les calculs TRIPOLI

    NASA Astrophysics Data System (ADS)

    Camand, Corentin

    Numerical simulation is an essential part of reactor physics in order to understand the behaviour of neutrons inside and outside nuclear reactors. The objective is to solve the neutron transport equation in order to know the neutron flux and the interactions between neutrons and materials. We use neutronic simulation codes in order to solve this equation for criticallity problem, where we have a neutron multiplying environment, and shielding problems. There are two different types of numerical simulation techniques. Deterministic methods solve directly the transport equation using some approximations. The energy domain is divided in regions called groups, we use a spatial mesh for the geometry treatment, transport operator may also be simplified. Those approximations invole an inherent error. However these methods provide high computation time performances. Monte Carlo or stochastic methods follow explicitly a large number of neutrons as they travel through materials minimizing approximations. Continuous-energy and multigroup treatment are both available. Quantities calculated are random variables to which are associated statistical error called standard deviations. We have to simulate a very large number of neutrons if we want the calculation to converge and the results to be precise enough. As a matter of fact, computation time of these methods can be excessively large and represent their main weakness. The objective of this study is to set up a chaining method from a deterministic code to a Monte Carlo code, in order to improve the convergence of Monte Carlo calculations performed by the code TRIPOLI. We want to use datas calculated by the deterministic code DRAGON and use them in TRIPOLI. We will develop two methods. The first one will calculate source distribution in DRAGON and implement them in TRIPOLI as initial sources of a criticallity calculation. The objective is to accelerate the convergence of the neutrons sources, and save the first batches that are

  19. The continuous adjoint approach to the k-ω SST turbulence model with applications in shape optimization

    NASA Astrophysics Data System (ADS)

    Kavvadias, I. S.; Papoutsis-Kiachagias, E. M.; Dimitrakopoulos, G.; Giannakoglou, K. C.

    2015-11-01

    In this article, the gradient of aerodynamic objective functions with respect to design variables, in problems governed by the incompressible Navier-Stokes equations coupled with the k-ω SST turbulence model, is computed using the continuous adjoint method, for the first time. Shape optimization problems for minimizing drag, in external aerodynamics (flows around isolated airfoils), or viscous losses in internal aerodynamics (duct flows) are considered. Sensitivity derivatives computed with the proposed adjoint method are compared to those computed with finite differences or a continuous adjoint variant based on the frequently used assumption of frozen turbulence; the latter proves the need for differentiating the turbulence model. Geometries produced by optimization runs performed with sensitivities computed by the proposed method and the 'frozen turbulence' assumption are also compared to quantify the gain from formulating and solving the adjoint to the turbulence model equations.

  20. Fractional Advective-Dispersive Equation as a Model of Solute Transport in Porous Media

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Understanding and modeling transport of solutes in porous media is a critical issue in the environmental protection. The common model is the advective-dispersive equation (ADE) describing the superposition of the advective transport and the Brownian motion in water-filled pore space. Deviations from...

  1. Conservative differencing of the electron Fokker-Planck transport equation

    SciTech Connect

    Langdon, A.B.

    1981-01-12

    We need to extend the applicability and improve the accuracy of kinetic electron transport codes. In this paper, special attention is given to modelling of e-e collisions, including the dominant contributions arising from anisotropy. The electric field and spatial gradient terms are also considered. I construct finite-difference analogues to the Fokker-Planck integral-differential collision operator, which conserve the particle number, momentum and energy integrals (sums) regardless of the coarseness of the velocity zoning. Such properties are usually desirable, but are especially useful, for example, when there are spatial regions and/or time intervals in which the plasma is cool, so that the collision operator acts rapidly and the velocity distribution is poorly resolved, yet it is crucial that gross conservation properties be respected in hydro-transport applications, such as in the LASNEX code. Some points are raised concerning spatial differencing and time integration.

  2. Analytical Theory of the Destruction Terms in Dissipation Rate Transport Equations

    NASA Technical Reports Server (NTRS)

    Rubinstein, Robert; Zhou, Ye

    1996-01-01

    Modeled dissipation rate transport equations are often derived by invoking various hypotheses to close correlations in the corresponding exact equations. D. C. Leslie suggested that these models might be derived instead from Kraichnan's wavenumber space integrals for inertial range transport power. This suggestion is applied to the destruction terms in the dissipation rate equations for incompressible turbulence, buoyant turbulence, rotating incompressible turbulence, and rotating buoyant turbulence. Model constants like C(epsilon 2) are expressed as integrals; convergence of these integrals implies the absence of Reynolds number dependence in the corresponding destruction term. The dependence of C(epsilon 2) on rotation rate emerges naturally; sensitization of the modeled dissipation rate equation to rotation is not required. A buoyancy related effect which is absent in the exact transport equation for temperature variance dissipation, but which sometimes improves computational predictions, also arises naturally. Both the presence of this effect and the appropriate time scale in the modeled transport equation depend on whether Bolgiano or Kolmogorov inertial range scaling applies. A simple application of these methods leads to a preliminary, dissipation rate equation for rotating buoyant turbulence.

  3. Radiative or neutron transport modeling using a lattice Boltzmann equation framework

    NASA Astrophysics Data System (ADS)

    Bindra, H.; Patil, D. V.

    2012-07-01

    In this paper, the lattice Boltzmann equation (LBE)-based framework is used to obtain the solution for the linear radiative or neutron transport equation. The LBE framework is devised for the integrodifferential forms of these equations which arise due to the inclusion of the scattering terms. The interparticle collisions are neglected, hence omitting the nonlinear collision term. Furthermore, typical representative examples for one-dimensional or two-dimensional geometries and inclusion or exclusion of the scattering term (isotropic and anisotropic) in the Boltzmann transport equation are illustrated to prove the validity of the method. It has been shown that the solution from the LBE methodology is equivalent to the well-known Pn and Sn methods. This suggests that the LBE can potentially provide a more convenient and easy approach to solve the physical problems of neutron and radiation transport.

  4. Radiative or neutron transport modeling using a lattice Boltzmann equation framework.

    PubMed

    Bindra, H; Patil, D V

    2012-07-01

    In this paper, the lattice Boltzmann equation (LBE)-based framework is used to obtain the solution for the linear radiative or neutron transport equation. The LBE framework is devised for the integrodifferential forms of these equations which arise due to the inclusion of the scattering terms. The interparticle collisions are neglected, hence omitting the nonlinear collision term. Furthermore, typical representative examples for one-dimensional or two-dimensional geometries and inclusion or exclusion of the scattering term (isotropic and anisotropic) in the Boltzmann transport equation are illustrated to prove the validity of the method. It has been shown that the solution from the LBE methodology is equivalent to the well-known P(n) and S(n) methods. This suggests that the LBE can potentially provide a more convenient and easy approach to solve the physical problems of neutron and radiation transport.

  5. Solutions to bi-Maxwellian transport equations for SAR-arc conditions

    NASA Technical Reports Server (NTRS)

    Demars, H. G.; Schunk, R. W.

    1986-01-01

    The first subsonic solutions of the bi-Maxwellian-based 16-moment set of transport equations for stable auroral red (SAR) arc conditions are presented. These are compared with the solutions obtained from the Maxwellian-based 13-moment transport equations for the same boundary conditions. Close agreement between the 16-moment and 13-moment solutions was obtained for the drift velocity, total electron temperature, total proton heat flow, and total electron heat flow profiles. On the other hand, significant discrepancies were found. Thus, the 16-moment density profile falls off more rapidly with increasing altitude than that computed with the 13-moment equations; the total proton temperature is less in the 16-moment case than in the 13-moment case by several thousand degrees at most altitudes; and differences exist in the ratios of the proton and electron temperature anisotropies with the altitude. A simplified set of transport equations was obtained by dropping terms which remain relatively small at all altitudes.

  6. Least-squares finite element discretizations of neutron transport equations in 3 dimensions

    SciTech Connect

    Manteuffel, T.A; Ressel, K.J.; Starkes, G.

    1996-12-31

    The least-squares finite element framework to the neutron transport equation introduced in is based on the minimization of a least-squares functional applied to the properly scaled neutron transport equation. Here we report on some practical aspects of this approach for neutron transport calculations in three space dimensions. The systems of partial differential equations resulting from a P{sub 1} and P{sub 2} approximation of the angular dependence are derived. In the diffusive limit, the system is essentially a Poisson equation for zeroth moment and has a divergence structure for the set of moments of order 1. One of the key features of the least-squares approach is that it produces a posteriori error bounds. We report on the numerical results obtained for the minimum of the least-squares functional augmented by an additional boundary term using trilinear finite elements on a uniform tesselation into cubes.

  7. Adjoint estimation of ozone climate penalties

    NASA Astrophysics Data System (ADS)

    Zhao, Shunliu; Pappin, Amanda J.; Morteza Mesbah, S.; Joyce Zhang, J. Y.; MacDonald, Nicole L.; Hakami, Amir

    2013-10-01

    adjoint of a regional chemical transport model is used to calculate location-specific temperature influences (climate penalties) on two policy-relevant ozone metrics: concentrations in polluted regions (>65 ppb) and short-term mortality in Canada and the U.S. Temperature influences through changes in chemical reaction rates, atmospheric moisture content, and biogenic emissions exhibit significant spatial variability. In particular, high-NOx, polluted regions are prominently distinguished by substantial climate penalties (up to 6.2 ppb/K in major urban areas) as a result of large temperature influences through increased biogenic emissions and nonnegative water vapor sensitivities. Temperature influences on ozone mortality, when integrated across the domain, result in 369 excess deaths/K in Canada and the U.S. over a summer season—an impact comparable to a 5% change in anthropogenic NOx emissions. As such, we suggest that NOx control can be also regarded as a climate change adaptation strategy with regard to ozone air quality.

  8. Rayleigh streaming simulation in a cylindrical tube using the vorticity transport equation

    NASA Astrophysics Data System (ADS)

    Sastrapradja, Debbie; Sparrow, Victor W.

    2006-05-01

    Current numerical calculation of acoustic streaming can involve major computing time and resources. To develop a quicker model, the vorticity transport equation (VTE) is used. In this paper Rayleigh streaming in a cylindrical tube is simulated using the VTE. The goal of using the VTE is to obtain a relatively fast solution with minimal computational resources, which in this case is a single PC. A clustered grid is utilized to capture the boundary layer effect on the acoustic streaming. The governing equations used are the VTE, Poisson's equation, and an equation that relates the stream function with the velocity. It is demonstrated that the VTE method to calculate Rayleigh streaming works well.

  9. Generalized parallel heat transport equations in collisional to weakly collisional plasmas

    SciTech Connect

    Zawaideh, E.; Kim, N.S.; Najmabadi, F.

    1988-11-01

    A new set of two-fluid heat transport equations that is valid from collisional to weakly collisional limits is derived. Starting from gyrokinetic equations in flux coordinates, a set of moment equations describing plasma energy transport along the field lines of a space- and time-dependent magnetic field is derived. No restrictions on the anisotropy of the ion distribution function or collisionality are imposed. In the highly collisional limit, these equations reduce to the classical heat conduction equation (e.g., Spitzer and Haerm or Braginskii), while in the weakly collisional limit, they describe a saturated heat flux (flux limited). Numerical examples comparing these equations with conventional heat transport equations show that in the limit where the ratio of the mean free path lambda to the scale length of the temperature gradient L/sub T/ approaches zero, there is no significant difference between the solutions of the new and conventional heat transport equations. As lambda/L/sub T/..-->..1, the conventional heat conduction equation contains a significantly larger error than (lambda/L/sub T/)/sup 2/. The error is found to be O(lambda/L)/sup 2/, where L is the smallest of the scale lengths of the gradient in the magnetic field, or the macroscopic plasma parameters (e.g., velocity scale length, temperature scale length, and density scale length). The accuracy of the flux-limited model depends significantly on the value of the flux limit parameter which, in general, is not known. The new set of equations shows that the flux-limited parameter is a function of the magnetic field and plasma parameter profiles.

  10. On the adjoint operator in photoacoustic tomography

    NASA Astrophysics Data System (ADS)

    Arridge, Simon R.; Betcke, Marta M.; Cox, Ben T.; Lucka, Felix; Treeby, Brad E.

    2016-11-01

    Photoacoustic tomography (PAT) is an emerging biomedical imaging from coupled physics technique, in which the image contrast is due to optical absorption, but the information is carried to the surface of the tissue as ultrasound pulses. Many algorithms and formulae for PAT image reconstruction have been proposed for the case when a complete data set is available. In many practical imaging scenarios, however, it is not possible to obtain the full data, or the data may be sub-sampled for faster data acquisition. In such cases, image reconstruction algorithms that can incorporate prior knowledge to ameliorate the loss of data are required. Hence, recently there has been an increased interest in using variational image reconstruction. A crucial ingredient for the application of these techniques is the adjoint of the PAT forward operator, which is described in this article from physical, theoretical and numerical perspectives. First, a simple mathematical derivation of the adjoint of the PAT forward operator in the continuous framework is presented. Then, an efficient numerical implementation of the adjoint using a k-space time domain wave propagation model is described and illustrated in the context of variational PAT image reconstruction, on both 2D and 3D examples including inhomogeneous sound speed. The principal advantage of this analytical adjoint over an algebraic adjoint (obtained by taking the direct adjoint of the particular numerical forward scheme used) is that it can be implemented using currently available fast wave propagation solvers.

  11. Adjoint-Based Sensitivity Maps for the Nearshore

    NASA Astrophysics Data System (ADS)

    Orzech, Mark; Veeramony, Jay; Ngodock, Hans

    2013-04-01

    The wave model SWAN (Booij et al., 1999) solves the spectral action balance equation to produce nearshore wave forecasts and climatologies. It is widely used by the coastal modeling community and is part of a variety of coupled ocean-wave-atmosphere model systems. A variational data assimilation system (Orzech et al., 2013) has recently been developed for SWAN and is presently being transitioned to operational use by the U.S. Naval Oceanographic Office. This system is built around a numerical adjoint to the fully nonlinear, nonstationary SWAN code. When provided with measured or artificial "observed" spectral wave data at a location of interest on a given nearshore bathymetry, the adjoint can compute the degree to which spectral energy levels at other locations are correlated with - or "sensitive" to - variations in the observed spectrum. Adjoint output may be used to construct a sensitivity map for the entire domain, tracking correlations of spectral energy throughout the grid. When access is denied to the actual locations of interest, sensitivity maps can be used to determine optimal alternate locations for data collection by identifying regions of greatest sensitivity in the mapped domain. The present study investigates the properties of adjoint-generated sensitivity maps for nearshore wave spectra. The adjoint and forward SWAN models are first used in an idealized test case at Duck, NC, USA, to demonstrate the system's effectiveness at optimizing forecasts of shallow water wave spectra for an inaccessible surf-zone location. Then a series of simulations is conducted for a variety of different initializing conditions, to examine the effects of seasonal changes in wave climate, errors in bathymetry, and variations in size and shape of the inaccessible region of interest. Model skill is quantified using two methods: (1) a more traditional correlation of observed and modeled spectral statistics such as significant wave height, and (2) a recently developed RMS

  12. Adjoint Sensitivity Analysis of a Coupled Groundwater-Surface Water Model

    NASA Astrophysics Data System (ADS)

    Kelley, V. A.

    2013-12-01

    Derivation of the exact equations of Adjoint Sensitivity Analysis for a coupled Groundwater-Surface water model is presented here, with reference to the Stream package in MODFLOW-2005. MODFLOW-2005 offers two distinct packages to simulate river boundary conditions in an aquifer model. They are the RIV (RIVer) Package and the STR (STReam) Package. The STR package simulates a coupled Groundwater and Surface Water flow model. As a result of coupling between the Groundwater and the Surface Water flows, the flows to/from the aquifer depend not just on the river stage and aquifer head at that location (as would happen in the RIV package); but on the river stages and aquifer heads at all upstream locations, in the complex network of streams with all its distributaries and diversions. This requires a substantial modification of the adjoint state equations (not required in RIV Package). The necessary equations for the STR Package have now been developed and implemented the MODFLOW-ADJOINT Code. The exact STR Adjoint code has been validated by comparing with the results from the parameter perturbation method, for the case of San Pedro Model (USGS) and Northern Arizona Regional Aquifer Model (USGS). When the RIV package is used for the same models, the sensitivity analysis results are incorrect for some nodes, indicating the advantage of using the exact methods of the STR Package in MODFLOW-Adjoint code. This exact analysis has been used for deriving the capture functions in the management of groundwater, subject to the constraints on the depletion of surface water supplies. Capture maps are used for optimal location of the pumping wells, their rates of withdrawals, and their timing. Because of the immense savings in computational times, with this Adjoint strategy, it is feasible to embed the groundwater management problem in a stochastic framework (probabilistic approach) to address the uncertainties in the groundwater model.

  13. Modeling ballistic effects in frequency-dependent transient thermal transport using diffusion equations

    NASA Astrophysics Data System (ADS)

    Maassen, Jesse; Lundstrom, Mark

    2016-03-01

    Understanding ballistic phonon transport effects in transient thermoreflectance experiments and explaining the observed deviations from classical theory remains a challenge. Diffusion equations are simple and computationally efficient but are widely believed to break down when the characteristic length scale is similar or less than the phonon mean-free-path. Building on our prior work, we demonstrate how well-known diffusion equations, namely, the hyperbolic heat equation and the Cattaneo equation, can be used to model ballistic phonon effects in frequency-dependent periodic steady-state thermal transport. Our analytical solutions are found to compare excellently to rigorous numerical results of the phonon Boltzmann transport equation. The correct physical boundary conditions can be different from those traditionally used and are paramount for accurately capturing ballistic effects. To illustrate the technique, we consider a simple model problem using two different, commonly used heating conditions. We demonstrate how this framework can easily handle detailed material properties, by considering the case of bulk silicon using a full phonon dispersion and mean-free-path distribution. This physically transparent approach provides clear insights into the nonequilibrium physics of quasi-ballistic phonon transport and its impact on thermal transport properties.

  14. A hybrid multigroup/continuous-energy Monte Carlo method for solving the Boltzmann-Fokker-Planck equation

    SciTech Connect

    Morel, J.E.; Lorence, L.J. Jr.; Kensek, R.P.; Halbleib, J.A.; Sloan, D.P.

    1996-11-01

    A hybrid multigroup/continuous-energy Monte Carlo algorithm is developed for solving the Boltzmann-Fokker-Planck equation. This algorithm differs significantly from previous charged-particle Monte Carlo algorithms. Most importantly, it can be used to perform both forward and adjoint transport calculations, using the same basic multigroup cross-section data. The new algorithm is fully described, computationally tested, and compared with a standard condensed history algorithm for coupled electron-photon transport calculations.

  15. Coupled electron-photon radiation transport

    SciTech Connect

    Lorence, L.; Kensek, R.P.; Valdez, G.D.; Drumm, C.R.; Fan, W.C.; Powell, J.L.

    2000-01-17

    Massively-parallel computers allow detailed 3D radiation transport simulations to be performed to analyze the response of complex systems to radiation. This has been recently been demonstrated with the coupled electron-photon Monte Carlo code, ITS. To enable such calculations, the combinatorial geometry capability of ITS was improved. For greater geometrical flexibility, a version of ITS is under development that can track particles in CAD geometries. Deterministic radiation transport codes that utilize an unstructured spatial mesh are also being devised. For electron transport, the authors are investigating second-order forms of the transport equations which, when discretized, yield symmetric positive definite matrices. A novel parallelization strategy, simultaneously solving for spatial and angular unknowns, has been applied to the even- and odd-parity forms of the transport equation on a 2D unstructured spatial mesh. Another second-order form, the self-adjoint angular flux transport equation, also shows promise for electron transport.

  16. Solution and Study of the Two-Dimensional Nodal Neutron Transport Equation

    SciTech Connect

    Panta Pazos, Ruben; Biasotto Hauser, Eliete; Tullio de Vilhena, Marco

    2002-07-01

    In the last decade Vilhena and coworkers reported an analytical solution to the two-dimensional nodal discrete-ordinates approximations of the neutron transport equation in a convex domain. The key feature of these works was the application of the combined collocation method of the angular variable and nodal approach in the spatial variables. By nodal approach we mean the transverse integration of the SN equations. This procedure leads to a set of one-dimensional S{sub N} equations for the average angular fluxes in the variables x and y. These equations were solved by the old version of the LTS{sub N} method, which consists in the application of the Laplace transform to the set of nodal S{sub N} equations and solution of the resulting linear system by symbolic computation. It is important to recall that this procedure allow us to increase N the order of S{sub N} up to 16. To overcome this drawback we step forward performing a spectral painstaking analysis of the nodal S{sub N} equations for N up to 16 and we begin the convergence of the S{sub N} nodal equations defining an error for the angular flux and estimating the error in terms of the truncation error of the quadrature approximations of the integral term. Furthermore, we compare numerical results of this approach with those of other techniques used to solve the two-dimensional discrete approximations of the neutron transport equation. (authors)

  17. A time dependent mixing model to close PDF equations for transport in heterogeneous aquifers

    NASA Astrophysics Data System (ADS)

    Schüler, L.; Suciu, N.; Knabner, P.; Attinger, S.

    2016-10-01

    Probability density function (PDF) methods are a promising alternative to predicting the transport of solutes in groundwater under uncertainty. They make it possible to derive the evolution equations of the mean concentration and the concentration variance, used in moment methods. The mixing model, describing the transport of the PDF in concentration space, is essential for both methods. Finding a satisfactory mixing model is still an open question and due to the rather elaborate PDF methods, a difficult undertaking. Both the PDF equation and the concentration variance equation depend on the same mixing model. This connection is used to find and test an improved mixing model for the much easier to handle concentration variance. Subsequently, this mixing model is transferred to the PDF equation and tested. The newly proposed mixing model yields significantly improved results for both variance modelling and PDF modelling.

  18. Efficient, Automated Monte Carlo Methods for Radiation Transport.

    PubMed

    Kong, Rong; Ambrose, Martin; Spanier, Jerome

    2008-11-20

    Monte Carlo simulations provide an indispensible model for solving radiative transport problems, but their slow convergence inhibits their use as an everyday computational tool. In this paper, we present two new ideas for accelerating the convergence of Monte Carlo algorithms based upon an efficient algorithm that couples simulations of forward and adjoint transport equations. Forward random walks are first processed in stages, each using a fixed sample size, and information from stage k is used to alter the sampling and weighting procedure in stage k + 1. This produces rapid geometric convergence and accounts for dramatic gains in the efficiency of the forward computation. In case still greater accuracy is required in the forward solution, information from an adjoint simulation can be added to extend the geometric learning of the forward solution. The resulting new approach should find widespread use when fast, accurate simulations of the transport equation are needed. PMID:23226872

  19. Transport equations for low-energy solar particles in evolving interplanetary magnetic fields

    NASA Technical Reports Server (NTRS)

    Ng, C. K.

    1988-01-01

    Two new forms of a simplified Fokker-Planck equation are derived for the transport of low-energy solar energetic particles in an evolving interplanetary magnetic field, carried by a variable radial solar wind. An idealized solution suggests that the 'invariant' anisotropy direction reported by Allum et al. (1974) may be explained within the conventional theoretical framework. The equations may be used to relate studies of solar particle propagation to solar wind transients, and vice versa.

  20. Lorentz force correction to the Boltzmann radiation transport equation and its implications for Monte Carlo algorithms.

    PubMed

    Bouchard, Hugo; Bielajew, Alex

    2015-07-01

    To establish a theoretical framework for generalizing Monte Carlo transport algorithms by adding external electromagnetic fields to the Boltzmann radiation transport equation in a rigorous and consistent fashion. Using first principles, the Boltzmann radiation transport equation is modified by adding a term describing the variation of the particle distribution due to the Lorentz force. The implications of this new equation are evaluated by investigating the validity of Fano's theorem. Additionally, Lewis' approach to multiple scattering theory in infinite homogeneous media is redefined to account for the presence of external electromagnetic fields. The equation is modified and yields a description consistent with the deterministic laws of motion as well as probabilistic methods of solution. The time-independent Boltzmann radiation transport equation is generalized to account for the electromagnetic forces in an additional operator similar to the interaction term. Fano's and Lewis' approaches are stated in this new equation. Fano's theorem is found not to apply in the presence of electromagnetic fields. Lewis' theory for electron multiple scattering and moments, accounting for the coupling between the Lorentz force and multiple elastic scattering, is found. However, further investigation is required to develop useful algorithms for Monte Carlo and deterministic transport methods. To test the accuracy of Monte Carlo transport algorithms in the presence of electromagnetic fields, the Fano cavity test, as currently defined, cannot be applied. Therefore, new tests must be designed for this specific application. A multiple scattering theory that accurately couples the Lorentz force with elastic scattering could improve Monte Carlo efficiency. The present study proposes a new theoretical framework to develop such algorithms.

  1. Transient 1D transport equation simulated by a mixed Green element formulation

    NASA Astrophysics Data System (ADS)

    Taigbenu, Akpofure Efemena; Onyejekwe, Okey Oseloka

    1997-08-01

    New discrete element equations or coefficients are derived for the transient 1D diffusion-advection or transport equation based on the Green element replication of the differential equation using linear elements. The Green element method (GEM), which solves the singular boundary integral theory (a Fredholm integral equation of the second kind) on a typical element, gives rise to a banded global coefficient matrix which is amenable to efficient matrix solvers. It is herein derived for the transient 1D transport equation with uniform and non-uniform ambient flow conditions and in which first-order decay of the containment is allowed to take place. Because the GEM implements the singular boundary integral theory within each element at a time, the integrations are carried out in exact fashion, thereby making the application of the boundary integral theory more utilitarian. This system of discrete equations, presented herein for the first time, using linear interpolating functions in the spatial dimensions shows promising stable characteristics for advection-dominant transport. Three numerical examples are used to demonstrate the capabilities of the method. The second-order-correct Crank-Nicolson scheme and the modified fully implicit scheme with a difference weighting value of two give superior solutions in all simulated examples.

  2. Solutions to bi-Maxwellian transport equations for radial solar wind beyond 28 R(S)

    NASA Technical Reports Server (NTRS)

    Demars, H. G.; Schunk, R. W.

    1991-01-01

    This paper presents solar wind solutions for radial flow between 28 solar radii and 1 AU using the bi-Maxwellian-based 16-moment set of transport equations. In addition to the number density, drift velocity, and parallel and perpendicular temperatures, the 16-moment equations account for the transport of both longitudinal and transverse thermal energies as well as stress. Also, using the 16-moment approximation for the distribution function and assuming plasma parameter values characteristic of the solar wind, contour plots are generated for the proton velocity distribution function. It is shown how the shape of these plots depends on various macroscopic plasma parameters.

  3. Receptivity in parallel flows: An adjoint approach

    NASA Technical Reports Server (NTRS)

    Hill, D. Christopher

    1993-01-01

    Linear receptivity studies in parallel flows are aimed at understanding how external forcing couples to the natural unstable motions which a flow can support. The vibrating ribbon problem models the original Schubauer and Skramstad boundary layer experiment and represents the classic boundary layer receptivity problem. The process by which disturbances are initiated in convectively-unstable jets and shear layers has also received attention. Gaster was the first to handle the boundary layer analysis with the recognition that spatial modes, rather than temporal modes, were relevant when studying convectively-unstable flows that are driven by a time-harmonic source. The amplitude of the least stable spatial mode, far downstream of the source, is related to the source strength by a coupling coefficient. The determination of this coefficient is at the heart of this type of linear receptivity study. The first objective of the present study was to determine whether the various wave number derivative factors, appearing in the coupling coefficients for linear receptivity problems, could be reexpressed in a simpler form involving adjoint eigensolutions. Secondly, it was hoped that the general nature of this simplification could be shown; indeed, a rather elegant characterization of the receptivity properties of spatial instabilities does emerge. The analysis is quite distinct from the usual Fourier-inversion procedures, although a detailed knowledge of the spectrum of the Orr-Sommerfeld equation is still required. Since the cylinder wake analysis proved very useful in addressing control considerations, the final objective was to provide a foundation upon which boundary layer control theory may be developed.

  4. h-Refinement for simple corner balance scheme of SN transport equation on distorted meshes

    NASA Astrophysics Data System (ADS)

    Yang, Rong; Yuan, Guangwei

    2016-11-01

    The transport sweep algorithm is a common method for solving discrete ordinate transport equation, but it breaks down once a concave cell appears in spatial meshes. To deal with this issue a local h-refinement for simple corner balance (SCB) scheme of SN transport equation on arbitrary quadrilateral meshes is presented in this paper by using a new subcell partition. It follows that a hybrid mesh with both triangle and quadrilateral cells is generated, and the geometric quality of these cells improves, especially it is ensured that all cells become convex. Combining with the original SCB scheme, an adaptive transfer algorithm based on the hybrid mesh is constructed. Numerical experiments are presented to verify the utility and accuracy of the new algorithm, especially for some application problems such as radiation transport coupled with Lagrangian hydrodynamic flow. The results show that it performs well on extremely distorted meshes with concave cells, on which the original SCB scheme does not work.

  5. Variational approach to solving the spectral Boltzmann transport equation in transient thermal grating for thin films

    NASA Astrophysics Data System (ADS)

    Chiloyan, Vazrik; Zeng, Lingping; Huberman, Samuel; Maznev, Alexei A.; Nelson, Keith A.; Chen, Gang

    2016-07-01

    The phonon Boltzmann transport equation (BTE) is widely utilized to study non-diffusive thermal transport. We find a solution of the BTE in the thin film transient thermal grating (TTG) experimental geometry by using a recently developed variational approach with a trial solution supplied by the Fourier heat conduction equation. We obtain an analytical expression for the thermal decay rate that shows excellent agreement with Monte Carlo simulations. We also obtain a closed form expression for the effective thermal conductivity that demonstrates the full material property and heat transfer geometry dependence, and recovers the limits of the one-dimensional TTG expression for very thick films and the Fuchs-Sondheimer expression for very large grating spacings. The results demonstrate the utility of the variational technique for analyzing non-diffusive phonon-mediated heat transport for nanostructures in multi-dimensional transport geometries, and will assist the probing of the mean free path distribution of materials via transient grating experiments.

  6. Equations of state and transport properties of mixtures in the warm dense regime

    SciTech Connect

    Hou, Yong; Dai, Jiayu; Kang, Dongdong; Ma, Wen; Yuan, Jianmin

    2015-02-15

    We have performed average-atom molecular dynamics to simulate the CH and LiH mixtures in the warm dense regime, and obtained equations of state and the ionic transport properties. The electronic structures are calculated by using the modified average-atom model, which have included the broadening of energy levels, and the ion-ion pair potentials of mixtures are constructed based on the temperature-dependent density functional theory. The ionic transport properties, such as ionic diffusion and shear viscosity, are obtained through the ionic velocity correlation functions. The equations of state and transport properties for carbon, hydrogen and lithium, hydrogen mixtures in a wide region of density and temperature are calculated. Through our computing the average ionization degree, average ion-sphere diameter and transition properties in the mixture, it is shown that transport properties depend not only on the ionic mass but also on the average ionization degree.

  7. Un-collided-flux preconditioning for the first order transport equation

    SciTech Connect

    Rigley, M.; Koebbe, J.; Drumm, C.

    2013-07-01

    Two codes were tested for the first order neutron transport equation using finite element methods. The un-collided-flux solution is used as a preconditioner for each of these methods. These codes include a least squares finite element method and a discontinuous finite element method. The performance of each code is shown on problems in one and two dimensions. The un-collided-flux preconditioner shows good speedup on each of the given methods. The un-collided-flux preconditioner has been used on the second-order equation, and here we extend those results to the first order equation. (authors)

  8. Double-difference adjoint seismic tomography

    NASA Astrophysics Data System (ADS)

    Yuan, Yanhua O.; Simons, Frederik J.; Tromp, Jeroen

    2016-09-01

    We introduce a `double-difference' method for the inversion for seismic wave speed structure based on adjoint tomography. Differences between seismic observations and model predictions at individual stations may arise from factors other than structural heterogeneity, such as errors in the assumed source-time function, inaccurate timings and systematic uncertainties. To alleviate the corresponding non-uniqueness in the inverse problem, we construct differential measurements between stations, thereby reducing the influence of the source signature and systematic errors. We minimize the discrepancy between observations and simulations in terms of the differential measurements made on station pairs. We show how to implement the double-difference concept in adjoint tomography, both theoretically and practically. We compare the sensitivities of absolute and differential measurements. The former provide absolute information on structure along the ray paths between stations and sources, whereas the latter explain relative (and thus higher resolution) structural variations in areas close to the stations. Whereas in conventional tomography a measurement made on a single earthquake-station pair provides very limited structural information, in double-difference tomography one earthquake can actually resolve significant details of the structure. The double-difference methodology can be incorporated into the usual adjoint tomography workflow by simply pairing up all conventional measurements; the computational cost of the necessary adjoint simulations is largely unaffected. Rather than adding to the computational burden, the inversion of double-difference measurements merely modifies the construction of the adjoint sources for data assimilation.

  9. Double-difference adjoint seismic tomography

    NASA Astrophysics Data System (ADS)

    Yuan, Yanhua O.; Simons, Frederik J.; Tromp, Jeroen

    2016-06-01

    We introduce a `double-difference' method for the inversion for seismic wavespeed structure based on adjoint tomography. Differences between seismic observations and model predictions at individual stations may arise from factors other than structural heterogeneity, such as errors in the assumed source-time function, inaccurate timings, and systematic uncertainties. To alleviate the corresponding nonuniqueness in the inverse problem, we construct differential measurements between stations, thereby reducing the influence of the source signature and systematic errors. We minimize the discrepancy between observations and simulations in terms of the differential measurements made on station pairs. We show how to implement the double-difference concept in adjoint tomography, both theoretically and in practice. We compare the sensitivities of absolute and differential measurements. The former provide absolute information on structure along the ray paths between stations and sources, whereas the latter explain relative (and thus higher-resolution) structural variations in areas close to the stations. Whereas in conventional tomography a measurement made on a single earthquake-station pair provides very limited structural information, in double-difference tomography one earthquake can actually resolve significant details of the structure. The double-difference methodology can be incorporated into the usual adjoint tomography workflow by simply pairing up all conventional measurements; the computational cost of the necessary adjoint simulations is largely unaffected. Rather than adding to the computational burden, the inversion of double-difference measurements merely modifies the construction of the adjoint sources for data assimilation.

  10. New Travelling Wave Solutions of Burgers Equation with Finite Transport Memory

    NASA Astrophysics Data System (ADS)

    Sakthivel, Rathinasamy; Chun, Changbum; Lee, Jonu

    2010-09-01

    The nonlinear evolution equations with finite memory have a wide range of applications in science and engineering. The Burgers equation with finite memory transport (time-delayed) describes convection-diffusion processes. In this paper, we establish the new solitary wave solutions for the time-delayed Burgers equation. The extended tanh method and the exp-function method have been employed to reveal these new solutions. Further, we have calculated the numerical solutions of the time-delayed Burgers equation with initial conditions by using the homotopy perturbation method (HPM). Our results show that the extended tanh and exp-function methods are very effective in finding exact solutions of the considered problem and HPM is very powerful in finding numerical solutions with good accuracy for nonlinear partial differential equations without any need of transformation or perturbation

  11. Adjoint Techniques for Topology Optimization of Structures Under Damage Conditions

    NASA Technical Reports Server (NTRS)

    Akgun, Mehmet A.; Haftka, Raphael T.

    2000-01-01

    The objective of this cooperative agreement was to seek computationally efficient ways to optimize aerospace structures subject to damage tolerance criteria. Optimization was to involve sizing as well as topology optimization. The work was done in collaboration with Steve Scotti, Chauncey Wu and Joanne Walsh at the NASA Langley Research Center. Computation of constraint sensitivity is normally the most time-consuming step of an optimization procedure. The cooperative work first focused on this issue and implemented the adjoint method of sensitivity computation (Haftka and Gurdal, 1992) in an optimization code (runstream) written in Engineering Analysis Language (EAL). The method was implemented both for bar and plate elements including buckling sensitivity for the latter. Lumping of constraints was investigated as a means to reduce the computational cost. Adjoint sensitivity computation was developed and implemented for lumped stress and buckling constraints. Cost of the direct method and the adjoint method was compared for various structures with and without lumping. The results were reported in two papers (Akgun et al., 1998a and 1999). It is desirable to optimize topology of an aerospace structure subject to a large number of damage scenarios so that a damage tolerant structure is obtained. Including damage scenarios in the design procedure is critical in order to avoid large mass penalties at later stages (Haftka et al., 1983). A common method for topology optimization is that of compliance minimization (Bendsoe, 1995) which has not been used for damage tolerant design. In the present work, topology optimization is treated as a conventional problem aiming to minimize the weight subject to stress constraints. Multiple damage configurations (scenarios) are considered. Each configuration has its own structural stiffness matrix and, normally, requires factoring of the matrix and solution of the system of equations. Damage that is expected to be tolerated is local

  12. Analytical Tests for Ray Effect Errors in Discrete Ordinate Methods for Solving the Neutron Transport Equation

    SciTech Connect

    Chang, B

    2004-03-22

    This paper contains three analytical solutions of transport problems which can be used to test ray-effect errors in the numerical solutions of the Boltzmann Transport Equation (BTE). We derived the first two solutions and the third was shown to us by M. Prasad. Since this paper is intended to be an internal LLNL report, no attempt was made to find the original derivations of the solutions in the literature in order to cite the authors for their work.

  13. Adjoint-weighted variational formulation for a direct computational solution of an inverse heat conduction problem

    NASA Astrophysics Data System (ADS)

    Barbone, Paul E.; Oberai, Assad A.; Harari, Isaac

    2007-12-01

    We consider the direct (i.e. non-iterative) solution of the inverse problem of heat conduction for which at least two interior temperature fields are available. The strong form of the problem for the single, unknown, thermal conductivity field is governed by two partial differential equations of pure advective transport. The given temperature fields must satisfy a compatibility condition for the problem to have a solution. We introduce a novel variational formulation, the adjoint-weighted equation (AWE), for solving the two-field problem. In this case, the gradients of two given temperature fields must be linearly independent in the entire domain, a weaker condition than the compatibility required by the strong form. We show that the solution of the AWE formulation is equivalent to that of the strong form when both are well posed. We prove that the Galerkin discretization of the AWE formulation leads to a stable, convergent numerical method that has optimal rates of convergence. We show computational examples that confirm these optimal rates. The AWE formulation shows good numerical performance on problems with both smooth and rough coefficients and solutions.

  14. Adjoint variational methods in nonconservative stability problems.

    NASA Technical Reports Server (NTRS)

    Prasad, S. N.; Herrmann, G.

    1972-01-01

    A general nonself-adjoint eigenvalue problem is examined and it is shown that the commonly employed approximate methods, such as the Galerkin procedure, the method of weighted residuals and the least square technique lack variational descriptions. When used in their previously known forms they do not yield stationary eigenvalues and eigenfunctions. With the help of an adjoint system, however, several analogous variational descriptions may be developed and it is shown in the present study that by properly restating the method of least squares, stationary eigenvalues may be obtained. Several properties of the adjoint eigenvalue problem, known only for a restricted group, are shown to exist for the more general class selected for study.

  15. Time-independent one-speed neutron transport equation with anisotropic scattering in absorbing media

    SciTech Connect

    Hangelbroek, R. J.

    1980-06-01

    This report treats the time-independent, one-speed neutron transport equation with anisotropic scattering in absorbing media. For nuclear gain operators existence and uniqueness of solutions to the half-space and finite-slab problems are proved in L/sub 2/-space. The formulas needed for explicit calculations are derived by the use of perturbation theory techniques.

  16. Exact analytical solutions for contaminant transport in rivers 1. The equilibrium advection-dispersion equation

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Analytical solutions of the advection-dispersion equation and related models are indispensable for predicting or analyzing contaminant transport processes in streams and rivers, as well as in other surface water bodies. Many useful analytical solutions originated in disciplines other than surface-w...

  17. A variational solution to the transport equation subject to an affine constraint.

    SciTech Connect

    Pousin, Jerome G.; Najm, Habib N.; Picq, Martine; Pebay, Philippe Pierre

    2004-02-01

    We establish an existence and uniqueness theorem for the transport equation subject to an inequality affine constraint, viewed as a constrained optimization problem. Then we derive a Space-Time Integrated Least Squares (STILS) scheme for its numerical approximation. Furthermore, we discuss some L{sup 2}-projection strategies and with numerical examples we show that there are not relevant for that problem.

  18. Parallel algorithms for 2-D cylindrical transport equations of Eigenvalue problem

    SciTech Connect

    Wei, J.; Yang, S.

    2013-07-01

    In this paper, aimed at the neutron transport equations of eigenvalue problem under 2-D cylindrical geometry on unstructured grid, the discrete scheme of Sn discrete ordinate and discontinuous finite is built, and the parallel computation for the scheme is realized on MPI systems. Numerical experiments indicate that the designed parallel algorithm can reach perfect speedup, it has good practicality and scalability. (authors)

  19. Measuring the contour of a wavefront using the Irradiance Transport Equation (ITE)

    NASA Astrophysics Data System (ADS)

    Castillo-Rodríguez, Luis; Granados-Agustín, Fermín; Fernández-Guasti, Manuel; Cornejo-Rodríguez, Alejandro

    2006-01-01

    The Irradiance Transport Equation (ITE), found by Teague, had been used in optics with different applications. One of the field where had been used is in optical testing, for example, with the method developed by Takeda. In this paper following the idea of using different optical and mathematical analysis method, theorical and experimental results are presented.

  20. Number-resolved master equation approach to quantum measurement and quantum transport

    NASA Astrophysics Data System (ADS)

    Li, Xin-Qi

    2016-08-01

    In addition to the well-known Landauer-Büttiker scattering theory and the nonequilibrium Green's function technique for mesoscopic transports, an alternative (and very useful) scheme is quantum master equation approach. In this article, we review the particle-number ( n)-resolved master equation ( n-ME) approach and its systematic applications in quantum measurement and quantum transport problems. The n-ME contains rich dynamical information, allowing efficient study of topics such as shot noise and full counting statistics analysis. Moreover, we also review a newly developed master equation approach (and its n-resolved version) under self-consistent Born approximation. The application potential of this new approach is critically examined via its ability to recover the exact results for noninteracting systems under arbitrary voltage and in presence of strong quantum interference, and the challenging non-equilibrium Kondo effect.

  1. Coupling lattice Boltzmann and continuum equations for flow and reactive transport in porous media.

    SciTech Connect

    Coon, Ethan; Porter, Mark L.; Kang, Qinjun; Moulton, John D.; Lichtner, Peter C.

    2012-06-18

    In spatially and temporally localized instances, capturing sub-reservoir scale information is necessary. Capturing sub-reservoir scale information everywhere is neither necessary, nor computationally possible. The lattice Boltzmann Method for solving pore-scale systems. At the pore-scale, LBM provides an extremely scalable, efficient way of solving Navier-Stokes equations on complex geometries. Coupling pore-scale and continuum scale systems via domain decomposition. By leveraging the interpolations implied by pore-scale and continuum scale discretizations, overlapping Schwartz domain decomposition is used to ensure continuity of pressure and flux. This approach is demonstrated on a fractured medium, in which Navier-Stokes equations are solved within the fracture while Darcy's equation is solved away from the fracture Coupling reactive transport to pore-scale flow simulators allows hybrid approaches to be extended to solve multi-scale reactive transport.

  2. Benchmark solutions for the galactic ion transport equations: Energy and spatially dependent problems

    NASA Astrophysics Data System (ADS)

    Ganapol, Barry D.; Townsend, Lawrence W.; Wilson, John W.

    1989-03-01

    Nontrivial benchmark solutions are developed for the galactic ion transport (GIT) equations in the straight-ahead approximation. These equations are used to predict potential radiation hazards in the upper atmosphere and in space. Two levels of difficulty are considered: (1) energy independent, and (2) spatially independent. The analysis emphasizes analytical methods never before applied to the GIT equations. Most of the representations derived have been numerically implemented and compared to more approximate calculations. Accurate ion fluxes are obtained (3 to 5 digits) for nontrivial sources. For monoenergetic beams, both accurate doses and fluxes are found. The benchmarks presented are useful in assessing the accuracy of transport algorithms designed to accommodate more complex radiation protection problems. In addition, these solutions can provide fast and accurate assessments of relatively simple shield configurations.

  3. Vectorization of the time-dependent Boltzmann transport equation: Application to deep penetration problems

    NASA Astrophysics Data System (ADS)

    Cobos, Agustín C.; Poma, Ana L.; Alvarez, Guillermo D.; Sanz, Darío E.

    2016-10-01

    We introduce an alternative method to calculate the steady state solution of the angular photon flux after a numerical evolution of the time-dependent Boltzmann transport equation (BTE). After a proper discretization the transport equation was converted into an ordinary system of differential equations that can be iterated as a weighted Richardson algorithm. As a different approach, in this work the time variable regulates the iteration process and convergence criteria is based on physical parameters. Positivity and convergence was assessed from first principles and a modified Courant-Friedrichs-Lewy condition was devised to guarantee convergence. The Penelope Monte Carlo method was used to test the convergence and accuracy of our approach for different phase space discretizations. Benchmarking was performed by calculation of total fluence and photon spectra in different one-dimensional geometries irradiated with 60Co and 6 MV photon beams and radiological applications were devised.

  4. Asymptotic-preserving methods for hyperbolic and transport equations with random inputs and diffusive scalings

    SciTech Connect

    Jin, Shi; Xiu, Dongbin; Zhu, Xueyu

    2015-05-15

    In this paper we develop a set of stochastic numerical schemes for hyperbolic and transport equations with diffusive scalings and subject to random inputs. The schemes are asymptotic preserving (AP), in the sense that they preserve the diffusive limits of the equations in discrete setting, without requiring excessive refinement of the discretization. Our stochastic AP schemes are extensions of the well-developed deterministic AP schemes. To handle the random inputs, we employ generalized polynomial chaos (gPC) expansion and combine it with stochastic Galerkin procedure. We apply the gPC Galerkin scheme to a set of representative hyperbolic and transport equations and establish the AP property in the stochastic setting. We then provide several numerical examples to illustrate the accuracy and effectiveness of the stochastic AP schemes.

  5. Exact PDF equations and closure approximations for advective-reactive transport

    SciTech Connect

    Venturi, D.; Tartakovsky, Daniel M.; Tartakovsky, Alexandre M.; Karniadakis, George E.

    2013-06-01

    Mathematical models of advection–reaction phenomena rely on advective flow velocity and (bio) chemical reaction rates that are notoriously random. By using functional integral methods, we derive exact evolution equations for the probability density function (PDF) of the state variables of the advection–reaction system in the presence of random transport velocity and random reaction rates with rather arbitrary distributions. These PDF equations are solved analytically for transport with deterministic flow velocity and a linear reaction rate represented mathematically by a heterog eneous and strongly-correlated random field. Our analytical solution is then used to investigate the accuracy and robustness of the recently proposed large-eddy diffusivity (LED) closure approximation [1]. We find that the solution to the LED-based PDF equation, which is exact for uncorrelated reaction rates, is accurate even in the presence of strong correlations and it provides an upper bound of predictive uncertainty.

  6. Benchmark solutions for the galactic ion transport equations: Energy and spatially dependent problems

    NASA Technical Reports Server (NTRS)

    Ganapol, Barry D.; Townsend, Lawrence W.; Wilson, John W.

    1989-01-01

    Nontrivial benchmark solutions are developed for the galactic ion transport (GIT) equations in the straight-ahead approximation. These equations are used to predict potential radiation hazards in the upper atmosphere and in space. Two levels of difficulty are considered: (1) energy independent, and (2) spatially independent. The analysis emphasizes analytical methods never before applied to the GIT equations. Most of the representations derived have been numerically implemented and compared to more approximate calculations. Accurate ion fluxes are obtained (3 to 5 digits) for nontrivial sources. For monoenergetic beams, both accurate doses and fluxes are found. The benchmarks presented are useful in assessing the accuracy of transport algorithms designed to accommodate more complex radiation protection problems. In addition, these solutions can provide fast and accurate assessments of relatively simple shield configurations.

  7. An asymptotic-preserving Lagrangian algorithm for the time-dependent anisotropic heat transport equation

    SciTech Connect

    Chacon, Luis; del-Castillo-Negrete, Diego; Hauck, Cory D.

    2014-09-01

    We propose a Lagrangian numerical algorithm for a time-dependent, anisotropic temperature transport equation in magnetized plasmas in the large guide field regime. The approach is based on an analytical integral formal solution of the parallel (i.e., along the magnetic field) transport equation with sources, and it is able to accommodate both local and non-local parallel heat flux closures. The numerical implementation is based on an operator-split formulation, with two straightforward steps: a perpendicular transport step (including sources), and a Lagrangian (field-line integral) parallel transport step. Algorithmically, the first step is amenable to the use of modern iterative methods, while the second step has a fixed cost per degree of freedom (and is therefore scalable). Accuracy-wise, the approach is free from the numerical pollution introduced by the discrete parallel transport term when the perpendicular to parallel transport coefficient ratio X /X becomes arbitrarily small, and is shown to capture the correct limiting solution when ε = X⊥L2/X1L2 → 0 (with L∥∙ L⊥ , the parallel and perpendicular diffusion length scales, respectively). Therefore, the approach is asymptotic-preserving. We demonstrate the capabilities of the scheme with several numerical experiments with varying magnetic field complexity in two dimensions, including the case of transport across a magnetic island.

  8. Deterministic proton transport solving a one dimensional Fokker-Planck equation

    SciTech Connect

    Marr, D.; Prael, R.; Adams, K.; Alcouffe, R.

    1997-10-01

    The transport of protons through matter is characterized by many interactions which cause small deflections and slight energy losses. The few which are catastrophic or cause large angle scattering can be viewed as extinction for many applications. The transport of protons at this level of approximation can be described by a Fokker Planck Equation. This equation is solved using a deterministic multigroup differencing scheme with a highly resolved set of discrete ordinates centered around the beam direction which is adequate to properly account for deflections and energy losses due to multiple Coulomb scattering. Comparisons with LAHET for a large variety of problems ranging from 800 MeV protons on a copper step wedge to 10 GeV protons on a sandwich of material are presented. The good agreement with the Monte Carlo code shows that the solution method is robust and useful for approximate solutions of selected proton transport problems.

  9. Turbulence transport equations for variable-density turbulence and their relationship to two-field models

    SciTech Connect

    Besnard, D. CEA Centre d'Etudes de Limeil, 94 - Villeneuve-Saint-Georges ); Harlow, F.H.; Rauenzahn, R.M.; Zemach, C. )

    1992-06-01

    This study gives an updated account of our current ability to describe multimaterial compressible turbulent flows by means of a one-point transport model. Evolution equations are developed for a number of second-order correlations of turbulent data, and approximations of the gradient type are applied to additional correlations to close the system of equations. The principal fields of interest are the one- point Reynolds tensor for variable-density flow, the turbulent energy dissipation rate, and correlations for density-velocity and density- density fluctuations. This single-field description of turbulent flows is compared in some detail to two-field flow equations for nonturbulent, highly dispersed flow with separate variables for each field. This comparison suggests means for improved modeling of some correlations not subjected to evolution equations.

  10. Examining Tropical Cyclone - Kelvin Wave Interactions using Adjoint Diagnostics

    NASA Astrophysics Data System (ADS)

    Reynolds, C. A.; Doyle, J. D.; Hong, X.

    2015-12-01

    Adjoint-based tools can provide valuable insight into the mechanisms that influence the evolution and predictability of atmospheric phenomena, as they allow for the efficient and rigorous computation of forecast sensitivity to changes in the initial state. We apply adjoint-based tools from the non-hydrostatic Coupled Atmosphere/Ocean Mesoscale Prediction System (COAMPS) to explore the initial-state sensitivity and interactions between a tropical cyclone and atmospheric equatorial waves associated with the Madden Julian Oscillation (MJO) in the Indian Ocean during the DYNAMO field campaign. The development of Tropical Cyclone 5 (TC05) coincided with the passage of an equatorial Kelvin wave and westerly wind burst associated with an MJO that developed in the Indian Ocean in late November 2011, but it was unclear if and how one affected the other. COAMPS 24-h and 36-h adjoint sensitivities are analyzed for both TC05 and the equatorial waves to understand how the evolution of each system is sensitive to the other. The sensitivity of equatorial westerlies in the western Indian Ocean on 23 November shares characteristics with the classic Gill (1980) Rossby and Kelvin wave response to symmetric heating about the equator, including symmetric cyclonic circulations to the north and south of the westerlies, and enhanced heating in the area of convergence between the equatorial westerlies and easterlies. In addition, there is sensitivity in the Bay of Bengal associated with the cyclonic circulation that eventually develops into TC05. At the same time, the developing TC05 system shows strongest sensitivity to local wind and heating perturbations, but sensitivity to the equatorial westerlies is also clear. On 24 November, when the Kelvin wave is immediately south of the developing tropical cyclone, both phenomena are sensitive to each other. On 25 November TC05 no longer shows sensitivity to the Kelvin wave, while the Kelvin Wave still exhibits some weak sensitivity to TC05. In

  11. Multi-term approximation to the Boltzmann transport equation for electron energy distribution functions in nitrogen

    NASA Astrophysics Data System (ADS)

    Feng, Yue

    Plasma is currently a hot topic and it has many significant applications due to its composition of both positively and negatively charged particles. The energy distribution function is important in plasma science since it characterizes the ability of the plasma to affect chemical reactions, affect physical outcomes, and drive various applications. The Boltzmann Transport Equation is an important kinetic equation that provides an accurate basis for characterizing the distribution function---both in energy and space. This dissertation research proposes a multi-term approximation to solve the Boltzmann Transport Equation by treating the relaxation process using an expansion of the electron distribution function in Legendre polynomials. The elastic and 29 inelastic cross sections for electron collisions with nitrogen molecules (N2) and singly ionized nitrogen molecules ( N+2 ) have been used in this application of the Boltzmann Transport Equation. Different numerical methods have been considered to compare the results. The numerical methods discussed in this thesis are the implicit time-independent method, the time-dependent Euler method, the time-dependent Runge-Kutta method, and finally the implicit time-dependent relaxation method by generating the 4-way grid with a matrix solver. The results show that the implicit time-dependent relaxation method is the most accurate and stable method for obtaining reliable results. The results were observed to match with the published experimental data rather well.

  12. Solutions to bi-Maxwellian transport equations for the polar wind

    NASA Technical Reports Server (NTRS)

    Demars, H. G.; Schunk, R. W.

    1989-01-01

    In this study, polar wind solutions are obtained for a broad range of O(+) density, H(+) drift velocity, electron temperature and H(+) temperature boundary conditions. The bi-Maxwellian-based 16-moment set of transport equations is used, since this set is expected to be superior to Maxwellian-based equations in describing large temperature anisotropies and heat flows. The present solutions corroborate earlier results when similar boundary conditions are used. Also, for previously unexplored combinations of boundary conditions, the present solutions are often qualitatively different from any obtained before.

  13. Petrov-galerkin finite element method for solving the neutron transport equation

    SciTech Connect

    Greenbaum, A.; Ferguson, J.M.

    1986-05-01

    A finite element using different trial and test spaces in introduced for solving the neutron transport equation in spherical geometry. It is shown that the widely used discrete ordinates method can also be thought of as such a finite element technique, in which integrals appearing in the difference equations are replaced by one-point Gauss quadrature formulas (midpoint rule). Comparison of accuracy between the new method and the discrete ordinates method is discussed, and numerical examples are given to illustrate the greater accuracy of the new technique.

  14. H-mode transitions and limit cycle oscillations from mean field transport equations

    NASA Astrophysics Data System (ADS)

    Staebler, Gary M.; Groebner, R. J.

    2015-01-01

    The mean field toroidal and parallel momentum transport equations will be shown to admit both one-step transitions to suppressed transport (L/H) and limit cycle oscillations (LCO). Both types of transitions are driven by the suppression of turbulence by the mean field ExB velocity shear. Using experimental data to evaluate the coefficients of a reduced transport model, the observed frequency of the LCO can be matched. The increase in the H-mode power threshold above and below a minimum density agrees with the trends in the model. Both leading and lagging phase relations between the turbulent density fluctuation amplitude and the ExB velocity shear can occur depending on the evolution of the linear growth rate of the turbulence. The transport solutions match the initial phase of the L/H transition where the poloidal and ExB velocities are observed to change, and the density fluctuations drop, faster than the diamagnetic velocity.

  15. Analytical solution of the advection-diffusion transport equation using a change-of-variable and integral transform technique

    Technology Transfer Automated Retrieval System (TEKTRAN)

    This paper presents a formal exact solution of the linear advection-diffusion transport equation with constant coefficients for both transient and steady-state regimes. A classical mathematical substitution transforms the original advection-diffusion equation into an exclusively diffusive equation. ...

  16. The MASH 1.0 code system: Utilization of morse in the adjoint mode

    SciTech Connect

    Johnson, J.O.; Santoro, R.T.

    1993-06-01

    The Monte Carlo Adjoint Shielding Code System -- MASH 1.0, principally developed at Oak Ridge National Laboratory (ORNL), represents an advanced method of calculating neutron and gamma-ray environments and radiation protection factors for complex shielding configurations by coupling a forward discrete ordinates radiation environment (i.e. air-over-ground) transport calculation with an adjoint Monte Carlo treatment of the shielding geometry. The primary application to date has been to determine the radiation shielding characteristics of armored vehicles exposed to prompt radiation from a nuclear weapon detonation. Other potential applications include analyses of the mission equipment associated with space exploration, the civilian airline industry, and other problems associated with an external neutron and gamma-ray radiation environment. This paper will provide an overview of the MASH 1.0 code system, including the verification, validation, and application to {open_quotes}benchmark{close_quotes} experimental data. Attention will be given to the adjoint Monte Carlo calculation, the use of {open_quotes}in-group{close_quotes} biasing to control the weights of the adjoint particles, and the coupling of a new graphics package for the diagnosis of combinatorial geometry descriptions and visualization of radiation transport results.

  17. Electron and ion transport equations in computational weakly-ionized plasmadynamics

    SciTech Connect

    Parent, Bernard; Macheret, Sergey O.; Shneider, Mikhail N.

    2014-02-15

    A new set of ion and electron transport equations is proposed to simulate steady or unsteady quasi-neutral or non-neutral multicomponent weakly-ionized plasmas through the drift–diffusion approximation. The proposed set of equations is advantaged over the conventional one by being considerably less stiff in quasi-neutral regions because it can be integrated in conjunction with a potential equation based on Ohm's law rather than Gauss's law. The present approach is advantaged over previous attempts at recasting the system by being applicable to plasmas with several types of positive ions and negative ions and by not requiring changes to the boundary conditions. Several test cases of plasmas enclosed by dielectrics and of glow discharges between electrodes show that the proposed equations yield the same solution as the standard equations but require 10 to 100 times fewer iterations to reach convergence whenever a quasi-neutral region forms. Further, several grid convergence studies indicate that the present approach exhibits a higher resolution (and hence requires fewer nodes to reach a given level of accuracy) when ambipolar diffusion is present. Because the proposed equations are not intrinsically linked to specific discretization or integration schemes and exhibit substantial advantages with no apparent disadvantage, they are generally recommended as a substitute to the fluid models in which the electric field is obtained from Gauss's law as long as the plasma remains weakly-ionized and unmagnetized.

  18. TRANSPORT EQUATION FOR MHD TURBULENCE: APPLICATION TO PARTICLE ACCELERATION AT INTERPLANETARY SHOCKS

    SciTech Connect

    Sokolov, Igor V.; Gombosi, Tamas I.; Roussev, Ilia I.; Skender, Marina; Usmanov, Arcadi V. E-mail: tamas@umich.edu E-mail: Arcadi.Usmanov.1@gsfc.nasa.gov

    2009-05-01

    The aim of the present paper is to unify the various transport equations for turbulent waves that are used in different areas of space physics. Here, we mostly focus on the magnetohydrodynamic turbulence, in particular the Alfvenic turbulence. The applied methods, however, are general and can be extended to other forms of turbulence, for example the acoustic turbulence, or Langmuir plasma waves. With minor modifications, the derivations followed here can be extended for relativistic motions, thus making it possible to apply them to the wave transport in astrophysical objects with high plasma speeds (radiojets), or strong gravity (black hole surroundings)

  19. Exponentially-convergent Monte Carlo for the 1-D transport equation

    SciTech Connect

    Peterson, J. R.; Morel, J. E.; Ragusa, J. C.

    2013-07-01

    We define a new exponentially-convergent Monte Carlo method for solving the one-speed 1-D slab-geometry transport equation. This method is based upon the use of a linear discontinuous finite-element trial space in space and direction to represent the transport solution. A space-direction h-adaptive algorithm is employed to restore exponential convergence after stagnation occurs due to inadequate trial-space resolution. This methods uses jumps in the solution at cell interfaces as an error indicator. Computational results are presented demonstrating the efficacy of the new approach. (authors)

  20. Green function solution of the Boltzmann transport equation for semiconducting thin film with rough boundaries

    NASA Astrophysics Data System (ADS)

    Ketenoğlu, D.; Ünal, B.

    2012-08-01

    In this study the Green function solution of the Boltzmann transport equation on semiconducting thin film with irregular walls has been applied for the first time. The effects of electron scattering caused by these irregularities on the electrical conductivity have been investigated. First of all by using coordinate transformations, the irregularities on the walls have been transferred into the volume and in this way the both surfaces have been brought into flat forms. By taking two models, Gaussian and exponential, for random potential energy term contained in the transformed Hamiltonian as the perturbation, the resistivity results have been calculated and compared with the ones obtained from the methods widely known in the literature. The Boltzmann transport equation has been solved in relaxation time approximation for the irregular walled system in the case of no magnetic field.

  1. Numerical solution of the time dependent neutron transport equation by the method of the characteristics

    SciTech Connect

    Talamo, Alberto

    2013-05-01

    This study presents three numerical algorithms to solve the time dependent neutron transport equation by the method of the characteristics. The algorithms have been developed taking into account delayed neutrons and they have been implemented into the novel MCART code, which solves the neutron transport equation for two-dimensional geometry and an arbitrary number of energy groups. The MCART code uses regular mesh for the representation of the spatial domain, it models up-scattering, and takes advantage of OPENMP and OPENGL algorithms for parallel computing and plotting, respectively. The code has been benchmarked with the multiplication factor results of a Boiling Water Reactor, with the analytical results for a prompt jump transient in an infinite medium, and with PARTISN and TDTORT results for cross section and source transients. The numerical simulations have shown that only two numerical algorithms are stable for small time steps.

  2. Improved master equation approach to quantum transport: From Born to self-consistent Born approximation

    SciTech Connect

    Jin, Jinshuang; Li, Jun; Liu, Yu; Li, Xin-Qi; Yan, YiJing

    2014-06-28

    Beyond the second-order Born approximation, we propose an improved master equation approach to quantum transport under self-consistent Born approximation. The basic idea is to replace the free Green's function in the tunneling self-energy diagram by an effective reduced propagator under the Born approximation. This simple modification has remarkable consequences. It not only recovers the exact results for quantum transport through noninteracting systems under arbitrary voltages, but also predicts the challenging nonequilibrium Kondo effect. Compared to the nonequilibrium Green's function technique that formulates the calculation of specific correlation functions, the master equation approach contains richer dynamical information to allow more efficient studies for such as the shot noise and full counting statistics.

  3. Wave-front sensing by use of a Green's function solution to the intensity transport equation.

    PubMed

    Woods, Simon C; Greenaway, Alan H

    2003-03-01

    A method for reconstructing an unknown wave front from measurements of its intensity distribution on two planes along the direction of propagation is described. The method solves the intensity transport equation by use of Neumann boundary conditions, leading to a solution that requires only matrix multiplication. The method provides real-time wave-front reconstruction with high accuracy and is easily reposed to permit reconstruction of the wave front in any orthonormal basis set. PMID:12630836

  4. Discontinuous Galerkin finite element method applied to the 1-D spherical neutron transport equation

    SciTech Connect

    Machorro, Eric . E-mail: machorro@amath.washington.edu

    2007-04-10

    Discontinuous Galerkin finite element methods are used to estimate solutions to the non-scattering 1-D spherical neutron transport equation. Various trial and test spaces are compared in the context of a few sample problems whose exact solution is known. Certain trial spaces avoid unphysical behaviors that seem to plague other methods. Comparisons with diamond differencing and simple corner-balancing are presented to highlight these improvements.

  5. Benchmark solutions for the galactic heavy-ion transport equations with energy and spatial coupling

    NASA Technical Reports Server (NTRS)

    Ganapol, Barry D.; Townsend, Lawrence W.; Lamkin, Stanley L.; Wilson, John W.

    1991-01-01

    Nontrivial benchmark solutions are developed for the galactic heavy ion transport equations in the straightahead approximation with energy and spatial coupling. Analytical representations of the ion fluxes are obtained for a variety of sources with the assumption that the nuclear interaction parameters are energy independent. The method utilizes an analytical LaPlace transform inversion to yield a closed form representation that is computationally efficient. The flux profiles are then used to predict ion dose profiles, which are important for shield design studies.

  6. Existence of weak solutions for compressible Navier-Stokes equations with entropy transport

    NASA Astrophysics Data System (ADS)

    Maltese, David; Michálek, Martin; Mucha, Piotr B.; Novotný, Antonin; Pokorný, Milan; Zatorska, Ewelina

    2016-10-01

    We consider the compressible Navier-Stokes system with variable entropy. The pressure is a nonlinear function of the density and the entropy/potential temperature which, unlike in the Navier-Stokes-Fourier system, satisfies only the transport equation. We provide existence results within three alternative weak formulations of the corresponding classical problem. Our constructions hold for the optimal range of the adiabatic coefficients from the point of view of the nowadays existence theory.

  7. Two-dimensional boltzmann transport equation approach to simulation of local ion implantation

    NASA Astrophysics Data System (ADS)

    Komarov, F. F.; Mozolevski, I. E.; Rogach, V. P.

    1995-05-01

    A new theoretical model and software tool is proposed for simulation of two-dimensional local ion implantation in a target of arbitrary geometry. The program uses an algorithm of numerical solution of the boundary value problem for Boltzmann transport equation in two dimensions and permits to calculate the angular and energy distribution function of the particles moving in a multilayered multicomponent target. The program is essentially time saving and can be implemented on an IBM PC AT standard configuration computer.

  8. A stable scheme for computation of coupled transport and equilibrium equations in tokamaks

    NASA Astrophysics Data System (ADS)

    Fable, E.; Angioni, C.; Ivanov, A. A.; Lackner, K.; Maj, O.; Yu, S.; Medvedev; Pautasso, G.; Pereverzev, G. V.

    2013-03-01

    The coupled system consisting of 1D radial transport equations and the quasi-static 2D magnetic equilibrium equation for axisymmetric systems (tokamaks) is known to be prone to numerical instabilities, either due to propagation of numerical errors in the iteration process, or due to the choice of the numerical scheme itself. In this paper, a possible origin of these instabilities, specifically associated with the latter condition, is discussed and an approach is chosen, which is shown to have good accuracy and stability properties. This scheme is proposed to be used within those codes for which the poloidal flux ψ is the quantity solved for in the current diffusion equation. Mathematical arguments are used to study the convergence properties of the proposed scheme.

  9. A level-set adjoint-state method for crosswell transmission-reflection traveltime tomography

    NASA Astrophysics Data System (ADS)

    Li, Wenbin; Leung, Shingyu; Qian, Jianliang

    2014-10-01

    We propose a level-set adjoint-state method for crosswell traveltime tomography using both first-arrival transmission and reflection traveltime data. Since our entire formulation is based on solving eikonal and advection equations on finite-difference meshes, our traveltime tomography strategy is carried out without computing rays explicitly. We incorporate reflection traveltime data into the formulation so that possible reflectors (slowness interfaces) in the targeted subsurface model can be recovered as well as the slowness distribution itself. Since a reflector may assume a variety of irregular geometries, we propose to use a level-set function to implicitly parametrize the shape of a reflector. Therefore, a mismatch functional is established to minimize the traveltime data misfit with respect to both the slowness distribution and the level-set function, and the minimization is achieved by using a gradient descent method with gradients computed by solving adjoint state equations. To assess uncertainty or reliability of reconstructed slowness models, we introduce a labelling function to characterize first-arrival ray coverage of the computational domain, and this labelling function satisfies an advection equation. We apply fast-sweeping type methods to solve eikonal, adjoint-state and advection equations arising in our formulation. Numerical examples demonstrate that the proposed algorithm is robust to noise in the measurements, and can recover complicated structure even with little information on the reflector.

  10. Adjoint sensitivity studies of loop current and eddy shedding in the Gulf of Mexico

    NASA Astrophysics Data System (ADS)

    Gopalakrishnan, Ganesh; Cornuelle, Bruce D.; Hoteit, Ibrahim

    2013-07-01

    Adjoint model sensitivity analyses were applied for the loop current (LC) and its eddy shedding in the Gulf of Mexico (GoM) using the MIT general circulation model (MITgcm). The circulation in the GoM is mainly driven by the energetic LC and subsequent LC eddy separation. In order to understand which ocean regions and features control the evolution of the LC, including anticyclonic warm-core eddy shedding in the GoM, forward and adjoint sensitivities with respect to previous model state and atmospheric forcing were computed using the MITgcm and its adjoint. Since the validity of the adjoint model sensitivities depends on the capability of the forward model to simulate the real LC system and the eddy shedding processes, a 5 year (2004-2008) forward model simulation was performed for the GoM using realistic atmospheric forcing, initial, and boundary conditions. This forward model simulation was compared to satellite measurements of sea-surface height (SSH) and sea-surface temperature (SST), and observed transport variability. Despite realistic mean state, standard deviations, and LC eddy shedding period, the simulated LC extension shows less variability and more regularity than the observations. However, the model is suitable for studying the LC system and can be utilized for examining the ocean influences leading to a simple, and hopefully generic LC eddy separation in the GoM. The adjoint sensitivities of the LC show influences from the Yucatan Channel (YC) flow and Loop Current Frontal Eddy (LCFE) on both LC extension and eddy separation, as suggested by earlier work. Some of the processes that control LC extension after eddy separation differ from those controlling eddy shedding, but include YC through-flow. The sensitivity remains stable for more than 30 days and moves generally upstream, entering the Caribbean Sea. The sensitivities of the LC for SST generally remain closer to the surface and move at speeds consistent with advection by the high-speed core of

  11. From analytical solutions of solute transport equations to multidimensional time-domain random walk (TDRW) algorithms

    NASA Astrophysics Data System (ADS)

    Bodin, Jacques

    2015-03-01

    In this study, new multi-dimensional time-domain random walk (TDRW) algorithms are derived from approximate one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) analytical solutions of the advection-dispersion equation and from exact 1-D, 2-D, and 3-D analytical solutions of the pure-diffusion equation. These algorithms enable the calculation of both the time required for a particle to travel a specified distance in a homogeneous medium and the mass recovery at the observation point, which may be incomplete due to 2-D or 3-D transverse dispersion or diffusion. The method is extended to heterogeneous media, represented as a piecewise collection of homogeneous media. The particle motion is then decomposed along a series of intermediate checkpoints located on the medium interface boundaries. The accuracy of the multi-dimensional TDRW method is verified against (i) exact analytical solutions of solute transport in homogeneous media and (ii) finite-difference simulations in a synthetic 2-D heterogeneous medium of simple geometry. The results demonstrate that the method is ideally suited to purely diffusive transport and to advection-dispersion transport problems dominated by advection. Conversely, the method is not recommended for highly dispersive transport problems because the accuracy of the advection-dispersion TDRW algorithms degrades rapidly for a low Péclet number, consistent with the accuracy limit of the approximate analytical solutions. The proposed approach provides a unified methodology for deriving multi-dimensional time-domain particle equations and may be applicable to other mathematical transport models, provided that appropriate analytical solutions are available.

  12. Using adjoint-based optimization to study wing flexibility in flapping flight

    NASA Astrophysics Data System (ADS)

    Wei, Mingjun; Xu, Min; Dong, Haibo

    2014-11-01

    In the study of flapping-wing flight of birds and insects, it is important to understand the impact of wing flexibility/deformation on aerodynamic performance. However, the large control space from the complexity of wing deformation and kinematics makes usual parametric study very difficult or sometimes impossible. Since the adjoint-based approach for sensitivity study and optimization strategy is a process with its cost independent of the number of input parameters, it becomes an attractive approach in our study. Traditionally, adjoint equation and sensitivity are derived in a fluid domain with fixed solid boundaries. Moving boundary is only allowed when its motion is not part of control effort. Otherwise, the derivation becomes either problematic or too complex to be feasible. Using non-cylindrical calculus to deal with boundary deformation solves this problem in a very simple and still mathematically rigorous manner. Thus, it allows to apply adjoint-based optimization in the study of flapping wing flexibility. We applied the ``improved'' adjoint-based method to study the flexibility of both two-dimensional and three-dimensional flapping wings, where the flapping trajectory and deformation are described by either model functions or real data from the flight of dragonflies. Supported by AFOSR.

  13. GRASP (GRound-Water Adjunct Sensitivity Program): A computer code to perform post-SWENT (simulator for water, energy, and nuclide transport) adjoint sensitivity analysis of steady-state ground-water flow: Technical report

    SciTech Connect

    Wilson, J.L.; RamaRao, B.S.; McNeish, J.A.

    1986-11-01

    GRASP (GRound-Water Adjunct Senstivity Program) computes measures of the behavior of a ground-water system and the system's performance for waste isolation, and estimates the sensitivities of these measures to system parameters. The computed measures are referred to as ''performance measures'' and include weighted squared deviations of computed and observed pressures or heads, local Darcy velocity components and magnitudes, boundary fluxes, and travel distance and time along travel paths. The sensitivities are computed by the adjoint method and are exact derivatives of the performance measures with respect to the parameters for the modeled system, taken about the assumed parameter values. GRASP presumes steady-state, saturated grondwater flow, and post-processes the results of a multidimensional (1-D, 2-D, 3-D) finite-difference flow code. This document describes the mathematical basis for the model, the algorithms and solution techniques used, and the computer code design. The implementation of GRASP is verified with simple one- and two-dimensional flow problems, for which analytical expressions of performance measures and sensitivities are derived. The linkage between GRASP and multidimensional finite-difference flow codes is described. This document also contains a detailed user's manual. The use of GRASP to evaluate nuclear waste disposal issues has been emphasized throughout the report. The performance measures and their sensitivities can be employed to assist in directing data collection programs, expedite model calibration, and objectively determine the sensitivity of projected system performance to parameters.

  14. Aerodynamic Shape Optimization of Supersonic Aircraft Configurations via an Adjoint Formulation on Parallel Computers

    NASA Technical Reports Server (NTRS)

    Reuther, James; Alonso, Juan Jose; Rimlinger, Mark J.; Jameson, Antony

    1996-01-01

    This work describes the application of a control theory-based aerodynamic shape optimization method to the problem of supersonic aircraft design. The design process is greatly accelerated through the use of both control theory and a parallel implementation on distributed memory computers. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is then implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) Standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on higher order computational fluid dynamics methods (CFD). In our earlier studies, the serial implementation of this design method was shown to be effective for the optimization of airfoils, wings, wing-bodies, and complex aircraft configurations using both the potential equation and the Euler equations. In our most recent paper, the Euler method was extended to treat complete aircraft configurations via a new multiblock implementation. Furthermore, during the same conference, we also presented preliminary results demonstrating that this basic methodology could be ported to distributed memory parallel computing architectures. In this paper, our concern will be to demonstrate that the combined power of these new technologies can be used routinely in an industrial design environment by applying it to the case study of the design of typical supersonic transport configurations. A particular difficulty of this test case is posed by the propulsion/airframe integration.

  15. Aerodynamic Shape Optimization of Supersonic Aircraft Configurations via an Adjoint Formulation on Parallel Computers

    NASA Technical Reports Server (NTRS)

    Reuther, James; Alonso, Juan Jose; Rimlinger, Mark J.; Jameson, Antony

    1996-01-01

    This work describes the application of a control theory-based aerodynamic shape optimization method to the problem of supersonic aircraft design. The design process is greatly accelerated through the use of both control theory and a parallel implementation on distributed memory computers. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods (13, 12, 44, 38). The resulting problem is then implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) Standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on higher order computational fluid dynamics methods (CFD). In our earlier studies, the serial implementation of this design method (19, 20, 21, 23, 39, 25, 40, 41, 42, 43, 9) was shown to be effective for the optimization of airfoils, wings, wing-bodies, and complex aircraft configurations using both the potential equation and the Euler equations (39, 25). In our most recent paper, the Euler method was extended to treat complete aircraft configurations via a new multiblock implementation. Furthermore, during the same conference, we also presented preliminary results demonstrating that the basic methodology could be ported to distributed memory parallel computing architectures [241. In this paper, our concem will be to demonstrate that the combined power of these new technologies can be used routinely in an industrial design environment by applying it to the case study of the design of typical supersonic transport configurations. A particular difficulty of this test case is posed by the propulsion/airframe integration.

  16. A transport equation for the scalar dissipation in reacting flows with variable density: First results

    NASA Technical Reports Server (NTRS)

    Mantel, T.

    1993-01-01

    Although the different regimes of premixed combustion are not well defined, most of the recent developments in turbulent combustion modeling are led in the so-called flamelet regime. The goal of these models is to give a realistic expression to the mean reaction rate (w). Several methods can be used to estimate (w). Bray and coworkers (Libby & Bray 1980, Bray 1985, Bray & Libby 1986) express the instantaneous reaction rate by means of a flamelet library and a frequency which describes the local interaction between the laminar flamelets and the turbulent flowfield. In another way, the mean reaction rate can be directly connected to the flame surface density (Sigma). This quantity can be given by the transport equation of the coherent flame model initially proposed by Marble & Broadwell 1977 and developed elsewhere. The mean reaction rate, (w), can also be estimated thanks to the evolution of an arbitrary scalar field G(x, t) = G(sub O) which represents the flame sheet. G(x, t) is obtained from the G-equation proposed by Williams 1985, Kerstein et al. 1988 and Peters 1993. Another possibility proposed in a recent study by Mantel & Borghi 1991, where a transport equation for the mean dissipation rate (epsilon(sub c)) of the progress variable c is used to determine (w). In their model, Mantel & Borghi 1991 considered a medium with constant density and constant diffusivity in the determination of the transport equation for (epsilon(sub c)). A comparison of different flamelet models made by Duclos et al. 1993 shows the realistic behavior of this model even in the case of constant density. Our objective in this present report is to present preliminary results on the study of this equation in the case of variable density and variable diffusivity. Assumptions of constant pressure and a Lewis number equal to unity allow us to significantly simplify the equation. A systematic order of magnitude analysis based on adequate scale relations is performed on each term of the

  17. Analytical Solutions of a Fractional Diffusion-advection Equation for Solar Cosmic-Ray Transport

    NASA Astrophysics Data System (ADS)

    Litvinenko, Yuri E.; Effenberger, Frederic

    2014-12-01

    Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we analytically solve a one-dimensional fractional diffusion-advection equation for the particle density. We derive an exact Fourier transform solution, simplify it in a weak diffusion approximation, and compare the new solution with previously available analytical results and with a semi-numerical solution based on a Fourier series expansion. We apply the results to the problem of describing the transport of energetic particles, accelerated at a traveling heliospheric shock. Our analysis shows that significant errors may result from assuming an infinite initial distance between the shock and the observer. We argue that the shock travel time should be a parameter of a realistic superdiffusive transport model.

  18. Analytical solutions of a fractional diffusion-advection equation for solar cosmic-ray transport

    SciTech Connect

    Litvinenko, Yuri E.; Effenberger, Frederic

    2014-12-01

    Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we analytically solve a one-dimensional fractional diffusion-advection equation for the particle density. We derive an exact Fourier transform solution, simplify it in a weak diffusion approximation, and compare the new solution with previously available analytical results and with a semi-numerical solution based on a Fourier series expansion. We apply the results to the problem of describing the transport of energetic particles, accelerated at a traveling heliospheric shock. Our analysis shows that significant errors may result from assuming an infinite initial distance between the shock and the observer. We argue that the shock travel time should be a parameter of a realistic superdiffusive transport model.

  19. The derivation and moments solution of approximate transport equations for the implantation of ions into amorphous targets

    NASA Astrophysics Data System (ADS)

    Ashworth, D. G.; Bowyer, M. D. J.; Oven, R.

    1995-06-01

    Commencing with the LSS integro-differential equation, an approximate transport equation is derived from which the moments of the range distribution may be obtained. The resulting equation set is known as the Kent Range ALgorithm (KRAL). The method for numerical solution of these equations, when written as a set of coupled second order ordinary differential equations (ODEs) of the initial value type, is then outlined. Solution is achieved by recasting the equation set in the form of first order ODEs designed for iterative solution. The technique used is an iterative refinement (or residual correction) procedure and the set of first order ODEs is called the Kent Optimised Range ALgorithm (KORAL). Finally, the first three moments from KORAL, first and second order PRAL codes and the full transport equation code KUBBIC-91 are compared with Monte Carlo data obtained from a TRIM code modified to treat targets of infinite extent. Comparisons are performed using consistent nuclear and electronic energy loss models.

  20. Coupling of Monte Carlo adjoint leakages with three-dimensional discrete ordinates forward fluences

    SciTech Connect

    Slater, C.O.; Lillie, R.A.; Johnson, J.O.; Simpson, D.B.

    1998-04-01

    A computer code, DRC3, has been developed for coupling Monte Carlo adjoint leakages with three-dimensional discrete ordinates forward fluences in order to solve a special category of geometrically-complex deep penetration shielding problems. The code extends the capabilities of earlier methods that coupled Monte Carlo adjoint leakages with two-dimensional discrete ordinates forward fluences. The problems involve the calculation of fluences and responses in a perturbation to an otherwise simple two- or three-dimensional radiation field. In general, the perturbation complicates the geometry such that it cannot be modeled exactly using any of the discrete ordinates geometry options and thus a direct discrete ordinates solution is not possible. Also, the calculation of radiation transport from the source to the perturbation involves deep penetration. One approach to solving such problems is to perform the calculations in three steps: (1) a forward discrete ordinates calculation, (2) a localized adjoint Monte Carlo calculation, and (3) a coupling of forward fluences from the first calculation with adjoint leakages from the second calculation to obtain the response of interest (fluence, dose, etc.). A description of this approach is presented along with results from test problems used to verify the method. The test problems that were selected could also be solved directly by the discrete ordinates method. The good agreement between the DRC3 results and the direct-solution results verify the correctness of DRC3.

  1. 3D unstructured-mesh radiation transport codes

    SciTech Connect

    Morel, J.

    1997-12-31

    Three unstructured-mesh radiation transport codes are currently being developed at Los Alamos National Laboratory. The first code is ATTILA, which uses an unstructured tetrahedral mesh in conjunction with standard Sn (discrete-ordinates) angular discretization, standard multigroup energy discretization, and linear-discontinuous spatial differencing. ATTILA solves the standard first-order form of the transport equation using source iteration in conjunction with diffusion-synthetic acceleration of the within-group source iterations. DANTE is designed to run primarily on workstations. The second code is DANTE, which uses a hybrid finite-element mesh consisting of arbitrary combinations of hexahedra, wedges, pyramids, and tetrahedra. DANTE solves several second-order self-adjoint forms of the transport equation including the even-parity equation, the odd-parity equation, and a new equation called the self-adjoint angular flux equation. DANTE also offers three angular discretization options: $S{_}n$ (discrete-ordinates), $P{_}n$ (spherical harmonics), and $SP{_}n$ (simplified spherical harmonics). DANTE is designed to run primarily on massively parallel message-passing machines, such as the ASCI-Blue machines at LANL and LLNL. The third code is PERICLES, which uses the same hybrid finite-element mesh as DANTE, but solves the standard first-order form of the transport equation rather than a second-order self-adjoint form. DANTE uses a standard $S{_}n$ discretization in angle in conjunction with trilinear-discontinuous spatial differencing, and diffusion-synthetic acceleration of the within-group source iterations. PERICLES was initially designed to run on workstations, but a version for massively parallel message-passing machines will be built. The three codes will be described in detail and computational results will be presented.

  2. Towards efficient backward-in-time adjoint computations using data compression techniques

    SciTech Connect

    Cyr, E. C.; Shadid, J. N.; Wildey, T.

    2014-12-16

    In the context of a posteriori error estimation for nonlinear time-dependent partial differential equations, the state-of-the-practice is to use adjoint approaches which require the solution of a backward-in-time problem defined by a linearization of the forward problem. One of the major obstacles in the practical application of these approaches, we found, is the need to store, or recompute, the forward solution to define the adjoint problem and to evaluate the error representation. Our study considers the use of data compression techniques to approximate forward solutions employed in the backward-in-time integration. The development derives an error representation that accounts for the difference between the standard-approach and the compressed approximation of the forward solution. This representation is algorithmically similar to the standard representation and only requires the computation of the quantity of interest for the forward solution and the data-compressed reconstructed solution (i.e. scalar quantities that can be evaluated as the forward problem is integrated). This approach is then compared with existing techniques, such as checkpointing and time-averaged adjoints. Lastly, we provide numerical results indicating the potential efficiency of our approach on a transient diffusion–reaction equation and on the Navier–Stokes equations. These results demonstrate memory compression ratios up to 450×450× while maintaining reasonable accuracy in the error-estimates.

  3. Towards efficient backward-in-time adjoint computations using data compression techniques

    DOE PAGES

    Cyr, E. C.; Shadid, J. N.; Wildey, T.

    2014-12-16

    In the context of a posteriori error estimation for nonlinear time-dependent partial differential equations, the state-of-the-practice is to use adjoint approaches which require the solution of a backward-in-time problem defined by a linearization of the forward problem. One of the major obstacles in the practical application of these approaches, we found, is the need to store, or recompute, the forward solution to define the adjoint problem and to evaluate the error representation. Our study considers the use of data compression techniques to approximate forward solutions employed in the backward-in-time integration. The development derives an error representation that accounts for themore » difference between the standard-approach and the compressed approximation of the forward solution. This representation is algorithmically similar to the standard representation and only requires the computation of the quantity of interest for the forward solution and the data-compressed reconstructed solution (i.e. scalar quantities that can be evaluated as the forward problem is integrated). This approach is then compared with existing techniques, such as checkpointing and time-averaged adjoints. Lastly, we provide numerical results indicating the potential efficiency of our approach on a transient diffusion–reaction equation and on the Navier–Stokes equations. These results demonstrate memory compression ratios up to 450×450× while maintaining reasonable accuracy in the error-estimates.« less

  4. Effects of microscopic transport coefficients on fission observables calculated by the Langevin equation

    NASA Astrophysics Data System (ADS)

    Usang, M. D.; Ivanyuk, F. A.; Ishizuka, C.; Chiba, S.

    2016-10-01

    Nuclear fission is treated by using the Langevin dynamical description with macroscopic and microscopic transport coefficients (mass and friction tensors), and it is elucidated how the microscopic (shell and pairing) effects in the transport coefficients, especially their dependence on temperature, affects various fission observables. We found that the microscopic transport coefficients, calculated by linear response theory, change drastically as a function of temperature: in general, the friction increases with growing temperature while the mass tensor decreases. This temperature dependence brings a noticeable change in the mass distribution and kinetic energies of fission fragments from nuclei around 236U at an excitation energy of 20 MeV. The prescission kinetic energy decreases from 25 MeV at low temperature to about 2.5 MeV at high temperature. In contrast, the Coulomb kinetic energy increases as the temperature increases. Interpolating the microscopic transport coefficients among the various temperatures enabled our Langevin equation to use the microscopic transport coefficients at a deformation-dependent local temperature of the dynamical evolution. This allowed us to compare directly the fission observables of both macroscopic and microscopic calculations, and we found almost identical results under the conditions considered in this work.

  5. Temperature-dependent thermal conductivity in silicon nanostructured materials studied by the Boltzmann transport equation

    NASA Astrophysics Data System (ADS)

    Romano, Giuseppe; Esfarjani, Keivan; Strubbe, David A.; Broido, David; Kolpak, Alexie M.

    2016-01-01

    Nanostructured materials exhibit low thermal conductivity because of the additional scattering due to phonon-boundary interactions. As these interactions are highly sensitive to the mean free path (MFP) of phonons, MFP distributions in nanostructures can be dramatically distorted relative to bulk. Here we calculate the MFP distribution in periodic nanoporous Si for different temperatures, using the recently developed MFP-dependent Boltzmann transport equation. After analyzing the relative contribution of each phonon branch to thermal transport in nanoporous Si, we find that at room temperature optical phonons contribute 17 % to heat transport, compared to 5 % in bulk Si. Interestingly, we observe a constant thermal conductivity over the range 200 K transport of acoustic phonons with long intrinsic MFP and the temperature dependence of the heat capacity. Our findings, which are in qualitative agreement with the temperature trend of thermal conductivities measured in nanoporous Si-based systems, shed light on the origin of the reduction of thermal conductivity in nanostructured materials and demonstrate the necessity of multiscale heat transport engineering, in which the bulk material and geometry are optimized concurrently.

  6. Analytical solution of equations describing slow axonal transport based on the stop-and-go hypothesis

    NASA Astrophysics Data System (ADS)

    Kuznetsov, Andrey

    2011-06-01

    This paper presents an analytical solution for slow axonal transport in an axon. The governing equations for slow axonal transport are based on the stop-and-go hypothesis which assumes that organelles alternate between short periods of rapid movement on microtubules (MTs), short on-track pauses, and prolonged off-track pauses, when they temporarily disengage from MTs. The model includes six kinetic states for organelles: two for off-track organelles (anterograde and retrograde), two for running organelles, and two for pausing organelles. An analytical solution is obtained for a steady-state situation. To obtain the analytical solution, the governing equations are uncoupled by using a perturbation method. The solution is validated by comparing it with a high-accuracy numerical solution. Results are presented for neurofilaments (NFs), which are characterized by small diffusivity, and for tubulin oligomers, which are characterized by large diffusivity. The difference in transport modes between these two types of organelles in a short axon is discussed. A comparison between zero-order and first-order approximations makes it possible to obtain a physical insight into the effects of organelle reversals (when organelles change the type of a molecular motor they are attached to, an anterograde versus retrograde motor).

  7. Two-dimensional phase unwrapping using the transport of intensity equation.

    PubMed

    Pandey, Neeraj; Ghosh, Amitava; Khare, Kedar

    2016-03-20

    We report a method for two-dimensional phase unwrapping based on the transport of intensity equation (TIE). Given a wrapped phase profile, we generate an auxiliary complex field and propagate it to small distances to simulate two intensity images on closely spaced planes. Using the longitudinal intensity derivative of the auxiliary field as an input, the TIE is solved by employing the regularized Fourier-transform-based approach. The resultant phase profile is automatically in the unwrapped form, as it has been obtained as a solution of a partial differential equation rather than as an argument of a complex-valued function. Our simulations and experimental results suggest that this approach is fast and accurate and provides a simple and practical solution for routine phase unwrapping tasks in interferometry and digital holography. PMID:27140583

  8. A coupling model of the radiative transport equation for calculating photon migration in biological tissue

    NASA Astrophysics Data System (ADS)

    Fujii, Hiroyuki; Okawa, Shinpei; Yamada, Yukio; Hoshi, Yoko; Watanabe, Masao

    2015-12-01

    Development of a physically accurate and computationally efficient photon migration model for turbid media is crucial for optical computed tomography such as diffuse optical tomography. For the development, this paper constructs a space-time coupling model of the radiative transport equation with the photon diffusion equation. In the coupling model, a space-time regime of the photon migration is divided into the ballistic and diffusive regimes with the interaction between the both regimes to improve the accuracy of the results and the efficiency of computation. The coupling model provides an accurate description of the photon migration in various turbid media in a wide range of the optical properties, and reduces computational loads when compared with those of full calculation of the RTE.

  9. Modeling Heat Conduction and Radiation Transport with the Diffusion Equation in NIF ALE-AMR

    SciTech Connect

    Fisher, A C; Bailey, D S; Kaiser, T B; Gunney, B N; Masters, N D; Koniges, A E; Eder, D C; Anderson, R W

    2009-10-06

    The ALE-AMR code developed for NIF is a multi-material hydro-code that models target assembly fragmentation in the aftermath of a shot. The combination of ALE (Arbitrary Lagrangian Eulerian) hydro with AMR (Adaptive Mesh Refinement) allows the code to model a wide range of physical conditions and spatial scales. The large range of temperatures encountered in the NIF target chamber can lead to significant fluxes of energy due to thermal conduction and radiative transport. These physical effects can be modeled approximately with the aid of the diffusion equation. We present a novel method for the solution of the diffusion equation on a composite mesh in order to capture these physical effects.

  10. The use of Galerkin finite-element methods to solve mass-transport equations

    USGS Publications Warehouse

    Grove, David B.

    1977-01-01

    The partial differential equation that describes the transport and reaction of chemical solutes in porous media was solved using the Galerkin finite-element technique. These finite elements were superimposed over finite-difference cells used to solve the flow equation. Both convection and flow due to hydraulic dispersion were considered. Linear and Hermite cubic approximations (basis functions) provided satisfactory results: however, the linear functions were computationally more efficient for two-dimensional problems. Successive over relaxation (SOR) and iteration techniques using Tchebyschef polynomials were used to solve the sparce matrices generated using the linear and Hermite cubic functions, respectively. Comparisons of the finite-element methods to the finite-difference methods, and to analytical results, indicated that a high degree of accuracy may be obtained using the method outlined. The technique was applied to a field problem involving an aquifer contaminated with chloride, tritium, and strontium-90. (Woodard-USGS)

  11. Generalized uncertainty principle and self-adjoint operators

    SciTech Connect

    Balasubramanian, Venkat; Das, Saurya; Vagenas, Elias C.

    2015-09-15

    In this work we explore the self-adjointness of the GUP-modified momentum and Hamiltonian operators over different domains. In particular, we utilize the theorem by von-Neumann for symmetric operators in order to determine whether the momentum and Hamiltonian operators are self-adjoint or not, or they have self-adjoint extensions over the given domain. In addition, a simple example of the Hamiltonian operator describing a particle in a box is given. The solutions of the boundary conditions that describe the self-adjoint extensions of the specific Hamiltonian operator are obtained.

  12. Stochastic interpretation of the advection-diffusion equation and its relevance to bed load transport

    NASA Astrophysics Data System (ADS)

    Ancey, C.; Bohorquez, P.; Heyman, J.

    2015-12-01

    The advection-diffusion equation is one of the most widespread equations in physics. It arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Phenomenological laws are usually sufficient to derive this equation and interpret its terms. Stochastic models can also be used to derive it, with the significant advantage that they provide information on the statistical properties of particle activity. These models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. Among these stochastic models, the most common approach consists of random walk models. For instance, they have been used to model the random displacement of tracers in rivers. Here we explore an alternative approach, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. Birth-death Markov processes are well suited to this objective. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received no attention. We therefore look into the possibility of deriving the advection-diffusion equation (with a source term) within the framework of birth-death Markov processes. We show that in the continuum limit (when the cell size becomes vanishingly small), we can derive an advection-diffusion equation for particle activity. Yet while this derivation is formally valid in the continuum limit, it runs into difficulty in practical applications involving cells or meshes of finite length. Indeed, within our stochastic framework, particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particle velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due

  13. Really TVD advection schemes for the depth-integrated transport equation

    NASA Astrophysics Data System (ADS)

    Mercier, Ch.; Delhez, E. J. M.

    This paper explores the use of TVD advection schemes to solve the depth-integrated transport equation for tracers in finite volume marine models. Numerical experiments show that the blind application of the usual TVD schemes and associated flux limiters can lead to non-TVD solutions when applied in complex geometries. Spatial and/or temporal variations of the local bathymetry can indeed break the TVD property of the usual schemes. Really TVD schemes can be recovered by taking into account the local depth and its variations in the formulation of the flux limiters. Using this approach, a generalized superbee limiter is introduced and validated.

  14. Gluon transport equation with effective mass and dynamical onset of Bose–Einstein condensation

    DOE PAGES

    Blaizot, Jean-Paul; Jiang, Yin; Liao, Jinfeng

    2016-05-01

    In this paper we study the transport equation describing a dense system of gluons, in the small scattering angle approximation, taking into account medium-generated effective masses of the gluons. We focus on the case of overpopulated systems that are driven to Bose–Einstein condensation on their way to thermalization. Lastly, the presence of a mass modifies the dispersion relation of the gluon, as compared to the massless case, but it is shown that this does not change qualitatively the scaling behavior in the vicinity of the onset.

  15. Phase retrieval by using the transport-of-intensity equation with Hilbert transform.

    PubMed

    Li, Wei-Shuo; Chen, Chun-Wei; Lin, Kuo-Feng; Chen, Hou-Ren; Tsai, Chih-Ya; Chen, Chyong-Hua; Hsieh, Wen-Feng

    2016-04-01

    Phase recovery by solving the transport-of-intensity equation (TIE) is a non-iterative and non-interferometric phase retrieval technique. From solving the TIE with conventional, one partial derivative and Hilbert transform methods for both the periodic and aperiodic samples, we demonstrate that the Hilbert transform method can provide the smoother phase images with edge enhancement and fine structures. Furthermore, compared with the images measured by optical and atomic force microscopy, the Hilbert transform method has the ability to quantitatively map out the phase images for both the periodic and aperiodic structures. PMID:27192301

  16. Unified description of equation of state and transport properties of nuclear matter

    SciTech Connect

    Benhar, Omar; Farina, Nicola; Valli, Marco; Fiorilla, Salvatore

    2008-10-13

    Correlated basis function perturbation theory and the formalism of cluster expansions have been recently employed to obtain an effective interaction from a state-of-the-art nucleon nucleon potential model. The approach based on the effective interaction allows for a consistent description of the nuclear matter ground state and nucleon-nucleon scattering in the nuclear medium. This paper reports the the results of numerical calculations of different properties of nuclear and neutron matter, including the equation of state and the shear viscosity and thermal conductivity transport coefficients, carried out using the effective interaction.

  17. Transport equations of energy for ferromagnetic insulators in contact with electrodes.

    PubMed

    Wegrowe, J-E

    2013-09-11

    A phenomenological derivation of the transport equations for ferromagnetic moments and associated energy and heat is proposed. The model describes the transfer of energy through an interface composed of a ferromagnetic insulator in contact with normal electrodes. A reduction method applied to the ferromagnetic degrees of freedom allows a two-channel model to be defined for the transport of magnetic moments. It is shown that a heat current flowing into the insulating ferromagnet-produced e.g. by electromagnetic resonance, thermal gradient, magneto-mechanical or magneto-optical excitations-can generate a magneto-voltaic potential and a pure spin-current in the non-ferromagnetic electrode. PMID:23941895

  18. Theoretical analysis of integral neutron transport equation using collision probability method with quadratic flux approach

    SciTech Connect

    Shafii, Mohammad Ali Meidianti, Rahma Wildian, Fitriyani, Dian; Tongkukut, Seni H. J.; Arkundato, Artoto

    2014-09-30

    Theoretical analysis of integral neutron transport equation using collision probability (CP) method with quadratic flux approach has been carried out. In general, the solution of the neutron transport using the CP method is performed with the flat flux approach. In this research, the CP method is implemented in the cylindrical nuclear fuel cell with the spatial of mesh being conducted into non flat flux approach. It means that the neutron flux at any point in the nuclear fuel cell are considered different each other followed the distribution pattern of quadratic flux. The result is presented here in the form of quadratic flux that is better understanding of the real condition in the cell calculation and as a starting point to be applied in computational calculation.

  19. A Piecewise Bi-Linear Discontinuous Finite Element Spatial Discretization of the Sn Transport Equation

    SciTech Connect

    Bailey, T S; Chang, J H; Warsa, J S; Adams, M L

    2010-12-22

    We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.

  20. Representative equations for the thermodynamic and transport properties of fluids near the gas-liquid critical point

    NASA Technical Reports Server (NTRS)

    Sengers, J. V.; Basu, R. S.; Sengers, J. M. H. L.

    1981-01-01

    A survey is presented of representative equations for various thermophysical properties of fluids in the critical region. Representative equations for the transport properties are included. Semi-empirical modifications of the theoretically predicted asymtotic critical behavior that yield simple and practical representations of the fluid properties in the critical region are emphasized.

  1. A numerical spectral approach to solve the dislocation density transport equation

    NASA Astrophysics Data System (ADS)

    Djaka, K. S.; Taupin, V.; Berbenni, S.; Fressengeas, C.

    2015-09-01

    A numerical spectral approach is developed to solve in a fast, stable and accurate fashion, the quasi-linear hyperbolic transport equation governing the spatio-temporal evolution of the dislocation density tensor in the mechanics of dislocation fields. The approach relies on using the Fast Fourier Transform algorithm. Low-pass spectral filters are employed to control both the high frequency Gibbs oscillations inherent to the Fourier method and the fast-growing numerical instabilities resulting from the hyperbolic nature of the transport equation. The numerical scheme is validated by comparison with an exact solution in the 1D case corresponding to dislocation dipole annihilation. The expansion and annihilation of dislocation loops in 2D and 3D settings are also produced and compared with finite element approximations. The spectral solutions are shown to be stable, more accurate for low Courant numbers and much less computation time-consuming than the finite element technique based on an explicit Galerkin-least squares scheme.

  2. Application of the multigrid amplitude function method for time-dependent transport equation using MOC

    SciTech Connect

    Tsujita, K.; Endo, T.; Yamamoto, A.

    2013-07-01

    An efficient numerical method for time-dependent transport equation, the mutigrid amplitude function (MAF) method, is proposed. The method of characteristics (MOC) is being widely used for reactor analysis thanks to the advances of numerical algorithms and computer hardware. However, efficient kinetic calculation method for MOC is still desirable since it requires significant computation time. Various efficient numerical methods for solving the space-dependent kinetic equation, e.g., the improved quasi-static (IQS) and the frequency transform methods, have been developed so far mainly for diffusion calculation. These calculation methods are known as effective numerical methods and they offer a way for faster computation. However, they have not been applied to the kinetic calculation method using MOC as the authors' knowledge. Thus, the MAF method is applied to the kinetic calculation using MOC aiming to reduce computation time. The MAF method is a unified numerical framework of conventional kinetic calculation methods, e.g., the IQS, the frequency transform, and the theta methods. Although the MAF method is originally developed for the space-dependent kinetic calculation based on the diffusion theory, it is extended to transport theory in the present study. The accuracy and computational time are evaluated though the TWIGL benchmark problem. The calculation results show the effectiveness of the MAF method. (authors)

  3. Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: Application to the theory of Neolithic transition

    NASA Astrophysics Data System (ADS)

    Vlad, Marcel Ovidiu; Ross, John

    2002-12-01

    We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are described by a set of transformation rates, which are nonlinear functions of the local concentrations of the different types of individuals. We use the time interval between two jumps (the transition time) as an additional state variable and obtain a set of evolution equations, which are local in time. In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations of the so-called generalized master equations. The method leads under different specified conditions to various types of nonlocal transport equations including a nonlinear generalization of fractional diffusion equations, hyperbolic reaction-diffusion equations, and delay-differential reaction-diffusion equations. Thus in the analysis of a given problem we can fit to the data the type of reaction-diffusion equation and the corresponding physical and kinetic parameters. The method is illustrated, as a test case, by the study of the neolithic transition. We introduce a set of assumptions which makes it possible to describe the transition from hunting and gathering to agriculture economics by a differential delay reaction-diffusion equation for the population density. We derive a delay evolution equation for the rate of advance of agriculture, which illustrates an application of our analysis.

  4. Application of Adjoint Methodology to Supersonic Aircraft Design Using Reversed Equivalent Areas

    NASA Technical Reports Server (NTRS)

    Rallabhandi, Sriram K.

    2013-01-01

    This paper presents an approach to shape an aircraft to equivalent area based objectives using the discrete adjoint approach. Equivalent areas can be obtained either using reversed augmented Burgers equation or direct conversion of off-body pressures into equivalent area. Formal coupling with CFD allows computation of sensitivities of equivalent area objectives with respect to aircraft shape parameters. The exactness of the adjoint sensitivities is verified against derivatives obtained using the complex step approach. This methodology has the benefit of using designer-friendly equivalent areas in the shape design of low-boom aircraft. Shape optimization results with equivalent area cost functionals are discussed and further refined using ground loudness based objectives.

  5. An Exact Dual Adjoint Solution Method for Turbulent Flows on Unstructured Grids

    NASA Technical Reports Server (NTRS)

    Nielsen, Eric J.; Lu, James; Park, Michael A.; Darmofal, David L.

    2003-01-01

    An algorithm for solving the discrete adjoint system based on an unstructured-grid discretization of the Navier-Stokes equations is presented. The method is constructed such that an adjoint solution exactly dual to a direct differentiation approach is recovered at each time step, yielding a convergence rate which is asymptotically equivalent to that of the primal system. The new approach is implemented within a three-dimensional unstructured-grid framework and results are presented for inviscid, laminar, and turbulent flows. Improvements to the baseline solution algorithm, such as line-implicit relaxation and a tight coupling of the turbulence model, are also presented. By storing nearest-neighbor terms in the residual computation, the dual scheme is computationally efficient, while requiring twice the memory of the flow solution. The scheme is expected to have a broad impact on computational problems related to design optimization as well as error estimation and grid adaptation efforts.

  6. Efficient Construction of Discrete Adjoint Operators on Unstructured Grids Using Complex Variables

    NASA Technical Reports Server (NTRS)

    Nielsen, Eric J.; Kleb, William L.

    2005-01-01

    A methodology is developed and implemented to mitigate the lengthy software development cycle typically associated with constructing a discrete adjoint solver for aerodynamic simulations. The approach is based on a complex-variable formulation that enables straightforward differentiation of complicated real-valued functions. An automated scripting process is used to create the complex-variable form of the set of discrete equations. An efficient method for assembling the residual and cost function linearizations is developed. The accuracy of the implementation is verified through comparisons with a discrete direct method as well as a previously developed handcoded discrete adjoint approach. Comparisons are also shown for a large-scale configuration to establish the computational efficiency of the present scheme. To ultimately demonstrate the power of the approach, the implementation is extended to high temperature gas flows in chemical nonequilibrium. Finally, several fruitful research and development avenues enabled by the current work are suggested.

  7. Efficient Construction of Discrete Adjoint Operators on Unstructured Grids by Using Complex Variables

    NASA Technical Reports Server (NTRS)

    Nielsen, Eric J.; Kleb, William L.

    2005-01-01

    A methodology is developed and implemented to mitigate the lengthy software development cycle typically associated with constructing a discrete adjoint solver for aerodynamic simulations. The approach is based on a complex-variable formulation that enables straightforward differentiation of complicated real-valued functions. An automated scripting process is used to create the complex-variable form of the set of discrete equations. An efficient method for assembling the residual and cost function linearizations is developed. The accuracy of the implementation is verified through comparisons with a discrete direct method as well as a previously developed handcoded discrete adjoint approach. Comparisons are also shown for a large-scale configuration to establish the computational efficiency of the present scheme. To ultimately demonstrate the power of the approach, the implementation is extended to high temperature gas flows in chemical nonequilibrium. Finally, several fruitful research and development avenues enabled by the current work are suggested.

  8. Equations of the surface harmonics method for solving time-dependent neutron transport problems and their verification

    NASA Astrophysics Data System (ADS)

    Boyarinov, V. F.; Kondrushin, A. E.; Fomichenko, P. A.

    2013-12-01

    Time-dependent equations of the surface harmonics method (SHM) are obtained for planar one-dimensional geometry. The equations are verified by calculations of test problems from Benchmark Problem Book ANL-7416, and the capabilities and efficiency of applying the SHM for solving the time-dependent neutron transport equation in the diffusion approximation are demonstrated. The results of the work show that the implementation of the SHG for full-scale computations will make possible substantial progress in the efficient solution of time-dependent problems of neutron transport in nuclear reactors.

  9. Adjoint sensitivity analysis of an ultrawideband antenna

    SciTech Connect

    Stephanson, M B; White, D A

    2011-07-28

    The frequency domain finite element method using H(curl)-conforming finite elements is a robust technique for full-wave analysis of antennas. As computers become more powerful, it is becoming feasible to not only predict antenna performance, but also to compute sensitivity of antenna performance with respect to multiple parameters. This sensitivity information can then be used for optimization of the design or specification of manufacturing tolerances. In this paper we review the Adjoint Method for sensitivity calculation, and apply it to the problem of optimizing a Ultrawideband antenna.

  10. Elementary operators on self-adjoint operators

    NASA Astrophysics Data System (ADS)

    Molnar, Lajos; Semrl, Peter

    2007-03-01

    Let H be a Hilbert space and let and be standard *-operator algebras on H. Denote by and the set of all self-adjoint operators in and , respectively. Assume that and are surjective maps such that M(AM*(B)A)=M(A)BM(A) and M*(BM(A)B)=M*(B)AM*(B) for every pair , . Then there exist an invertible bounded linear or conjugate-linear operator and a constant c[set membership, variant]{-1,1} such that M(A)=cTAT*, , and M*(B)=cT*BT, .

  11. Analytical solutions of the one-dimensional advection-dispersion solute transport equation subject to time-dependent boundary conditions

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Analytical solutions of the advection-dispersion solute transport equation remain useful for a large number of applications in science and engineering. In this paper we extend the Duhamel theorem, originally established for diffusion type problems, to the case of advective-dispersive transport subj...

  12. Predicting fractional bed load transport rates: Application of the Wilcock-Crowe equations to a regulated gravel bed river

    USGS Publications Warehouse

    Gaeuman, D.; Andrews, E.D.; Kraus, A.; Smith, W.

    2009-01-01

    Bed load samples from four locations in the Trinity River of northern California are analyzed to evaluate the performance of the Wilcock-Crowe bed load transport equations for predicting fractional bed load transport rates. Bed surface particles become smaller and the fraction of sand on the bed increases with distance downstream from Lewiston Dam. The dimensionless reference shear stress for the mean bed particle size (t*rm) is largest near the dam, but varies relatively little between the more downstream locations. The relation between t*rm and the reference shear stresses for other size fractions is constant across all locations. Total bed load transport rates predicted with the Wilcock-Crowe equations are within a factor of 2 of sampled transport rates for 68% of all samples. The Wilcock-Crowe equations nonetheless consistently under-predict the transport of particles larger than 128 mm, frequently by more than an order of magnitude. Accurate prediction of the transport rates of the largest particles is important for models in which the evolution of the surface grain size distribution determines subsequent bed load transport rates. Values of term estimated from bed load samples are up to 50% larger than those predicted with the Wilcock-Crowe equations, and sampled bed load transport approximates equal mobility across a wider range of grain sizes than is implied by the equations. Modifications to theWilcock-Crowe equation for determining t*rm and the hiding function used to scale term to other grain size fractions are proposed to achieve the best fit to observed bed load transport in the Trinity River. Copyright 2009 by the American eophysical Union.

  13. Performance assessment of several equations of state and second virial coefficients in modified Enskog theory: Results for transport properties

    NASA Astrophysics Data System (ADS)

    Kiani, M.; Alavianmehr, M. M.; Otoofat, M.; Mohsenipour, A. A.; Ghatee, A.

    2015-11-01

    In this work, we identify a simple method for predicting transport properties of fluids over wide ranges of temperatures and pressure. In this respect, the capability of several equations of state (EOS) and second virial coefficient correlations to predict transport properties of fluids including carbon dioxide, methane and argon using modified Enskog theory (MET) is investigated. The transport properties in question are viscosity and thermal conductivity. The results indicate that the SRK EOS employed in the modified Enskog theory outperforms other equations of state. The average absolute deviation was found to be 12.2 and 18.5% for, respectively, the calculated thermal conductivity and viscosity using the MET.

  14. Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians

    SciTech Connect

    Al-Hashimi, M.H.; Salman, M.; Shalaby, A.; Wiese, U.-J.

    2013-10-15

    We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant. -- Highlights: •Self-adjoint extension theory and contact interactions. •Application of self-adjoint extensions to supersymmetry. •Contact interactions in finite volume with Robin boundary condition.

  15. Improved Adjoint-Operator Learning For A Neural Network

    NASA Technical Reports Server (NTRS)

    Toomarian, Nikzad; Barhen, Jacob

    1995-01-01

    Improved method of adjoint-operator learning reduces amount of computation and associated computational memory needed to make electronic neural network learn temporally varying pattern (e.g., to recognize moving object in image) in real time. Method extension of method described in "Adjoint-Operator Learning for a Neural Network" (NPO-18352).

  16. Transport Equations Resolution By N-BEE Anti-Dissipative Scheme In 2D Model Of Low Pressure Glow Discharge

    SciTech Connect

    Kraloua, B.; Hennad, A.

    2008-09-23

    The aim of this paper is to determine electric and physical properties by 2D modelling of glow discharge low pressure in continuous regime maintained by term constant source. This electric discharge is confined in reactor plan-parallel geometry. This reactor is filled by Argon monatomic gas. Our continuum model the order two is composed the first three moments the Boltzmann's equations coupled with Poisson's equation by self consistent method. These transport equations are discretized by the finite volumes method. The equations system is resolved by a new technique, it is about the N-BEE explicit scheme using the time splitting method.

  17. Boltzmann equation and Monte Carlo studies of electron transport in resistive plate chambers

    NASA Astrophysics Data System (ADS)

    Bošnjaković, D.; Petrović, Z. Lj; White, R. D.; Dujko, S.

    2014-10-01

    A multi term theory for solving the Boltzmann equation and Monte Carlo simulation technique are used to investigate electron transport in Resistive Plate Chambers (RPCs) that are used for timing and triggering purposes in many high energy physics experiments at CERN and elsewhere. Using cross sections for electron scattering in C2H2F4, iso-C4H10 and SF6 as an input in our Boltzmann and Monte Carlo codes, we have calculated data for electron transport as a function of reduced electric field E/N in various C2H2F4/iso-C4H10/SF6 gas mixtures used in RPCs in the ALICE, CMS and ATLAS experiments. Emphasis is placed upon the explicit and implicit effects of non-conservative collisions (e.g. electron attachment and/or ionization) on the drift and diffusion. Among many interesting and atypical phenomena induced by the explicit effects of non-conservative collisions, we note the existence of negative differential conductivity (NDC) in the bulk drift velocity component with no indication of any NDC for the flux component in the ALICE timing RPC system. We systematically study the origin and mechanisms for such phenomena as well as the possible physical implications which arise from their explicit inclusion into models of RPCs. Spatially-resolved electron transport properties are calculated using a Monte Carlo simulation technique in order to understand these phenomena.

  18. Phase-space finite elements in a least-squares solution of the transport equation

    SciTech Connect

    Drumm, C.; Fan, W.; Pautz, S.

    2013-07-01

    The linear Boltzmann transport equation is solved using a least-squares finite element approximation in the space, angular and energy phase-space variables. The method is applied to both neutral particle transport and also to charged particle transport in the presence of an electric field, where the angular and energy derivative terms are handled with the energy/angular finite elements approximation, in a manner analogous to the way the spatial streaming term is handled. For multi-dimensional problems, a novel approach is used for the angular finite elements: mapping the surface of a unit sphere to a two-dimensional planar region and using a meshing tool to generate a mesh. In this manner, much of the spatial finite-elements machinery can be easily adapted to handle the angular variable. The energy variable and the angular variable for one-dimensional problems make use of edge/beam elements, also building upon the spatial finite elements capabilities. The methods described here can make use of either continuous or discontinuous finite elements in space, angle and/or energy, with the use of continuous finite elements resulting in a smaller problem size and the use of discontinuous finite elements resulting in more accurate solutions for certain types of problems. The work described in this paper makes use of continuous finite elements, so that the resulting linear system is symmetric positive definite and can be solved with a highly efficient parallel preconditioned conjugate gradients algorithm. The phase-space finite elements capability has been built into the Sceptre code and applied to several test problems, including a simple one-dimensional problem with an analytic solution available, a two-dimensional problem with an isolated source term, showing how the method essentially eliminates ray effects encountered with discrete ordinates, and a simple one-dimensional charged-particle transport problem in the presence of an electric field. (authors)

  19. Finite element approximation of the radiative transport equation in a medium with piece-wise constant refractive index

    SciTech Connect

    Lehtikangas, O.; Tarvainen, T.; Kim, A.D.; Arridge, S.R.

    2015-02-01

    The radiative transport equation can be used as a light transport model in a medium with scattering particles, such as biological tissues. In the radiative transport equation, the refractive index is assumed to be constant within the medium. However, in biomedical media, changes in the refractive index can occur between different tissue types. In this work, light propagation in a medium with piece-wise constant refractive index is considered. Light propagation in each sub-domain with a constant refractive index is modeled using the radiative transport equation and the equations are coupled using boundary conditions describing Fresnel reflection and refraction phenomena on the interfaces between the sub-domains. The resulting coupled system of radiative transport equations is numerically solved using a finite element method. The approach is tested with simulations. The results show that this coupled system describes light propagation accurately through comparison with the Monte Carlo method. It is also shown that neglecting the internal changes of the refractive index can lead to erroneous boundary measurements of scattered light.

  20. Optical cryptosystem based on phase-truncated Fresnel diffraction and transport of intensity equation.

    PubMed

    Zhang, Chenggong; He, Wenqi; Wu, Jiachen; Peng, Xiang

    2015-04-01

    A novel optical cryptosystem based on phase-truncated Fresnel diffraction (PTFD) and transport of intensity equation (TIE) is proposed. By using the phase truncation technique, a phase-encoded plaintext could be encrypted into a real-valued noise-like intensity distribution by employing a random amplitude mask (RAM) and a random phase mask (RPM), which are regarded as two secret keys. For decryption, a generalized amplitude-phase retrieval (GAPR) algorithm combined with the TIE method are proposed to recover the plaintext with the help of two keys. Different from the current phase-truncated-based optical cryptosystems which need record the truncated phase as decryption keys, our scheme do not need the truncated phase because of the introducing of the TIE method. Moreover, the proposed scheme is expected to against existing attacks. A set of numerical simulation results show the feasibility and security of the proposed method. PMID:25968722

  1. An asymptotic-preserving scheme for the semiconductor Boltzmann equation toward the energy-transport limit

    NASA Astrophysics Data System (ADS)

    Hu, Jingwei; Wang, Li

    2015-01-01

    We design an asymptotic-preserving scheme for the semiconductor Boltzmann equation which leads to an energy-transport system for electron mass and energy as mean free path goes to zero. As opposed to the classical drift-diffusion limit where the stiff collisions are all in one scale, new difficulties arise in the two-scale stiff collision terms because the simple BGK penalization [15] fails to drive the solution to the correct limit. We propose to set up a spatially dependent threshold on the penalization of the stiffer collision operator such that the evolution of the solution resembles a Hilbert expansion at the continuous level. Formal asymptotic analysis and numerical results confirm the efficiency and accuracy of our scheme.

  2. Silicon wafer microstructure imaging using InfraRed Transport of Intensity Equation

    NASA Astrophysics Data System (ADS)

    Li, Hongru; Feng, Guoying; Bourgade, Thomas; Zuo, Chao; Du, Yongzhao; Zhou, Shouhuan; Asundi, Anand

    2015-03-01

    A novel quantitative 3D imaging system of silicon microstructures using InfraRed Transport of Intensity Equation (IRTIE) is proposed in this paper. By recording the intensity at multiple planes and using FFT or DCT based TIE solver, fast and accurate phase retrieval for both uniform and non-uniform intensity distributions is proposed. Numerical simulation and experiments confirm the accuracy and reliability of the proposed method. The application of IR-TIE for inspection of micro-patterns in visibly opaque media using 1310 nm light source is demonstrated. For comparison, micro-patterns are also inspected by the contact scanning mode Taylor Hobson system. Quantitative agreement suggests the possibility of using IR-TIE for phase imaging of silicon wafers.

  3. A non-equilibrium equation-of-motion approach to quantum transport utilizing projection operators

    NASA Astrophysics Data System (ADS)

    Ochoa, Maicol A.; Galperin, Michael; Ratner, Mark A.

    2014-11-01

    We consider a projection operator approach to the non-equilbrium Green function equation-of-motion (PO-NEGF EOM) method. The technique resolves problems of arbitrariness in truncation of an infinite chain of EOMs and prevents violation of symmetry relations resulting from the truncation (equivalence of left- and right-sided EOMs is shown and symmetry with respect to interchange of Fermi or Bose operators before truncation is preserved). The approach, originally developed by Tserkovnikov (1999 Theor. Math. Phys. 118 85) for equilibrium systems, is reformulated to be applicable to time-dependent non-equilibrium situations. We derive a canonical form of EOMs, thus explicitly demonstrating a proper result for the non-equilibrium atomic limit in junction problems. A simple practical scheme applicable to quantum transport simulations is formulated. We perform numerical simulations within simple models and compare results of the approach to other techniques and (where available) also to exact results.

  4. An asymptotic-preserving scheme for the semiconductor Boltzmann equation toward the energy-transport limit

    SciTech Connect

    Hu, Jingwei; Wang, Li

    2015-01-15

    We design an asymptotic-preserving scheme for the semiconductor Boltzmann equation which leads to an energy-transport system for electron mass and energy as mean free path goes to zero. As opposed to the classical drift-diffusion limit where the stiff collisions are all in one scale, new difficulties arise in the two-scale stiff collision terms because the simple BGK penalization [15] fails to drive the solution to the correct limit. We propose to set up a spatially dependent threshold on the penalization of the stiffer collision operator such that the evolution of the solution resembles a Hilbert expansion at the continuous level. Formal asymptotic analysis and numerical results confirm the efficiency and accuracy of our scheme.

  5. Iterative feedback algorithm for phase retrieval based on transport of intensity equation

    NASA Astrophysics Data System (ADS)

    Liu, Kaifeng; Cheng, Hong; Zhang, Cheng; Shen, Chuan; Zhang, Fen; Wei, Sui

    2015-12-01

    In this paper, a novel phase retrieval algorithm is presented which combines the advantages of the Transport of Intensity Equation (TIE) method and the iteration method. TIE method is fast, but its precision is not high. Though the convergence rate of iteration method is slow, its result is more accurate. This algorithm consists of Iterative Angular Spectrum (IAS) method to utilize the physical constraints between the object and the spectral domain, and the relationship between the intensity and phase among the wave propagation. Firstly, the phase at the object plane is calculated from two intensity images by TIE. Then this result is treated as the initial phase of the IAS. Finally, the phase information at the object plane is acquired according the reversibility of the optical path. During the iteration process, the feedback mechanism is imposed on it that improve the convergence rate and the precision of phase retrieval and the simulation results are given.

  6. On a 1D nonlocal transport equation with nonlocal velocity and subcritical or supercritical diffusion

    NASA Astrophysics Data System (ADS)

    Lazar, Omar

    2016-11-01

    We study a 1D transport equation with nonlocal velocity with subcritical or supercritical dissipation. For all data in the weighted Sobolev space Hk (wλ,κ) ∩L∞, where k = max ⁡ (0 , 3 / 2 - α) and wλ,κ is a given family of Muckenhoupt weights, we prove a global existence result in the subcritical case α ∈ (1 , 2). We also prove a local existence theorem for large data in H2 (wλ,κ) ∩L∞ in the supercritical case α ∈ (0 , 1). The proofs are based on the use of the weighted Littlewood-Paley theory, interpolation along with some new commutator estimates.

  7. Parallel Simulation of Ion Implantation for Multi-Component Targets Using Boltzmann Transport Equation

    NASA Astrophysics Data System (ADS)

    Wang, Shyh-Wei; Guo, Shuang-Fa

    1998-07-01

    A stepwise Boltzmann transport equation (BTE) simulation using non-uniform energy grid momentum matrix and exact nuclear scattering cross-section is successfully parallelized to simulate the ion implantation of multi-component targets. Assuming that the interactions of ion with different target atoms are independent, the scattering of ions with different components can be calculated concurrently by different processors. It is developed on CONVEX SPP-1000 and the software environment of parallel virtual machine (PVM) with a master-slave paradigm. A speedup of 3.3 has been obtained for the simulation of As ions implanted into AZ1350 (C6.2H6O1N0.15S0.06) which is composed of five components. In addition, our new scheme gives better agreement with the experimental results for heavy ion implantation than the conventional method using a uniform energy grid and approximated scattering function.

  8. A discrete ordinates approximation to the neutron transport equation applied to generalized geometries

    SciTech Connect

    DeHart, M.D.

    1992-12-01

    A method for applying the discrete ordinates method for solution of the neutron transport equation in arbitary two-dimensional meshes has been developed. The finite difference approach normally used to approximate spatial derivatives in extrapolating angular fluxes across a cell is replaced by direct solution of the characteristic form of the transport equation for each discrete direction. Thus, computational cells are not restricted to the traditional shape of a mesh element within a given coordinate system. However, in terms of the treatment of energy and angular dependencies, this method resembles traditional discrete ordinates techniques. Using the method developed here, a general two-dimensional space can be approximated by an irregular mesh comprised of arbitrary polygons. The present work makes no assumptions about the orientations or the number of sides in a given cell, and computes all geometric relationships between each set of sides in each cell for each discrete direction. A set of non-reentrant polygons can therefore be used to represent any given two dimensional space. Results for a number of test problems have been compared to solutions obtained from traditional methods, with good agreement. Comparisons include benchmarks against analytical results for problems with simple geometry, as well numerical results obtained from traditional discrete ordinates methods by applying the ANISN and TWOTRAN computer programs. Numerical results were obtained for problems ranging from simple one-dimensional geometry to complicated multidimensional configurations. These results have demonstrated the ability of the developed method to closely approximate complex geometrical configurations and to obtain accurate results for problems that are extremely difficult to model using traditional methods.

  9. Master equation approach to charge injection and transport in organic insulators

    NASA Astrophysics Data System (ADS)

    Freire, José A.; Voss, Grasiela

    2005-03-01

    We develop a master equation model of a disordered organic insulator sandwiched between metallic electrodes by treating as rate processes both the injection and the internal transport. We show how the master equation model allows for the inclusion of crucial correlation effects in the charge transport, particularly of the Pauli exclusion principle and of space-charge effects, besides, being dependent on just the microscopic form of the transfer rate between the localized electronic states, it allows for the investigation of different microscopic scenarios in the organic, such as polaronic hopping, correlated energy levels, interaction with image charge, etc. The model allows for a separate analysis of the injection and the recombination currents. We find that the disorder, besides increasing the injection current, eliminates the possibility of observation of a Fowler-Nordheim injection current at zero temperature, and that it does not alter the Schottky barrier size of the zero-field thermionic injection current from the value based on the energy difference between the electrode Fermi level and the highest occupied molecular orbital/lowest unoccupied molecular orbital levels in the organic, but it makes the Arrhenius temperature dependence appear at larger temperatures. We investigate how the I(V ) characteristics of a device is affected by the presence of correlations in the site energy distribution and by the form of the internal hopping rate, specifically the Miller-Abrahams rate and the Marcus or small-polaron rate. We show that the disorder does not modify significantly the eβ√E field dependence of the net current due to the Schottky barrier lowering caused by the attraction between the charge and its image in the electrode.

  10. Adjoint-based error estimation and mesh adaptation for the correction procedure via reconstruction method

    NASA Astrophysics Data System (ADS)

    Shi, Lei; Wang, Z. J.

    2015-08-01

    Adjoint-based mesh adaptive methods are capable of distributing computational resources to areas which are important for predicting an engineering output. In this paper, we develop an adjoint-based h-adaptation approach based on the high-order correction procedure via reconstruction formulation (CPR) to minimize the output or functional error. A dual-consistent CPR formulation of hyperbolic conservation laws is developed and its dual consistency is analyzed. Super-convergent functional and error estimate for the output with the CPR method are obtained. Factors affecting the dual consistency, such as the solution point distribution, correction functions, boundary conditions and the discretization approach for the non-linear flux divergence term, are studied. The presented method is then used to perform simulations for the 2D Euler and Navier-Stokes equations with mesh adaptation driven by the adjoint-based error estimate. Several numerical examples demonstrate the ability of the presented method to dramatically reduce the computational cost comparing with uniform grid refinement.

  11. High Order Finite Volume Nonlinear Schemes for the Boltzmann Transport Equation

    SciTech Connect

    Bihari, B L; Brown, P N

    2005-03-29

    The authors apply the nonlinear WENO (Weighted Essentially Nonoscillatory) scheme to the spatial discretization of the Boltzmann Transport Equation modeling linear particle transport. The method is a finite volume scheme which ensures not only conservation, but also provides for a more natural handling of boundary conditions, material properties and source terms, as well as an easier parallel implementation and post processing. It is nonlinear in the sense that the stencil depends on the solution at each time step or iteration level. By biasing the gradient calculation towards the stencil with smaller derivatives, the scheme eliminates the Gibb's phenomenon with oscillations of size O(1) and reduces them to O(h{sup r}), where h is the mesh size and r is the order of accuracy. The current implementation is three-dimensional, generalized for unequally spaced meshes, fully parallelized, and up to fifth order accurate (WENO5) in space. For unsteady problems, the resulting nonlinear spatial discretization yields a set of ODE's in time, which in turn is solved via high order implicit time-stepping with error control. For the steady-state case, they need to solve the non-linear system, typically by Newton-Krylov iterations. There are several numerical examples presented to demonstrate the accuracy, non-oscillatory nature and efficiency of these high order methods, in comparison with other fixed-stencil schemes.

  12. First-principles calculation method for electron transport based on the grid Lippmann-Schwinger equation

    NASA Astrophysics Data System (ADS)

    Egami, Yoshiyuki; Iwase, Shigeru; Tsukamoto, Shigeru; Ono, Tomoya; Hirose, Kikuji

    2015-09-01

    We develop a first-principles electron-transport simulator based on the Lippmann-Schwinger (LS) equation within the framework of the real-space finite-difference scheme. In our fully real-space-based LS (grid LS) method, the ratio expression technique for the scattering wave functions and the Green's function elements of the reference system is employed to avoid numerical collapse. Furthermore, we present analytical expressions and/or prominent calculation procedures for the retarded Green's function, which are utilized in the grid LS approach. In order to demonstrate the performance of the grid LS method, we simulate the electron-transport properties of the semiconductor-oxide interfaces sandwiched between semi-infinite jellium electrodes. The results confirm that the leakage current through the (001 )Si -SiO2 model becomes much larger when the dangling-bond state is induced by a defect in the oxygen layer, while that through the (001 )Ge -GeO2 model is insensitive to the dangling bond state.

  13. Reentry-Vehicle Shape Optimization Using a Cartesian Adjoint Method and CAD Geometry

    NASA Technical Reports Server (NTRS)

    Nemec, Marian; Aftosmis, Michael J.

    2006-01-01

    A DJOINT solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (e.g., geometric parameters that control the shape). Classic aerodynamic applications of gradient-based optimization include the design of cruise configurations for transonic and supersonic flow, as well as the design of high-lift systems. are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric computer-aided design (CAD). In previous work on Cartesian adjoint solvers, Melvin et al. developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the two-dimensional Euler equations using a ghost-cell method to enforce the wall boundary conditions. In Refs. 18 and 19, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm were the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The accuracy of the gradient computation was verified using several three-dimensional test cases, which included design

  14. In-focus quantitative intensity and phase imaging with the numerical focusing transport of intensity equation method

    NASA Astrophysics Data System (ADS)

    Tian, Xiaolin; Meng, Xin; Yu, Wei; Song, Xiaojun; Xue, Liang; Liu, Cheng; Wang, Shouyu

    2016-10-01

    Microscopy combined with the transport of intensity equation is capable of retrieving both intensity and phase distributions of samples from both in-focus and defocus intensities. However, during measurements, the focal plane is often decided artificially and the improper choice may induce errors in quantitative intensity and phase retrieval. In order to obtain accurate in-focus information, quantitative intensity and phase imaging with the numerical focusing transport of intensity equation method combined with cellular duty ratio criterion and numerical wavefront propagation is introduced in this paper. Both numerical simulations and experimental measurements are provided proving this designed method can increase both retrieved in-focus intensity and phase accuracy and reduce dependence of focal plane determination in transport of intensity equation measurements. It is believed that the proposed method can be potentially applied in various fields as in-focus compensation for quantitative phase imaging and automatic focal plane determination, etc.

  15. TH-E-BRE-02: A Forward Scattering Approximation to Dose Calculation Using the Linear Boltzmann Transport Equation

    SciTech Connect

    Catt, B; Snyder, M

    2014-06-15

    Purpose: To investigate the use of the linear Boltzmann transport equation as a dose calculation tool which can account for interface effects, while still having faster computation times than Monte Carlo methods. In particular, we introduce a forward scattering approximation, in hopes of improving calculation time without a significant hindrance to accuracy. Methods: Two coupled Boltzmann transport equations were constructed, one representing the fluence of photons within the medium, and the other, the fluence of electrons. We neglect the scattering term within the electron transport equation, resulting in an extreme forward scattering approximation to reduce computational complexity. These equations were then solved using a numerical technique for solving partial differential equations, known as a finite difference scheme, where the fluence at each discrete point in space is calculated based on the fluence at the previous point in the particle's path. Using this scheme, it is possible to develop a solution to the Boltzmann transport equations by beginning with boundary conditions and iterating across the entire medium. The fluence of electrons can then be used to find the dose at any point within the medium. Results: Comparisons with Monte Carlo simulations indicate that even simplistic techniques for solving the linear Boltzmann transport equation yield expected interface effects, which many popular dose calculation algorithms are not capable of predicting. Implementation of a forward scattering approximation does not appear to drastically reduce the accuracy of this algorithm. Conclusion: Optimized implementations of this algorithm have been shown to be very accurate when compared with Monte Carlo simulations, even in build up regions where many models fail. Use of a forward scattering approximation could potentially give a reasonably accurate dose distribution in a shorter amount of time for situations where a completely accurate dose distribution is not

  16. A Novel Algorithm for Solving the Multidimensional Neutron Transport Equation on Massively Parallel Architectures

    SciTech Connect

    Azmy, Yousry

    2014-06-10

    We employ the Integral Transport Matrix Method (ITMM) as the kernel of new parallel solution methods for the discrete ordinates approximation of the within-group neutron transport equation. The ITMM abandons the repetitive mesh sweeps of the traditional source iterations (SI) scheme in favor of constructing stored operators that account for the direct coupling factors among all the cells' fluxes and between the cells' and boundary surfaces' fluxes. The main goals of this work are to develop the algorithms that construct these operators and employ them in the solution process, determine the most suitable way to parallelize the entire procedure, and evaluate the behavior and parallel performance of the developed methods with increasing number of processes, P. The fastest observed parallel solution method, Parallel Gauss-Seidel (PGS), was used in a weak scaling comparison with the PARTISN transport code, which uses the source iteration (SI) scheme parallelized with the Koch-baker-Alcouffe (KBA) method. Compared to the state-of-the-art SI-KBA with diffusion synthetic acceleration (DSA), this new method- even without acceleration/preconditioning-is completitive for optically thick problems as P is increased to the tens of thousands range. For the most optically thick cells tested, PGS reduced execution time by an approximate factor of three for problems with more than 130 million computational cells on P = 32,768. Moreover, the SI-DSA execution times's trend rises generally more steeply with increasing P than the PGS trend. Furthermore, the PGS method outperforms SI for the periodic heterogeneous layers (PHL) configuration problems. The PGS method outperforms SI and SI-DSA on as few as P = 16 for PHL problems and reduces execution time by a factor of ten or more for all problems considered with more than 2 million computational cells on P = 4.096.

  17. Adjoints and Low-rank Covariance Representation

    NASA Technical Reports Server (NTRS)

    Tippett, Michael K.; Cohn, Stephen E.

    2000-01-01

    Quantitative measures of the uncertainty of Earth System estimates can be as important as the estimates themselves. Second moments of estimation errors are described by the covariance matrix, whose direct calculation is impractical when the number of degrees of freedom of the system state is large. Ensemble and reduced-state approaches to prediction and data assimilation replace full estimation error covariance matrices by low-rank approximations. The appropriateness of such approximations depends on the spectrum of the full error covariance matrix, whose calculation is also often impractical. Here we examine the situation where the error covariance is a linear transformation of a forcing error covariance. We use operator norms and adjoints to relate the appropriateness of low-rank representations to the conditioning of this transformation. The analysis is used to investigate low-rank representations of the steady-state response to random forcing of an idealized discrete-time dynamical system.

  18. Development of an adjoint model of GRAPES-CUACE and its application in tracking influential haze source areas in north China

    NASA Astrophysics Data System (ADS)

    An, Xing Qin; Xian Zhai, Shi; Jin, Min; Gong, Sunling; Wang, Yu

    2016-06-01

    The aerosol adjoint module of the atmospheric chemical modeling system GRAPES-CUACE (Global-Regional Assimilation and Prediction System coupled with the CMA Unified Atmospheric Chemistry Environment) is constructed based on the adjoint theory. This includes the development and validation of the tangent linear and the adjoint models of the three parts involved in the GRAPES-CUACE aerosol module: CAM (Canadian Aerosol Module), interface programs that connect GRAPES and CUACE, and the aerosol transport processes that are embedded in GRAPES. Meanwhile, strict mathematical validation schemes for the tangent linear and the adjoint models are implemented for all input variables. After each part of the module and the assembled tangent linear and adjoint models is verified, the adjoint model of the GRAPES-CUACE aerosol is developed and used in a black carbon (BC) receptor-source sensitivity analysis to track influential haze source areas in north China. The sensitivity of the average BC concentration over Beijing at the highest concentration time point (referred to as the Objective Function) is calculated with respect to the BC amount emitted over the Beijing-Tianjin-Hebei region. Four types of regions are selected based on the administrative division or the sensitivity coefficient distribution. The adjoint sensitivity results are then used to quantify the effect of reducing the emission sources at different time intervals over different regions. It is indicated that the more influential regions (with relatively larger sensitivity coefficients) do not necessarily correspond to the administrative regions. Instead, the influence per unit area of the sensitivity selected regions is greater. Therefore, controlling the most influential regions during critical time intervals based on the results of the adjoint sensitivity analysis is much more efficient than controlling administrative regions during an experimental time period.

  19. GPU-Accelerated Adjoint Algorithmic Differentiation

    PubMed Central

    Gremse, Felix; Höfter, Andreas; Razik, Lukas; Kiessling, Fabian; Naumann, Uwe

    2015-01-01

    Many scientific problems such as classifier training or medical image reconstruction can be expressed as minimization of differentiable real-valued cost functions and solved with iterative gradient-based methods. Adjoint algorithmic differentiation (AAD) enables automated computation of gradients of such cost functions implemented as computer programs. To backpropagate adjoint derivatives, excessive memory is potentially required to store the intermediate partial derivatives on a dedicated data structure, referred to as the “tape”. Parallelization is difficult because threads need to synchronize their accesses during taping and backpropagation. This situation is aggravated for many-core architectures, such as Graphics Processing Units (GPUs), because of the large number of light-weight threads and the limited memory size in general as well as per thread. We show how these limitations can be mediated if the cost function is expressed using GPU-accelerated vector and matrix operations which are recognized as intrinsic functions by our AAD software. We compare this approach with naive and vectorized implementations for CPUs. We use four increasingly complex cost functions to evaluate the performance with respect to memory consumption and gradient computation times. Using vectorization, CPU and GPU memory consumption could be substantially reduced compared to the naive reference implementation, in some cases even by an order of complexity. The vectorization allowed usage of optimized parallel libraries during forward and reverse passes which resulted in high speedups for the vectorized CPU version compared to the naive reference implementation. The GPU version achieved an additional speedup of 7.5 ± 4.4, showing that the processing power of GPUs can be utilized for AAD using this concept. Furthermore, we show how this software can be systematically extended for more complex problems such as nonlinear absorption reconstruction for fluorescence-mediated tomography

  20. GPU-accelerated adjoint algorithmic differentiation

    NASA Astrophysics Data System (ADS)

    Gremse, Felix; Höfter, Andreas; Razik, Lukas; Kiessling, Fabian; Naumann, Uwe

    2016-03-01

    Many scientific problems such as classifier training or medical image reconstruction can be expressed as minimization of differentiable real-valued cost functions and solved with iterative gradient-based methods. Adjoint algorithmic differentiation (AAD) enables automated computation of gradients of such cost functions implemented as computer programs. To backpropagate adjoint derivatives, excessive memory is potentially required to store the intermediate partial derivatives on a dedicated data structure, referred to as the "tape". Parallelization is difficult because threads need to synchronize their accesses during taping and backpropagation. This situation is aggravated for many-core architectures, such as Graphics Processing Units (GPUs), because of the large number of light-weight threads and the limited memory size in general as well as per thread. We show how these limitations can be mediated if the cost function is expressed using GPU-accelerated vector and matrix operations which are recognized as intrinsic functions by our AAD software. We compare this approach with naive and vectorized implementations for CPUs. We use four increasingly complex cost functions to evaluate the performance with respect to memory consumption and gradient computation times. Using vectorization, CPU and GPU memory consumption could be substantially reduced compared to the naive reference implementation, in some cases even by an order of complexity. The vectorization allowed usage of optimized parallel libraries during forward and reverse passes which resulted in high speedups for the vectorized CPU version compared to the naive reference implementation. The GPU version achieved an additional speedup of 7.5 ± 4.4, showing that the processing power of GPUs can be utilized for AAD using this concept. Furthermore, we show how this software can be systematically extended for more complex problems such as nonlinear absorption reconstruction for fluorescence-mediated tomography.

  1. On the forward-backward-in-time approach for Monte Carlo solution of Parker's transport equation: One-dimensional case

    NASA Astrophysics Data System (ADS)

    Bobik, P.; Boschini, M. J.; Della Torre, S.; Gervasi, M.; Grandi, D.; La Vacca, G.; Pensotti, S.; Putis, M.; Rancoita, P. G.; Rozza, D.; Tacconi, M.; Zannoni, M.

    2016-05-01

    The cosmic rays propagation inside the heliosphere is well described by a transport equation introduced by Parker in 1965. To solve this equation, several approaches were followed in the past. Recently, a Monte Carlo approach became widely used in force of its advantages with respect to other numerical methods. In this approach the transport equation is associated to a fully equivalent set of stochastic differential equations (SDE). This set is used to describe the stochastic path of quasi-particle from a source, e.g., the interstellar space, to a specific target, e.g., a detector at Earth. We present a comparison of forward-in-time and backward-in-time methods to solve the cosmic rays transport equation in the heliosphere. The Parker equation and the related set of SDE in the several formulations are treated in this paper. For the sake of clarity, this work is focused on the one-dimensional solutions. Results were compared with an alternative numerical solution, namely, Crank-Nicolson method, specifically developed for the case under study. The methods presented are fully consistent each others for energy greater than 400 MeV. The comparison between stochastic integrations and Crank-Nicolson allows us to estimate the systematic uncertainties of Monte Carlo methods. The forward-in-time stochastic integrations method showed a systematic uncertainty <5%, while backward-in-time stochastic integrations method showed a systematic uncertainty <1% in the studied energy range.

  2. Real time quantitative phase microscopy based on single-shot transport of intensity equation (ssTIE) method

    NASA Astrophysics Data System (ADS)

    Yu, Wei; Tian, Xiaolin; He, Xiaoliang; Song, Xiaojun; Xue, Liang; Liu, Cheng; Wang, Shouyu

    2016-08-01

    Microscopy based on transport of intensity equation provides quantitative phase distributions which opens another perspective for cellular observations. However, it requires multi-focal image capturing while mechanical and electrical scanning limits its real time capacity in sample detections. Here, in order to break through this restriction, real time quantitative phase microscopy based on single-shot transport of the intensity equation method is proposed. A programmed phase mask is designed to realize simultaneous multi-focal image recording without any scanning; thus, phase distributions can be quantitatively retrieved in real time. It is believed the proposed method can be potentially applied in various biological and medical applications, especially for live cell imaging.

  3. Aerodynamic Shape Optimization of Complex Aircraft Configurations via an Adjoint Formulation

    NASA Technical Reports Server (NTRS)

    Reuther, James; Jameson, Antony; Farmer, James; Martinelli, Luigi; Saunders, David

    1996-01-01

    This work describes the implementation of optimization techniques based on control theory for complex aircraft configurations. Here control theory is employed to derive the adjoint differential equations, the solution of which allows for a drastic reduction in computational costs over previous design methods (13, 12, 43, 38). In our earlier studies (19, 20, 22, 23, 39, 25, 40, 41, 42) it was shown that this method could be used to devise effective optimization procedures for airfoils, wings and wing-bodies subject to either analytic or arbitrary meshes. Design formulations for both potential flows and flows governed by the Euler equations have been demonstrated, showing that such methods can be devised for various governing equations (39, 25). In our most recent works (40, 42) the method was extended to treat wing-body configurations with a large number of mesh points, verifying that significant computational savings can be gained for practical design problems. In this paper the method is extended for the Euler equations to treat complete aircraft configurations via a new multiblock implementation. New elements include a multiblock-multigrid flow solver, a multiblock-multigrid adjoint solver, and a multiblock mesh perturbation scheme. Two design examples are presented in which the new method is used for the wing redesign of a transonic business jet.

  4. Adjoint sensitivity analysis of plasmonic structures using the FDTD method.

    PubMed

    Zhang, Yu; Ahmed, Osman S; Bakr, Mohamed H

    2014-05-15

    We present an adjoint variable method for estimating the sensitivities of arbitrary responses with respect to the parameters of dispersive discontinuities in nanoplasmonic devices. Our theory is formulated in terms of the electric field components at the vicinity of perturbed discontinuities. The adjoint sensitivities are computed using at most one extra finite-difference time-domain (FDTD) simulation regardless of the number of parameters. Our approach is illustrated through the sensitivity analysis of an add-drop coupler consisting of a square ring resonator between two parallel waveguides. The computed adjoint sensitivities of the scattering parameters are compared with those obtained using the accurate but computationally expensive central finite difference approach.

  5. Three-dimensional transport with variational nodal methods

    SciTech Connect

    Lewis, E.E.; Palmiotti, G.; Shalil, H.S.; Laurin-Kovitz, K.; Fanning, T.; Hanebutte, U.R.

    1996-12-31

    The development of the variational nodal method contained in the three-dimensional transport code VARIANT is reviewed. This Argonne National Laboratory code treats two- and three- dimensional multigroup problems with anisotropic scattering in hexagonal and Cartesian geometries. The methodology couples hybrid finite elements in space, which enforce nodal balance, with spherical harmonics expansions in angle. The resulting response matrix equations are solved by red-black or four-color iterations. Several enhancements to VARIANT are discussed: The simplified spherical harmonics option provides near spherical harmonic accuracy for many problems at a fraction of the cost. Adjoint and perturbation calculations are performed without the physical- and mathematical adjoint dichotomy appearing in other nodal methods. Heterogeneous node methods extend the problem classes to which the method may be applied. Computational strategies and trade-offs are discussed and possible future research directions are outlined.

  6. Estimation of historical groundwater contaminant distribution using the adjoint state method applied to geostatistical inverse modeling

    NASA Astrophysics Data System (ADS)

    Michalak, Anna M.; Kitanidis, Peter K.

    2004-08-01

    As the incidence of groundwater contamination continues to grow, a number of inverse modeling methods have been developed to address forensic groundwater problems. In this work the geostatistical approach to inverse modeling is extended to allow for the recovery of the antecedent distribution of a contaminant at a given point back in time, which is critical to the assessment of historical exposure to contamination. Such problems are typically strongly underdetermined, with a large number of points at which the distribution is to be estimated. To address this challenge, the computational efficiency of the new method is increased through the application of the adjoint state method. In addition, the adjoint problem is presented in a format that allows for the reuse of existing groundwater flow and transport codes as modules in the inverse modeling algorithm. As demonstrated in the presented applications, the geostatistical approach combined with the adjoint state method allow for a historical multidimensional contaminant distribution to be recovered even in heterogeneous media, where a numerical solution is required for the forward problem.

  7. A fast, parallel algorithm to solve the basic fluvial erosion/transport equations

    NASA Astrophysics Data System (ADS)

    Braun, J.

    2012-04-01

    Quantitative models of landform evolution are commonly based on the solution of a set of equations representing the processes of fluvial erosion, transport and deposition, which leads to predict the geometry of a river channel network and its evolution through time. The river network is often regarded as the backbone of any surface processes model (SPM) that might include other physical processes acting at a range of spatial and temporal scales along hill slopes. The basic laws of fluvial erosion requires the computation of local (slope) and non-local (drainage area) quantities at every point of a given landscape, a computationally expensive operation which limits the resolution of most SPMs. I present here an algorithm to compute the various components required in the parameterization of fluvial erosion (and transport) and thus solve the basic fluvial geomorphic equation, that is very efficient because it is O(n) (the number of required arithmetic operations is linearly proportional to the number of nodes defining the landscape), and is fully parallelizable (the computation cost decreases in a direct inverse proportion to the number of processors used to solve the problem). The algorithm is ideally suited for use on latest multi-core processors. Using this new technique, geomorphic problems can be solved at an unprecedented resolution (typically of the order of 10,000 X 10,000 nodes) while keeping the computational cost reasonable (order 1 sec per time step). Furthermore, I will show that the algorithm is applicable to any regular or irregular representation of the landform, and is such that the temporal evolution of the landform can be discretized by a fully implicit time-marching algorithm, making it unconditionally stable. I will demonstrate that such an efficient algorithm is ideally suited to produce a fully predictive SPM that links observationally based parameterizations of small-scale processes to the evolution of large-scale features of the landscapes on

  8. A fully coupled Monte Carlo/discrete ordinates solution to the neutron transport equation. Final report

    SciTech Connect

    Filippone, W.L.; Baker, R.S.

    1990-12-31

    The neutron transport equation is solved by a hybrid method that iteratively couples regions where deterministic (S{sub N}) and stochastic (Monte Carlo) methods are applied. Unlike previous hybrid methods, the Monte Carlo and S{sub N} regions are fully coupled in the sense that no assumption is made about geometrical separation or decoupling. The hybrid method provides a new means of solving problems involving both optically thick and optically thin regions that neither Monte Carlo nor S{sub N} is well suited for by themselves. The fully coupled Monte Carlo/S{sub N} technique consists of defining spatial and/or energy regions of a problem in which either a Monte Carlo calculation or an S{sub N} calculation is to be performed. The Monte Carlo region may comprise the entire spatial region for selected energy groups, or may consist of a rectangular area that is either completely or partially embedded in an arbitrary S{sub N} region. The Monte Carlo and S{sub N} regions are then connected through the common angular boundary fluxes, which are determined iteratively using the response matrix technique, and volumetric sources. The hybrid method has been implemented in the S{sub N} code TWODANT by adding special-purpose Monte Carlo subroutines to calculate the response matrices and volumetric sources, and linkage subrountines to carry out the interface flux iterations. The common angular boundary fluxes are included in the S{sub N} code as interior boundary sources, leaving the logic for the solution of the transport flux unchanged, while, with minor modifications, the diffusion synthetic accelerator remains effective in accelerating S{sub N} calculations. The special-purpose Monte Carlo routines used are essentially analog, with few variance reduction techniques employed. However, the routines have been successfully vectorized, with approximately a factor of five increase in speed over the non-vectorized version.

  9. The piecewise linear discontinuous finite element method applied to the RZ and XYZ transport equations

    NASA Astrophysics Data System (ADS)

    Bailey, Teresa S.

    In this dissertation we discuss the development, implementation, analysis and testing of the Piecewise Linear Discontinuous Finite Element Method (PWLD) applied to the particle transport equation in two-dimensional cylindrical (RZ) and three-dimensional Cartesian (XYZ) geometries. We have designed this method to be applicable to radiative-transfer problems in radiation-hydrodynamics systems for arbitrary polygonal and polyhedral meshes. For RZ geometry, we have implemented this method in the Capsaicin radiative-transfer code being developed at Los Alamos National Laboratory. In XYZ geometry, we have implemented the method in the Parallel Deterministic Transport code being developed at Texas A&M University. We discuss the importance of the thick diffusion limit for radiative-transfer problems, and perform a thick diffusion-limit analysis on our discretized system for both geometries. This analysis predicts that the PWLD method will perform well in this limit for many problems of physical interest with arbitrary polygonal and polyhedral cells. Finally, we run a series of test problems to determine some useful properties of the method and verify the results of our thick diffusion limit analysis. Finally, we test our method on a variety of test problems and show that it compares favorably to existing methods. With these test problems, we also show that our method performs well in the thick diffusion limit as predicted by our analysis. Based on PWLD's solid finite-element foundation, the desirable properties it shows under analysis, and the excellent performance it demonstrates on test problems even with highly distorted spatial grids, we conclude that it is an excellent candidate for radiative-transfer problems that need a robust method that performs well in thick diffusive problems or on distorted grids.

  10. Sensitivity of Lumped Constraints Using the Adjoint Method

    NASA Technical Reports Server (NTRS)

    Akgun, Mehmet A.; Haftka, Raphael T.; Wu, K. Chauncey; Walsh, Joanne L.

    1999-01-01

    Adjoint sensitivity calculation of stress, buckling and displacement constraints may be much less expensive than direct sensitivity calculation when the number of load cases is large. Adjoint stress and displacement sensitivities are available in the literature. Expressions for local buckling sensitivity of isotropic plate elements are derived in this study. Computational efficiency of the adjoint method is sensitive to the number of constraints and, therefore, the method benefits from constraint lumping. A continuum version of the Kreisselmeier-Steinhauser (KS) function is chosen to lump constraints. The adjoint and direct methods are compared for three examples: a truss structure, a simple HSCT wing model, and a large HSCT model. These sensitivity derivatives are then used in optimization.

  11. Application of variational principles and adjoint integrating factors for constructing numerical GFD models

    NASA Astrophysics Data System (ADS)

    Penenko, Vladimir; Tsvetova, Elena; Penenko, Alexey

    2015-04-01

    The proposed method is considered on an example of hydrothermodynamics and atmospheric chemistry models [1,2]. In the development of the existing methods for constructing numerical schemes possessing the properties of total approximation for operators of multiscale process models, we have developed a new variational technique, which uses the concept of adjoint integrating factors. The technique is as follows. First, a basic functional of the variational principle (the integral identity that unites the model equations, initial and boundary conditions) is transformed using Lagrange's identity and the second Green's formula. As a result, the action of the operators of main problem in the space of state functions is transferred to the adjoint operators defined in the space of sufficiently smooth adjoint functions. By the choice of adjoint functions the order of the derivatives becomes lower by one than those in the original equations. We obtain a set of new balance relationships that take into account the sources and boundary conditions. Next, we introduce the decomposition of the model domain into a set of finite volumes. For multi-dimensional non-stationary problems, this technique is applied in the framework of the variational principle and schemes of decomposition and splitting on the set of physical processes for each coordinate directions successively at each time step. For each direction within the finite volume, the analytical solutions of one-dimensional homogeneous adjoint equations are constructed. In this case, the solutions of adjoint equations serve as integrating factors. The results are the hybrid discrete-analytical schemes. They have the properties of stability, approximation and unconditional monotony for convection-diffusion operators. These schemes are discrete in time and analytic in the spatial variables. They are exact in case of piecewise-constant coefficients within the finite volume and along the coordinate lines of the grid area in each

  12. Conservation laws of inviscid Burgers equation with nonlinear damping

    NASA Astrophysics Data System (ADS)

    Abdulwahhab, Muhammad Alim

    2014-06-01

    In this paper, the new conservation theorem presented in Ibragimov (2007) [14] is used to find conservation laws of the inviscid Burgers equation with nonlinear damping ut+g(u)ux+λh(u)=0. We show that this equation is both quasi self-adjoint and self-adjoint, and use these concepts to simplify conserved quantities for various choices of g(u) and h(u).

  13. The advective-dispersive equation with spatial fractional derivatives as a model for tracer transport in structured soil

    Technology Transfer Automated Retrieval System (TEKTRAN)

    The classical model to describe solute transport in soil is based on the advective-dispersive equation where Fick’s law is used to explain dispersion. From the microscopic point of view this is equivalent to consider that the motion of the particles of solute may be simulated by the Brownian motion....

  14. A space–angle DGFEM approach for the Boltzmann radiation transport equation with local angular refinement

    SciTech Connect

    Kópházi, József Lathouwers, Danny

    2015-09-15

    In this paper a new method for the discretization of the radiation transport equation is presented, based on a discontinuous Galerkin method in space and angle that allows for local refinement in angle where any spatial element can support its own angular discretization. To cope with the discontinuous spatial nature of the solution, a generalized Riemann procedure is required to distinguish between incoming and outgoing contributions of the numerical fluxes. A new consistent framework is introduced that is based on the solution of a generalized eigenvalue problem. The resulting numerical fluxes for the various possible cases where neighboring elements have an equal, higher or lower level of refinement in angle are derived based on tensor algebra and the resulting expressions have a very clear physical interpretation. The choice of discontinuous trial functions not only has the advantage of easing local refinement, it also facilitates the use of efficient sweep-based solvers due to decoupling of unknowns on a large scale thereby approaching the efficiency of discrete ordinates methods with local angular resolution. The approach is illustrated by a series of numerical experiments. Results show high orders of convergence for the scalar flux on angular refinement. The generalized Riemann upwinding procedure leads to stable and consistent solutions. Further the sweep-based solver performs well when used as a preconditioner for a Krylov method.

  15. Phase retrieval in arbitrarily shaped aperture with the transport-of-intensity equation

    NASA Astrophysics Data System (ADS)

    Huang, Lei; Zuo, Chao; Idir, Mourad; Qu, Weijuan; Asundi, Anand

    2015-03-01

    Phase is not easy to detect directly as intensity, but sometimes it contains the really desired information. The transport-of-intensity equation (TIE) is a powerful tool to retrieve the phase from the intensity. However, by considering the boundary energy exchange and the whole energy conversation in the field of view, the current popular Fast Fourier transform (FFT) based TIE solver can only retrieve the phase under homogeneous Neumann boundary condition. For many applications, the boundary condition could be more complex and general. A novel TIE phase retrieval method is proposed to deal with an optical field under a general boundary condition. In this method, an arbitrarily-shape hard aperture is added in the optical field. In our method, the TIE is solved by using iterative discrete cosine transforms (DCT) method, which contains a phase compensation mechanism to improve the retrieval results. The proposed method is verified in simulation with an arbitrary phase, an arbitrarily-shaped aperture, and non-uniform intensity distribution. Experiment is also carried out to check its feasibility and the method proposed in this work is very easy and straightforward to use in a practical measurement as a flexible phase retrieval tool.

  16. A Transport Equation Approach to Modeling the Influence of Surface Roughness on Boundary Layer Transition

    NASA Astrophysics Data System (ADS)

    Langel, Christopher Michael

    A computational investigation has been performed to better understand the impact of surface roughness on the flow over a contaminated surface. This thesis highlights the implementation and development of the roughness amplification model in the flow solver OVERFLOW-2. The model, originally proposed by Dassler, Kozulovic, and Fiala, introduces an additional scalar field roughness amplification quantity. This value is explicitly set at rough wall boundaries using surface roughness parameters and local flow quantities. This additional transport equation allows non-local effects of surface roughness to be accounted for downstream of rough sections. This roughness amplification variable is coupled with the Langtry-Menter model and used to modify the criteria for transition. Results from flat plate test cases show good agreement with experimental transition behavior on the flow over varying sand grain roughness heights. Additional validation studies were performed on a NACA 0012 airfoil with leading edge roughness. The computationally predicted boundary layer development demonstrates good agreement with experimental results. New tests using varying roughness configurations are being carried out at the Texas A&M Oran W. Nicks Low Speed Wind Tunnel to provide further calibration of the roughness amplification method. An overview and preliminary results are provided of this concurrent experimental investigation.

  17. Universal limiter for transient interpolation modeling of the advective transport equations: The ULTIMATE conservative difference scheme

    NASA Technical Reports Server (NTRS)

    Leonard, B. P.

    1988-01-01

    A fresh approach is taken to the embarrassingly difficult problem of adequately modeling simple pure advection. An explicit conservative control-volume formation makes use of a universal limiter for transient interpolation modeling of the advective transport equations. This ULTIMATE conservative difference scheme is applied to unsteady, one-dimensional scalar pure advection at constant velocity, using three critical test profiles: an isolated sine-squared wave, a discontinuous step, and a semi-ellipse. The goal, of course, is to devise a single robust scheme which achieves sharp monotonic resolution of the step without corrupting the other profiles. The semi-ellipse is particularly challenging because of its combination of sudden and gradual changes in gradient. The ULTIMATE strategy can be applied to explicit conservation schemes of any order of accuracy. Second-order schemes are unsatisfactory, showing steepening and clipping typical of currently popular so-called high resolution shock-capturing of TVD schemes. The ULTIMATE third-order upwind scheme is highly satisfactory for most flows of practical importance. Higher order methods give predictably better step resolution, although even-order schemes generate a (monotonic) waviness in the difficult semi-ellipse simulation. Little is to be gained above ULTIMATE fifth-order upwinding which gives results close to the ultimate for which one might hope.

  18. Multi-filter transport of intensity equation solver with equalized noise sensitivity.

    PubMed

    Martinez-Carranza, J; Falaggis, K; Kozacki, T

    2015-09-01

    Phase retrieval based on the Transport of Intensity Equation (TIE) has shown to be a powerful tool to obtain the phase of complex fields. Recently, it has been proven that the performance of TIE techniques can be improved when using unequally spaced measurement planes. In this paper, an algorithm is presented that recovers accurately the phase of a complex objects from a set of intensity measurements obtained at unequal plane separations. This technique employs multiple band-pass filters in the frequency domain of the axial derivative and uses these specific frequency bands for the calculation of the final phase. This provides highest accuracy for TIE based phase recovery giving minimal phase error for a given set of measurement planes. Moreover, because each of these band-pass filters has a distinct sensitivity to noise, a new plane selection strategy is derived that equalizes the error contribution of all frequency bands. It is shown that this new separation strategy allows controlling the final error of the retrieved phase without using a priori information of the object. This is an advantage compared to previous optimum phase retrieval techniques. In order to show the stability and robustness of this new technique, we present the numerical simulations.

  19. Optimal monotonization of a high-order accurate bicompact scheme for the nonstationary multidimensional transport equation

    NASA Astrophysics Data System (ADS)

    Aristova, E. N.; Rogov, B. V.; Chikitkin, A. V.

    2016-06-01

    A hybrid scheme is proposed for solving the nonstationary inhomogeneous transport equation. The hybridization procedure is based on two baseline schemes: (1) a bicompact one that is fourth-order accurate in all space variables and third-order accurate in time and (2) a monotone first-order accurate scheme from the family of short characteristic methods with interpolation over illuminated faces. It is shown that the first-order accurate scheme has minimal dissipation, so it is called optimal. The solution of the hybrid scheme depends locally on the solutions of the baseline schemes at each node of the space-time grid. A monotonization procedure is constructed continuously and uniformly in all mesh cells so as to keep fourth-order accuracy in space and third-order accuracy in time in domains where the solution is smooth, while maintaining a high level of accuracy in domains of discontinuous solution. Due to its logical simplicity and uniformity, the algorithm is well suited for supercomputer simulation.

  20. On the prediction of horizontal bubbly flows using the interfacial area transport equation

    SciTech Connect

    Talley, J. D.; Kim, S.

    2012-07-01

    To solve the two-fluid model utilized in current nuclear reactor system analysis codes, the interfacial area concentration (a i) is estimated through flow regime dependent correlations that rely on static regime transition criteria. This approach does not capture the continuous evolution of the interfacial structures, and thus, it can pose numerical issues near the transition boundaries. The interfacial area transport equation (IATE) can help address these shortcomings by providing a dynamic prediction of a a{sub i} through mechanistic source and sink terms that account for bubble coalescence and breakup. Most of the previous work for this approach has focused on vertical two-phase flow. However, relatively few studies have been performed for horizontal two-phase flows, where buoyancy strongly affects the phase distribution. To develop a one-dimensional, area-averaged form of the IATE for adiabatic, horizontal bubbly flows the following considerations are necessary: (1) pressure drop estimation, (2) bubble velocity/void fraction estimation, (3) determination of bubble interaction mechanisms, and (4) treatment of the asymmetric phase distribution. In the current work, treatment of the asymmetric phase distribution is presented. (authors)

  1. An inexact Newton method for fully-coupled solution of the Navier-Stokes equations with heat and mass transport

    SciTech Connect

    Shadid, J.N.; Tuminaro, R.S.; Walker, H.F.

    1997-02-01

    The solution of the governing steady transport equations for momentum, heat and mass transfer in flowing fluids can be very difficult. These difficulties arise from the nonlinear, coupled, nonsymmetric nature of the system of algebraic equations that results from spatial discretization of the PDEs. In this manuscript the authors focus on evaluating a proposed nonlinear solution method based on an inexact Newton method with backtracking. In this context they use a particular spatial discretization based on a pressure stabilized Petrov-Galerkin finite element formulation of the low Mach number Navier-Stokes equations with heat and mass transport. The discussion considers computational efficiency, robustness and some implementation issues related to the proposed nonlinear solution scheme. Computational results are presented for several challenging CFD benchmark problems as well as two large scale 3D flow simulations.

  2. A criterion of the continuous spectrum for elasticity and other self-adjoint systems on sharp peak-shaped domains*

    NASA Astrophysics Data System (ADS)

    Nazarov, Sergey A.

    2007-12-01

    The spectra of the elasticity and piezo-electricity systems for a solid with a sharp peak point on the boundary, which is free of traction, are not discrete. An algebraic criterion of non-empty continuous spectrum is found for the Neumann problem for rather arbitrary formally self-adjoint elliptic systems of second-order differential equations on a sharp peak-shaped domain. To cite this article: S.A. Nazarov, C. R. Mecanique 335 (2007).

  3. Global Adjoint Tomography: First-Generation Model

    NASA Astrophysics Data System (ADS)

    Bozdağ, Ebru; Peter, Daniel; Lefebvre, Matthieu; Komatitsch, Dimitri; Tromp, Jeroen; Hill, Judith; Podhorszki, Norbert; Pugmire, David

    2016-09-01

    We present the first-generation global tomographic model constructed based on adjoint tomography, an iterative full-waveform inversion technique. Synthetic seismograms were calculated using GPU-accelerated spectral-element simulations of global seismic wave propagation, accommodating effects due to 3D anelastic crust & mantle structure, topography & bathymetry, the ocean load, ellipticity, rotation, and self-gravitation. Fréchet derivatives were calculated in 3D anelastic models based on an adjoint-state method. The simulations were performed on the Cray XK7 named `Titan', a computer with 18,688 GPU accelerators housed at Oak Ridge National Laboratory. The transversely isotropic global model is the result of 15 tomographic iterations, which systematically reduced differences between observed and simulated three-component seismograms. Our starting model combined 3D mantle model S362ANI (Kustowski et al. 2008) with 3D crustal model Crust2.0 (Bassin et al. 2000). We simultaneously inverted for structure in the crust and mantle, thereby eliminating the need for widely used `crustal corrections'. We used data from 253 earthquakes in the magnitude range 5.8~ ≤ ~Mw~ ≤ ~7.0. For the first 12 iterations, we combined ˜30 s body-wave data with ˜60 s surface-wave data. The shortest period of the surface waves was gradually decreased, and in the last three iterations we combined ˜17 s body waves with ˜45 s surface waves. We started using 180 min-long seismograms after the 12th iteration and assimilated minor- and major-arc body and surface waves. The 15th iteration model features enhancements of well-known slabs, an enhanced image of the Samoa/Tahiti plume, as well as various other plumes and hotspots, such as Caroline, Galapagos, Yellowstone, and Erebus. Furthermore, we see clear improvements in slab resolution along the Hellenic and Japan Arcs, as well as subduction along the East of Scotia Plate, which does not exist in the starting model. Point-spread function

  4. Solution of the within-group multidimensional discrete ordinates transport equations on massively parallel architectures

    NASA Astrophysics Data System (ADS)

    Zerr, Robert Joseph

    2011-12-01

    The integral transport matrix method (ITMM) has been used as the kernel of new parallel solution methods for the discrete ordinates approximation of the within-group neutron transport equation. The ITMM abandons the repetitive mesh sweeps of the traditional source iterations (SI) scheme in favor of constructing stored operators that account for the direct coupling factors among all the cells and between the cells and boundary surfaces. The main goals of this work were to develop the algorithms that construct these operators and employ them in the solution process, determine the most suitable way to parallelize the entire procedure, and evaluate the behavior and performance of the developed methods for increasing number of processes. This project compares the effectiveness of the ITMM with the SI scheme parallelized with the Koch-Baker-Alcouffe (KBA) method. The primary parallel solution method involves a decomposition of the domain into smaller spatial sub-domains, each with their own transport matrices, and coupled together via interface boundary angular fluxes. Each sub-domain has its own set of ITMM operators and represents an independent transport problem. Multiple iterative parallel solution methods have investigated, including parallel block Jacobi (PBJ), parallel red/black Gauss-Seidel (PGS), and parallel GMRES (PGMRES). The fastest observed parallel solution method, PGS, was used in a weak scaling comparison with the PARTISN code. Compared to the state-of-the-art SI-KBA with diffusion synthetic acceleration (DSA), this new method without acceleration/preconditioning is not competitive for any problem parameters considered. The best comparisons occur for problems that are difficult for SI DSA, namely highly scattering and optically thick. SI DSA execution time curves are generally steeper than the PGS ones. However, until further testing is performed it cannot be concluded that SI DSA does not outperform the ITMM with PGS even on several thousand or tens of

  5. Transport Equations for CAD Modeling of Al(x)Ga(1-x)N/GaN HEMTs

    NASA Technical Reports Server (NTRS)

    Freeman, Jon C.

    2003-01-01

    BEMTs formed from Al(x)Ga(1-x)N/GaN heterostructures are being investigated for high RF power and efficiency around the world by many groups, both academic and industrial. In these devices, the 2DEG formation is dominated by both spontaneous and piezoelectric polarization fields, with each component having nearly the same order of magnitude. The piezoelectric portion is induced by the mechanical strain in the structure, and to analyze these devices, one must incorporate the stress/strain relationships, along with the standard semiconductor transport equations. These equations for Wurtzite GaN are not easily found in the open literature, hence this paper summarizes them, along with the constitutive equations for piezoelectric materials. The equations are cast into the format for the Wurtzite crystal class, which is the most common way GaN is grown epitaxially.

  6. Green's formula and variational principles for cosmic-ray transport with application to rotating and shearing flows

    NASA Technical Reports Server (NTRS)

    Webb, G. M.; Jokipii, J. R.; Morfill, G. E.

    1994-01-01

    Green's theorem and Green's formula for the diffusive cosmic-ray transport equation in relativistic flows are derived. Green's formula gives the solution of the transport equation in terms of the Green's function of the adjoint transport equation, and in terms of distributed sources throughout the region R of interest, plus terms involving the particle intensity and streaming on the boundary. The adjoint transport equation describes the time-reversed particle transport. An Euler-Lagrange variational principle is then obtained for both the mean scattering frame distribution function f, and its adjoint f(dagger). Variations of the variational functional with respect to f(dagger) yield the transport equation, whereas variations of f yield the adjoint transport equation. The variational principle, when combined with Noether's theorem, yields the conservation law associated with Green's theorem. An investigation of the transport equation for steady, azimuthal, rotating flows suggests the introduction of a new independent variable H to replace the comoving frame momentum variable p'. For the case of rigid rotating flows, H is conserved and is shown to be analogous to the Hamiltonian for a bead on a rigidly rotating wire. The variable H corresponds to a balance between the centrifugal force and the particle inertia in the rotating frame. The physical interpretation of H includes a discussion of nonrelativistic and special relativistic rotating flows as well as the cases of aziuthal, differentially rotating flows about Schwarzs-child and Kerr black holes. Green's formula is then applied to the problem of the acceleration of ultra-high-energy cosmic rays by galactic rotation. The model for galactic rotation assumes an angular velocity law Omega = Omega(sub 0)(omega(sub 0)/omega), where omega denotes radial distance from the axis of rotation. Green's functions for the galactic rotation problem are used to investigate the spectrum of accelerated particles arising from

  7. Green's formula and variational principles for cosmic-ray transport with application to rotating and shearing flows

    NASA Astrophysics Data System (ADS)

    Webb, G. M.; Jokipii, J. R.; Morfill, G. E.

    1994-03-01

    Green's theorem and Green's formula for the diffusive cosmic-ray transport equation in relativistic flows are derived. Green's formula gives the solution of the transport equation in terms of the Green's function of the adjoint transport equation, and in terms of distributed sources throughout the region R of interest, plus terms involving the particle intensity and streaming on the boundary. The adjoint transport equation describes the time-reversed particle transport. An Euler-Lagrange variational principle is then obtained for both the mean scattering frame distribution function f, and its adjoint f(dagger). Variations of the variational functional with respect to f(dagger) yield the transport equation, whereas variations of f yield the adjoint transport equation. The variational principle, when combined with Noether's theorem, yields the conservation law associated with Green's theorem. An investigation of the transport equation for steady, azimuthal, rotating flows suggests the introduction of a new independent variable H to replace the comoving frame momentum variable p'. For the case of rigid rotating flows, H is conserved and is shown to be analogous to the Hamiltonian for a bead on a rigidly rotating wire. The variable H corresponds to a balance between the centrifugal force and the particle inertia in the rotating frame. The physical interpretation of H includes a discussion of nonrelativistic and special relativistic rotating flows as well as the cases of azimuthal, differentially rotating flows about Schwarzs-child and Kerr black holes. Green's formula is then applied to the problem of the acceleration of ultra-high-energy cosmic rays by galactic rotation. The model for galactic rotation assumes an angular velocity law Omega = Omega0(omega0/omega), where omega denotes radial distance from the axis of rotation. Green's functions for the galactic rotation problem are used to investigate the spectrum of accelerated particles arising from monoenergetic and

  8. Baryogenesis via leptogenesis in adjoint SU(5)

    SciTech Connect

    Blanchet, Steve; Fileviez Perez, Pavel E-mail: fileviez@physics.wisc.edu

    2008-08-15

    The possibility of explaining the baryon asymmetry in the Universe through the leptogenesis mechanism in the context of adjoint SU(5) is investigated. In this model neutrino masses are generated through the type I and type III seesaw mechanisms, and the field responsible for the type III seesaw, called {rho}{sub 3}, generates the B-L asymmetry needed to satisfy the observed value of the baryon asymmetry in the Universe. We find that the CP asymmetry originates only from the vertex correction, since the self-energy contribution is not present. When neutrino masses have a normal hierarchy, successful leptogenesis is possible for 10{sup 11} GeV{approx}

  9. Adjoint methods for aerodynamic wing design

    NASA Technical Reports Server (NTRS)

    Grossman, Bernard

    1993-01-01

    A model inverse design problem is used to investigate the effect of flow discontinuities on the optimization process. The optimization involves finding the cross-sectional area distribution of a duct that produces velocities that closely match a targeted velocity distribution. Quasi-one-dimensional flow theory is used, and the target is chosen to have a shock wave in its distribution. The objective function which quantifies the difference between the targeted and calculated velocity distributions may become non-smooth due to the interaction between the shock and the discretization of the flowfield. This paper offers two techniques to resolve the resulting problems for the optimization algorithms. The first, shock-fitting, involves careful integration of the objective function through the shock wave. The second, coordinate straining with shock penalty, uses a coordinate transformation to align the calculated shock with the target and then adds a penalty proportional to the square of the distance between the shocks. The techniques are tested using several popular sensitivity and optimization methods, including finite-differences, and direct and adjoint discrete sensitivity methods. Two optimization strategies, Gauss-Newton and sequential quadratic programming (SQP), are used to drive the objective function to a minimum.

  10. Evaluation of an analytic linear Boltzmann transport equation solver for high-density inhomogeneities

    SciTech Connect

    Lloyd, S. A. M.; Ansbacher, W.

    2013-01-15

    Purpose: Acuros external beam (Acuros XB) is a novel dose calculation algorithm implemented through the ECLIPSE treatment planning system. The algorithm finds a deterministic solution to the linear Boltzmann transport equation, the same equation commonly solved stochastically by Monte Carlo methods. This work is an evaluation of Acuros XB, by comparison with Monte Carlo, for dose calculation applications involving high-density materials. Existing non-Monte Carlo clinical dose calculation algorithms, such as the analytic anisotropic algorithm (AAA), do not accurately model dose perturbations due to increased electron scatter within high-density volumes. Methods: Acuros XB, AAA, and EGSnrc based Monte Carlo are used to calculate dose distributions from 18 MV and 6 MV photon beams delivered to a cubic water phantom containing a rectangular high density (4.0-8.0 g/cm{sup 3}) volume at its center. The algorithms are also used to recalculate a clinical prostate treatment plan involving a unilateral hip prosthesis, originally evaluated using AAA. These results are compared graphically and numerically using gamma-index analysis. Radio-chromic film measurements are presented to augment Monte Carlo and Acuros XB dose perturbation data. Results: Using a 2% and 1 mm gamma-analysis, between 91.3% and 96.8% of Acuros XB dose voxels containing greater than 50% the normalized dose were in agreement with Monte Carlo data for virtual phantoms involving 18 MV and 6 MV photons, stainless steel and titanium alloy implants and for on-axis and oblique field delivery. A similar gamma-analysis of AAA against Monte Carlo data showed between 80.8% and 87.3% agreement. Comparing Acuros XB and AAA evaluations of a clinical prostate patient plan involving a unilateral hip prosthesis, Acuros XB showed good overall agreement with Monte Carlo while AAA underestimated dose on the upstream medial surface of the prosthesis due to electron scatter from the high-density material. Film measurements

  11. Equation of state and transport property measurements of warm dense matter.

    SciTech Connect

    Knudson, Marcus D.; Desjarlais, Michael Paul

    2009-10-01

    Location of the liquid-vapor critical point (c.p.) is one of the key features of equation of state models used in simulating high energy density physics and pulsed power experiments. For example, material behavior in the location of the vapor dome is critical in determining how and when coronal plasmas form in expanding wires. Transport properties, such as conductivity and opacity, can vary an order of magnitude depending on whether the state of the material is inside or outside of the vapor dome. Due to the difficulty in experimentally producing states near the vapor dome, for all but a few materials, such as Cesium and Mercury, the uncertainty in the location of the c.p. is of order 100%. These states of interest can be produced on Z through high-velocity shock and release experiments. For example, it is estimated that release adiabats from {approx}1000 GPa in aluminum would skirt the vapor dome allowing estimates of the c.p. to be made. This is within the reach of Z experiments (flyer plate velocity of {approx}30 km/s). Recent high-fidelity EOS models and hydrocode simulations suggest that the dynamic two-phase flow behavior observed in initial scoping experiments can be reproduced, providing a link between theory and experiment. Experimental identification of the c.p. in aluminum would represent the first measurement of its kind in a dynamic experiment. Furthermore, once the c.p. has been experimentally determined it should be possible to probe the electrical conductivity, opacity, reflectivity, etc. of the material near the vapor dome, using a variety of diagnostics. We propose a combined experimental and theoretical investigation with the initial emphasis on aluminum.

  12. A generalized Clebsch transformation leading to a first integral of Navier-Stokes equations

    NASA Astrophysics Data System (ADS)

    Scholle, M.; Marner, F.

    2016-09-01

    In fluid dynamics, the Clebsch transformation allows for the construction of a first integral of the equations of motion leading to a self-adjoint form of the equations. A remarkable feature is the description of the vorticity by means of only two potential fields fulfilling simple transport equations. Despite useful applications in fluid dynamics and other physical disciplines as well, the classical Clebsch transformation has ever been restricted to inviscid flow. In the present paper a novel, generalized Clebsch transformation is developed which also covers the case of incompressible viscous flow. The resulting field equations are discussed briefly and solved for a flow example. Perspectives for a further extension of the method as well as perspectives towards the development of new solution strategies are presented.

  13. Application of the three-dimensional telegraph equation to cosmic-ray transport

    NASA Astrophysics Data System (ADS)

    Tautz, Robert C.; Lerche, Ian

    2016-10-01

    An analytical solution to the three-dimensional telegraph equation is presented. This equation has recently received some attention but so far the treatment has been one-dimensional. By using the structural similarity to the Klein-Gordon equation, the telegraph equation can be solved in closed form. Illustrative examples are used to discuss the qualitative differences from the diffusion solution. A comparison with a numerical test-particle simulation reveals that some features of an intensity profile can be better explained using the telegraph approach.

  14. Analytical sensitivity analysis of transient groundwater flow in a bounded model domain using the adjoint method

    NASA Astrophysics Data System (ADS)

    Lu, Zhiming; Vesselinov, Velimir V.

    2015-07-01

    Sensitivity analyses are an important component of any modeling exercise. We have developed an analytical methodology based on the adjoint method to compute sensitivities of a state variable (hydraulic head) to model parameters (hydraulic conductivity and storage coefficient) for transient groundwater flow in a confined and randomly heterogeneous aquifer under ambient and pumping conditions. For a special case of two-dimensional rectangular domains, these sensitivities are represented in terms of the problem configuration (the domain size, boundary configuration, medium properties, pumping schedules and rates, and observation locations and times), and there is no need to actually solve the adjoint equations. As an example, we present analyses of the obtained solution for typical groundwater flow conditions. Analytical solutions allow us to calculate sensitivities efficiently, which can be useful for model-based analyses such as parameter estimation, data-worth evaluation, and optimal experimental design related to sampling frequency and locations of observation wells. The analytical approach is not limited to groundwater applications but can be extended to any other mathematical problem with similar governing equations and under similar conceptual conditions.

  15. A user's manual for MASH 1. 0: A Monte Carlo Adjoint Shielding Code System

    SciTech Connect

    Johnson, J.O.

    1992-03-01

    The Monte Carlo Adjoint Shielding Code System, MASH, calculates neutron and gamma-ray environments and radiation protection factors for armored military vehicles, structures, trenches, and other shielding configurations by coupling a forward discrete ordinates air-over-ground transport calculation with an adjoint Monte Carlo treatment of the shielding geometry. Efficiency and optimum use of computer time are emphasized. The code system include the GRTUNCL and DORT codes for air-over-ground transport calculations, the MORSE code with the GIFT5 combinatorial geometry package for adjoint shielding calculations, and several peripheral codes that perform the required data preparations, transformations, and coupling functions. MASH is the successor to the Vehicle Code System (VCS) initially developed at Oak Ridge National Laboratory (ORNL). The discrete ordinates calculation determines the fluence on a coupling surface surrounding the shielding geometry due to an external neutron/gamma-ray source. The Monte Carlo calculation determines the effectiveness of the fluence at that surface in causing a response in a detector within the shielding geometry, i.e., the dose importance'' of the coupling surface fluence. A coupling code folds the fluence together with the dose importance, giving the desired dose response. The coupling code can determine the dose response a a function of the shielding geometry orientation relative to the source, distance from the source, and energy response of the detector. This user's manual includes a short description of each code, the input required to execute the code along with some helpful input data notes, and a representative sample problem (input data and selected output edits) for each code.

  16. Charged-particle transport in gases in electric and magnetic fields crossed at arbitrary angles: Multiterm solution of Boltzmann's equation.

    PubMed

    White, R D; Ness, K F; Robson, R E; Li, B

    1999-08-01

    A multiterm solution of the Boltzmann equation has been developed and used to calculate transport coefficients of charged-particle swarms in gases under the influence of electric and magnetic fields crossed at arbitrary angles psi. The hierarchy resulting from a spherical harmonic decomposition of the Boltzmann equation in the hydrodynamic regime [Ness, Phys. Rev. A 47, 327 (1993)] is solved numerically by representing the speed dependence of the phase-space distribution function in terms of an expansion in Sonine polynomials about a weighted sum of Maxwellian distributions at different temperatures. Results are given for charged-particle swarms in certain model gases over a range of psi and field strengths. The variation of the transport coefficients with psi is addressed using physical arguments. The errors associated with the two-term approximation and inadequacies of Legendre polynomial expansions are highlighted.

  17. Quantitative TEM-based phase retrieval of MgO nano-cubes using the transport of intensity equation.

    PubMed

    Petersen, Tim C; Keast, Vicki J; Paganin, David M

    2008-08-01

    Through focus series of images are collected from MgO nano-cube crystals in the transmission electron microscope (TEM). The experimental data is used to solve the transport of intensity equation (TIE) to retrieve phase maps, which portray the morphology of the cubes and are quantified by the mean inner potential V(0). Particular attention is given to the practical difficulties associated with TIE phase retrieval of non-conducting polyhedron particles.

  18. Kershaw closures for linear transport equations in slab geometry II: High-order realizability-preserving discontinuous-Galerkin schemes

    NASA Astrophysics Data System (ADS)

    Schneider, Florian

    2016-10-01

    This paper provides a generalization of the realizability-preserving discontinuous-Galerkin scheme given in [3] to general full-moment models that can be closed analytically. It is applied to the class of Kershaw closures, which are able to provide a cheap closure of the moment problem. This results in an efficient algorithm for the underlying linear transport equation. The efficiency of high-order methods is demonstrated using numerical convergence tests and non-smooth benchmark problems.

  19. Determination of transport wind speed in the gaussian plume diffusion equation for low-lying point sources

    NASA Astrophysics Data System (ADS)

    Wang, I. T.

    A general method for determining the effective transport wind speed, overlineu, in the Gaussian plume equation is discussed. Physical arguments are given for using the generalized overlineu instead of the often adopted release-level wind speed with the plume diffusion equation. Simple analytical expressions for overlineu applicable to low-level point releases and a wide range of atmospheric conditions are developed. A non-linear plume kinematic equation is derived using these expressions. Crosswind-integrated SF 6 concentration data from the 1983 PNL tracer experiment are used to evaluate the proposed analytical procedures along with the usual approach of using the release-level wind speed. Results of the evaluation are briefly discussed.

  20. A Spatial Discretization Scheme for Solving the Transport Equation on Unstructured Grids of Polyhedra

    SciTech Connect

    Thompson, K.G.

    2000-11-01

    In this work, we develop a new spatial discretization scheme that may be used to numerically solve the neutron transport equation. This new discretization extends the family of corner balance spatial discretizations to include spatial grids of arbitrary polyhedra. This scheme enforces balance on subcell volumes called corners. It produces a lower triangular matrix for sweeping, is algebraically linear, is non-negative in a source-free absorber, and produces a robust and accurate solution in thick diffusive regions. Using an asymptotic analysis, we design the scheme so that in thick diffusive regions it will attain the same solution as an accurate polyhedral diffusion discretization. We then refine the approximations in the scheme to reduce numerical diffusion in vacuums, and we attempt to capture a second order truncation error. After we develop this Upstream Corner Balance Linear (UCBL) discretization we analyze its characteristics in several limits. We complete a full diffusion limit analysis showing that we capture the desired diffusion discretization in optically thick and highly scattering media. We review the upstream and linear properties of our discretization and then demonstrate that our scheme captures strictly non-negative solutions in source-free purely absorbing media. We then demonstrate the minimization of numerical diffusion of a beam and then demonstrate that the scheme is, in general, first order accurate. We also note that for slab-like problems our method actually behaves like a second-order method over a range of cell thicknesses that are of practical interest. We also discuss why our scheme is first order accurate for truly 3D problems and suggest changes in the algorithm that should make it a second-order accurate scheme. Finally, we demonstrate 3D UCBL's performance on several very different test problems. We show good performance in diffusive and streaming problems. We analyze truncation error in a 3D problem and demonstrate robustness in a

  1. A Reynolds-averaged turbulence modeling approach using three transport equations for the turbulent viscosity, kinetic energy, and dissipation rate

    NASA Astrophysics Data System (ADS)

    Yoshizawa, Akira; Abe, Hiroyuki; Matsuo, Yuichi; Fujiwara, Hitoshi; Mizobuchi, Yasuhiro

    2012-07-01

    A Reynolds-averaged approach to turbulent shear flows is sought with resort to a three-equation method. Its novelty is the introduction of a turbulent-viscosity transport equation through the transport equation for the Reynolds stress in addition to those for the turbulent kinetic energy and the dissipation rate. The latter two equations are used for evaluating the dimensional coefficients in the former. The aim of this model is to enhance the capability to cope with nonstationary and advection effects in various turbulent flows. The adaptability to them is confirmed through the application to homogeneous-shear and supersonic free-shear flows. In particular, the reasonable prediction is obtained in the latter where the growth rate of the shear layer is suppressed with the increase in the convective Mach number. The present model is also applied to a three-dimensional flow past a wing tip as an instance of complex aeronautical flows, and the excessive diffusion of the trailing vortices is shown to be suppressed. The turbulent-viscosity representation for the Reynolds stress is systematically supplemented with nonlinear effects of mean-velocity gradient tensors, and its adequacy is verified in a channel flow.

  2. Thermoelectric coefficients of n -doped silicon from first principles via the solution of the Boltzmann transport equation

    NASA Astrophysics Data System (ADS)

    Fiorentini, Mattia; Bonini, Nicola

    2016-08-01

    We present a first-principles computational approach to calculate thermoelectric transport coefficients via the exact solution of the linearized Boltzmann transport equation, also including the effect of nonequilibrium phonon populations induced by a temperature gradient. We use density functional theory and density functional perturbation theory for an accurate description of the electronic and vibrational properties of a system, including electron-phonon interactions; carriers' scattering rates are computed using standard perturbation theory. We exploit Wannier interpolation (both for electronic bands and electron-phonon matrix elements) for an efficient sampling of the Brillouin zone, and the solution of the Boltzmann equation is achieved via a fast and stable conjugate gradient scheme. We discuss the application of this approach to n -doped silicon. In particular, we discuss a number of thermoelectric properties such as the thermal and electrical conductivities of electrons, the Lorenz number and the Seebeck coefficient, including the phonon drag effect, in a range of temperatures and carrier concentrations. This approach gives results in good agreement with experimental data and provides a detailed characterization of the nature and the relative importance of the individual scattering mechanisms. Moreover, the access to the exact solution of the Boltzmann equation for a realistic system provides a direct way to assess the accuracy of different flavors of relaxation time approximation, as well as of models that are popular in the thermoelectric community to estimate transport coefficients.

  3. Macroscopic transport equations in many-body systems from microscopic exclusion processes in disordered media: a review

    NASA Astrophysics Data System (ADS)

    Galanti, Marta; Fanelli, Duccio; Piazza, Francesco

    2016-08-01

    Describing particle transport at the macroscopic or mesoscopic level in non-ideal environments poses fundamental theoretical challenges in domains ranging from inter and intra-cellular transport in biology to diffusion in porous media. Yet, often the nature of the constraints coming from many-body interactions or reflecting a complex and confining environment are better understood and modeled at the microscopic level. In this paper we review the subtle link between microscopic exclusion processes and the mean-field equations that ensue from them in the continuum limit. We show that in an inhomogeneous medium, i.e. when jumps are controlled by site-dependent hopping rates, one can obtain three different nonlinear advection-diffusion equations in the continuum limit, suitable for describing transport in the presence of quenched disorder and external fields, depending on the particular rule embodying site inequivalence at the microscopic level. In a situation that might be termed point-like scenario, when particles are treated as point-like objects, the effect of crowding as imposed at the microscopic level manifests in the mean-field equations only if some degree of inhomogeneity is enforced into the model. Conversely, when interacting agents are assigned a finite size, under the more realistic extended crowding framework, exclusion constraints persist in the unbiased macroscopic representation.

  4. Adjoint free four-dimensional variational data assimilation for a storm surge model of the German North Sea

    NASA Astrophysics Data System (ADS)

    Zheng, Xiangyang; Mayerle, Roberto; Xing, Qianguo; Fernández Jaramillo, José Manuel

    2016-08-01

    In this paper, a data assimilation scheme based on the adjoint free Four-Dimensional Variational(4DVar) method is applied to an existing storm surge model of the German North Sea. To avoid the need of an adjoint model, an ensemble-like method to explicitly represent the linear tangent equation is adopted. Results of twin experiments have shown that the method is able to recover the contaminated low dimension model parameters to their true values. The data assimilation scheme was applied to a severe storm surge event which occurred in the North Sea in December 5, 2013. By adjusting wind drag coefficient, the predictive ability of the model increased significantly. Preliminary experiments have shown that an increase in the predictive ability is attained by narrowing the data assimilation time window.

  5. Investigating transport capacity equations in sediment yield modelling for the Cariri semi-arid region of Paraiba-PB/Brazil

    NASA Astrophysics Data System (ADS)

    De Figueiredo, E. E.; Souto, C. C. R. A.; Vieira, Z. C.

    2015-03-01

    In the semi arid Cariri region of the state of Paraiba, Brazil, runoff is of the Hortonian type generated by excess of rainfall over infiltration capacity, and soil erosion is governed by rainfall intensity and sediment size. However, the governing sediment transport mechanism is not well understood. Sediment transport generally depends on the load of sediment provided by soil erosion and on the transport capacity of the flow. The latter is mainly governed by mechanisms such as water shear stress, or stream power. Accordingly, the load of sediment transported by the flow may vary depending on the mechanism involved in the equation of estimation. Investigation of the sediment transport capacity of the flow via a distributed physically-based model is an important and necessary task, but quite rare in semi-arid climates, and particularly in the Cariri region of the state of Paraíba/Brazil. In this study, the equations of Yalin, Engelund & Hansen, Laursen, DuBoys and Bagnold have been coupled with the MOSEE distributed physically based model aiming at identifying the mechanisms leading to the best model simulations when compared with data observed at various basin scales and land uses in the study region. The results obtained with the investigated methods were quite similar and satisfactory suggesting the feasibility of the mechanisms involved, but the observed values were better represented with Bagnold's equation, which is physically grounded on the stream power, and we recommend it for simulations of similar climate, runoff generation mechanisms and sediment characteristics as in the study region.

  6. Adaptively Learning an Importance Function Using Transport Constrained Monte Carlo

    SciTech Connect

    Booth, T.E.

    1998-06-22

    It is well known that a Monte Carlo estimate can be obtained with zero-variance if an exact importance function for the estimate is known. There are many ways that one might iteratively seek to obtain an ever more exact importance function. This paper describes a method that has obtained ever more exact importance functions that empirically produce an error that is dropping exponentially with computer time. The method described herein constrains the importance function to satisfy the (adjoint) Boltzmann transport equation. This constraint is provided by using the known form of the solution, usually referred to as the Case eigenfunction solution.

  7. Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers

    NASA Technical Reports Server (NTRS)

    Reuther, James; Jameson, Antony; Alonso, Juan Jose; Rimlinger, Mark J.; Saunders, David

    1997-01-01

    An aerodynamic shape optimization method that treats the design of complex aircraft configurations subject to high fidelity computational fluid dynamics (CFD), geometric constraints and multiple design points is described. The design process will be greatly accelerated through the use of both control theory and distributed memory computer architectures. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on a higher order CFD method. In order to facilitate the integration of these high fidelity CFD approaches into future multi-disciplinary optimization (NW) applications, new methods must be developed which are capable of simultaneously addressing complex geometries, multiple objective functions, and geometric design constraints. In our earlier studies, we coupled the adjoint based design formulations with unconstrained optimization algorithms and showed that the approach was effective for the aerodynamic design of airfoils, wings, wing-bodies, and complex aircraft configurations. In many of the results presented in these earlier works, geometric constraints were satisfied either by a projection into feasible space or by posing the design space parameterization such that it automatically satisfied constraints. Furthermore, with the exception of reference 9 where the second author initially explored the use of multipoint design in conjunction with adjoint formulations, our earlier works have focused on single point design efforts. Here we demonstrate that the same methodology may be extended to treat

  8. A one-equation turbulence transport model for high Reynolds number wall-bounded flows

    NASA Technical Reports Server (NTRS)

    Baldwin, Barrett S.; Barth, Timothy J.

    1990-01-01

    A one-equation turbulence model that avoids the need for an algebraic length scale is derived from a simplified form of the standard k-epsilon model equations. After calibration based on well established properties of the flow over a flat plate, predictions of several other flows are compared with experiment. The preliminary results presented indicate that the model has predictive and numerical properties of sufficient interest to merit further investigation and refinement. The one-equation model is also analyzed numerically and robust solution methods are presented.

  9. 3D Multigroup Sn Neutron Transport Code

    2001-02-14

    ATTILA is a 3D multigroup transport code with arbitrary order ansotropic scatter. The transport equation is solved in first order form using a tri-linear discontinuous spatial differencing on an arbitrary tetrahedral mesh. The overall solution technique is source iteration with DSA acceleration of the scattering source. Anisotropic boundary and internal sources may be entered in the form of spherical harmonics moments. Alpha and k eigenvalue problems are allowed, as well as fixed source problems. Forwardmore » and adjoint solutions are available. Reflective, vacumn, and source boundary conditions are available. ATTILA can perform charged particle transport calculations using slowing down (CSD) terms. ATTILA can also be used to peform infra-red steady-state calculations for radiative transfer purposes.« less

  10. Towards adjoint-based inversion for rheological parameters in nonlinear viscous mantle flow

    NASA Astrophysics Data System (ADS)

    Worthen, Jennifer; Stadler, Georg; Petra, Noemi; Gurnis, Michael; Ghattas, Omar

    2014-09-01

    We address the problem of inferring mantle rheological parameter fields from surface velocity observations and instantaneous nonlinear mantle flow models. We formulate this inverse problem as an infinite-dimensional nonlinear least squares optimization problem governed by nonlinear Stokes equations. We provide expressions for the gradient of the cost functional of this optimization problem with respect to two spatially-varying rheological parameter fields: the viscosity prefactor and the exponent of the second invariant of the strain rate tensor. Adjoint (linearized) Stokes equations, which are characterized by a 4th order anisotropic viscosity tensor, facilitates efficient computation of the gradient. A quasi-Newton method for the solution of this optimization problem is presented, which requires the repeated solution of both nonlinear forward Stokes and linearized adjoint Stokes equations. For the solution of the nonlinear Stokes equations, we find that Newton’s method is significantly more efficient than a Picard fixed point method. Spectral analysis of the inverse operator given by the Hessian of the optimization problem reveals that the numerical eigenvalues collapse rapidly to zero, suggesting a high degree of ill-posedness of the inverse problem. To overcome this ill-posedness, we employ Tikhonov regularization (favoring smooth parameter fields) or total variation (TV) regularization (favoring piecewise-smooth parameter fields). Solution of two- and three-dimensional finite element-based model inverse problems show that a constant parameter in the constitutive law can be recovered well from surface velocity observations. Inverting for a spatially-varying parameter field leads to its reasonable recovery, in particular close to the surface. When inferring two spatially varying parameter fields, only an effective viscosity field and the total viscous dissipation are recoverable. Finally, a model of a subducting plate shows that a localized weak zone at the

  11. An Adjoint-Based Analysis of the Sampling Footprints of Tall Tower, Aircraft and Potential Future Lidar Observations of CO2

    NASA Technical Reports Server (NTRS)

    Andrews, Arlyn; Kawa, Randy; Zhu, Zhengxin; Burris, John; Abshire, Jim

    2004-01-01

    A detailed mechanistic understanding of the sources and sinks of CO2 will be required to reliably predict future CO2 levels and climate. A commonly used technique for deriving information about CO2 exchange with surface reservoirs is to solve an 'inverse problem', where CO2 observations are used with an atmospheric transport model to find the optimal distribution of sources and sinks. Synthesis inversion methods are powerful tools for addressing this question, but the results are disturbingly sensitive to the details of the calculation. Studies done using different atmospheric transport models and combinations of surface station data have produced substantially different distributions of surface fluxes. Adjoint methods are now being developed that will more effectively incorporate diverse datasets in estimates of surface fluxes of CO2. In an adjoint framework, it will be possible to combine CO2 concentration data from longterm surface and aircraft monitoring stations with data from intensive field campaigns and with proposed future satellite observations. We have recently developed an adjoint for the GSFC 3-D Parameterized Chemistry and Transport Model (PCTM). Here, we will present results from a PCTM Adjoint study comparing the sampling footprints of tall tower, aircraft and potential future lidar observations of CO2. The vertical resolution and extent of the profiles and the observation frequency will be considered for several sites in North America.

  12. Influence of surface water/groundwater interactions on stream and wetland water quality: analytical solutions for coupled contaminant transport equations

    NASA Astrophysics Data System (ADS)

    Melek Kazezyilmaz-Alhan, Cevza

    2014-05-01

    Wetlands are located in transitional zones between uplands and downstream flooded systems and surface water/groundwater interactions are frequently observed especially in riparian wetlands where the water level fluctuates frequently during the rainy season. Moreover, surface water/groundwater interactions also influence the characteristics of contaminant transport in pools and riffles, and in meandering type of streams. Therefore, it is important to investigate and solve these processes accurately to improve the prediction of downstream water quality. Although there are many experimental and numerical studies available in the literature which discuss and model the surface water/ground water interactions in streams and wetlands, very few analytical solutions have been conducted. Analytical solutions are helpful tools for verification of numerical solutions and they provide fast and accurate results for practical problems. Furthermore, they provide an understanding to the influence of each parameter in hydrological and contaminant transport models for streams and wetlands. In order to contribute to the research in understanding the behavior of water quality in streams and wetlands, analytical solutions are developed for the coupled contaminant transport equations of several transient storage and wetland models. Among these models are the wetland model WETland Solute TrANsport Dynamics (WETSAND) developed by Kazezyilmaz-Alhan et al. (2007), the transient storage models developed by Bencala and Walters (1983), and Kazezyilmaz-Alhan and Medina (2006). WETSAND is a general comprehensive wetland model, which has both surface flow and solute transport components. In this wetland model, water quality components are solved by advection-dispersion-reaction equations which incorporate surface water/groundwater interactions by including the incoming/outgoing mass due to the groundwater recharge/discharge. The transient storage model developed by Bencala and Walters (1983

  13. Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry

    NASA Technical Reports Server (NTRS)

    Nemec, Marian; Aftosmis,Michael J.

    2006-01-01

    Cartesian-mesh methods are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric Computer-Aided Design (CAD) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm included the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach

  14. Predictions of Separated and Transitional Boundary Layers Under Low-Pressure Turbine Airfoil Conditions Using an Intermittency Transport Equation

    NASA Technical Reports Server (NTRS)

    Suzen, Y. B.; Huang, P. G.; Hultgren, Lennart S.; Ashpis, David E.

    2003-01-01

    A new transport equation for the intermittency factor was proposed to predict separated and transitional boundary layers under low-pressure turbine airfoil conditions. The intermittent behavior of the transitional flows is taken into account and incorporated into computations by modifying the eddy viscosity, t , with the intermittency factor, y. Turbulent quantities are predicted by using Menter s two-equation turbulence model (SST). The intermittency factor is obtained from a transport equation model, which not only can reproduce the experimentally observed streamwise variation of the intermittency in the transition zone, but also can provide a realistic cross-stream variation of the intermittency profile. In this paper, the intermittency model is used to predict a recent separated and transitional boundary layer experiment under low pressure turbine airfoil conditions. The experiment provides detailed measurements of velocity, turbulent kinetic energy and intermittency profiles for a number of Reynolds numbers and freestream turbulent intensity conditions and is suitable for validation purposes. Detailed comparisons of computational results with experimental data are presented and good agreements between the experiments and predictions are obtained.

  15. Implementation of the LAX-Wendroff Method in Cobra-TF for Solving Two-Phase Flow Transport Equations

    SciTech Connect

    Salko, Robert K; Wang, Dean; Ren, Kangyu

    2016-01-01

    COBRA-TF (Coolant Boiling in Rod Arrays Two Fluid), or CTF, is a subchannel code used to conduct the reactor core thermal hydraulic (T/H) solution in both standalone and coupled multi-physics applications. CTF applies the first-order upwind spatial discretization scheme for solving two-phase flow conservation equations. In this work, the second-order Lax-Wendroff (L-W) scheme has been implemented in CTF to solve the two-phase flow transport equations to improve numerical accuracy in both temporal and spatial discretization. To avoid the oscillation issue, a non-linear flux limiter VA (Van Albada) is employed for the convective terms in the transport equations. Assessments have been carried out to evaluate the performance and stability of the implemented second-order L-W scheme. It has been found that the L-W scheme performs better than the upwind scheme for the single-phase and two-phase flow problems in terms of numerical accuracy and computational efficiency.

  16. Transport solutions of the Lamé equations and shock elastic waves

    NASA Astrophysics Data System (ADS)

    Alexeyeva, L. A.; Kaishybaeva, G. K.

    2016-07-01

    The Lamé system describing the dynamics of an isotropic elastic medium affected by a steady transport load moving at subsonic, transonic, or supersonic speed is considered. Its fundamental and generalized solutions in a moving frame of reference tied to the transport load are analyzed. Shock waves arising in the medium at supersonic speeds are studied. Conditions on the jump in the stress, displacement rate, and energy across the shock front are obtained using distribution theory. Numerical results concerning the dynamics of an elastic medium influenced by concentrated transport loads moving at sub-, tran- and supersonic speeds are presented.

  17. Ocean acoustic tomography from different receiver geometries using the adjoint method.

    PubMed

    Zhao, Xiaofeng; Wang, Dongxiao

    2015-12-01

    In this paper, an ocean acoustic tomography inversion using the adjoint method in a shallow water environment is presented. The propagation model used is an implicit Crank-Nicolson finite difference parabolic equation solver with a non-local boundary condition. Unlike previous matched-field processing works using the complex pressure fields as the observations, here, the observed signals are the transmission losses. Based on the code tests of the tangent linear model, the adjoint model, and the gradient, the optimization problem is solved by a gradient-based minimization algorithm. The inversions are performed in numerical simulations for two geometries: one in which hydrophones are sparsely distributed in the horizontal direction, and another in which the hydrophones are distributed vertically. The spacing in both cases is well beyond the half-wavelength threshold at which beamforming could be used. To deal with the ill-posedness of the inverse problem, a linear differential regularization operator of the sound-speed profile is used to smooth the inversion results. The L-curve criterion is adopted to select the regularization parameter, and the optimal value can be easily determined at the elbow of the logarithms of the residual norm of the measured-predicted fields and the norm of the penalty function.

  18. Adjoint Optimization of Multistage Axial Compressor Blades with Static Pressure Constraint at Blade Row Interface

    NASA Astrophysics Data System (ADS)

    Yu, Jia; Ji, Lucheng; Li, Weiwei; Yi, Weilin

    2016-06-01

    Adjoint method is an important tool for design refinement of multistage compressors. However, the radial static pressure distribution deviates during the optimization procedure and deteriorates the overall performance, producing final designs that are not well suited for realistic engineering applications. In previous development work on multistage turbomachinery blade optimization using adjoint method and thin shear-layer N-S equations, the entropy production is selected as the objective function with given mass flow rate and total pressure ratio as imposed constraints. The radial static pressure distribution at the interfaces between rows is introduced as a new constraint in the present paper. The approach is applied to the redesign of a five-stage axial compressor, and the results obtained with and without the constraint on the radial static pressure distribution at the interfaces between rows are discussed in detail. The results show that the redesign without the radial static pressure distribution constraint (RSPDC) gives an optimal solution that shows deviations on radial static pressure distribution, especially at rotor exit tip region. On the other hand, the redesign with the RSPDC successfully keeps the radial static pressure distribution at the interfaces between rows and make sure that the optimization results are applicable in a practical engineering design.

  19. The nature and role of advection in advection-diffusion equations used for modelling bed load transport

    NASA Astrophysics Data System (ADS)

    Ancey, Christophe; Bohorquez, Patricio; Heyman, Joris

    2016-04-01

    The advection-diffusion equation arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Stochastic models can also be used to derive this equation, with the significant advantage that they provide information on the statistical properties of particle activity. Stochastic models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. We develop an approach based on birth-death Markov processes, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received little attention. We show that particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particle velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due to velocity fluctuations), with the important consequence that local measurements depend on both the intrinsic properties of particle displacement and the dimensions of the measurement system.

  20. Non-self-adjoint hamiltonians defined by Riesz bases

    SciTech Connect

    Bagarello, F.; Inoue, A.; Trapani, C.

    2014-03-15

    We discuss some features of non-self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a Riesz basis of Hilbert space. Among other things, we give conditions under which these Hamiltonians can be factorized in terms of generalized lowering and raising operators.

  1. Assimilating Remote Ammonia Observations with a Refined Aerosol Thermodynamics Adjoint"

    EPA Science Inventory

    Ammonia emissions parameters in North America can be refined in order to improve the evaluation of modeled concentrations against observations. Here, we seek to do so by developing and applying the GEOS-Chem adjoint nested over North America to conductassimilation of observations...

  2. Higher-order approximation of contaminant transport equation for turbulent channel flows based on centre manifolds and its numerical solution

    NASA Astrophysics Data System (ADS)

    Ngo-Cong, D.; Mohammed, F. J.; Strunin, D. V.; Skvortsov, A. T.; Mai-Duy, N.; Tran-Cong, T.

    2015-06-01

    The contaminant transport process governed by the advection-diffusion equation plays an important role in modelling industrial and environmental flows. In this article, our aim is to accurately reduce the 2-D advection-diffusion equation governing the dispersion of a contaminant in a turbulent open channel flow to its 1-D approximation. The 1-D model helps to quickly estimate the horizontal size of contaminant clouds based on the values of the model coefficients. We derive these coefficients analytically and investigate numerically the model convergence. The derivation is based on the centre manifold theory to obtain successively more accurate approximations in a consistent manner. Two types of the average velocity profile are considered: the classical logarithmic profile and the power profile. We further develop the one-dimensional integrated radial basis function network method as a numerical approach to obtain the numerical solutions to both the original 2-D equation and the approximate 1-D equations. We compare the solutions of the original models with their centre-manifold approximations at very large Reynolds numbers. The numerical results obtained from the approximate 1-D models are in good agreement with those of the original 2-D model for both the logarithmic and power velocity profiles.

  3. Bombardment induced ion transport. Part I: Numerical investigation of bombardment induced ion transport through glasses and membranes on the basis of the Nernst-Planck-Poisson equations.

    PubMed

    Schäfer, M; Weitzel, K-M

    2011-12-01

    The bombardment of condensed matter by low energy ion beams induces ion transport through the material. A general theory for bombardment induced ion transport (BIIT) based on numerical solutions of the well known Nernst-Planck-Poisson equations is presented. The theory is applicable to polymer membranes as well as ion-conducting glasses with the implementation of appropriate boundary conditions. The fundamental properties of the theory, i.e. the capability to describe the potential, the field and the concentration/charge density profile within the two classes of materials mentioned above are demonstrated. In particular, the theory is capable of describing experimental observables which will be further elaborated in part II of this miniseries.

  4. Transport Equation Based Wall Distance Computations Aimed at Flows With Time-Dependent Geometry

    NASA Technical Reports Server (NTRS)

    Tucker, Paul G.; Rumsey, Christopher L.; Bartels, Robert E.; Biedron, Robert T.

    2003-01-01

    Eikonal, Hamilton-Jacobi and Poisson equations can be used for economical nearest wall distance computation and modification. Economical computations may be especially useful for aeroelastic and adaptive grid problems for which the grid deforms, and the nearest wall distance needs to be repeatedly computed. Modifications are directed at remedying turbulence model defects. For complex grid structures, implementation of the Eikonal and Hamilton-Jacobi approaches is not straightforward. This prohibits their use in industrial CFD solvers. However, both the Eikonal and Hamilton-Jacobi equations can be written in advection and advection-diffusion forms, respectively. These, like the Poisson s Laplacian, are commonly occurring industrial CFD solver elements. Use of the NASA CFL3D code to solve the Eikonal and Hamilton-Jacobi equations in advective-based forms is explored. The advection-based distance equations are found to have robust convergence. Geometries studied include single and two element airfoils, wing body and double delta configurations along with a complex electronics system. It is shown that for Eikonal accuracy, upwind metric differences are required. The Poisson approach is found effective and, since it does not require offset metric evaluations, easiest to implement. The sensitivity of flow solutions to wall distance assumptions is explored. Generally, results are not greatly affected by wall distance traits.

  5. Transport Equation Based Wall Distance Computations Aimed at Flows With Time-Dependent Geometry

    NASA Technical Reports Server (NTRS)

    Tucker, Paul G.; Rumsey, Christopher L.; Bartels, Robert E.; Biedron, Robert T.

    2003-01-01

    Eikonal, Hamilton-Jacobi and Poisson equations can be used for economical nearest wall distance computation and modification. Economical computations may be especially useful for aeroelastic and adaptive grid problems for which the grid deforms, and the nearest wall distance needs to be repeatedly computed. Modifications are directed at remedying turbulence model defects. For complex grid structures, implementation of the Eikonal and Hamilton-Jacobi approaches is not straightforward. This prohibits their use in industrial CFD solvers. However, both the Eikonal and Hamilton-Jacobi equations can be written in advection and advection-diffusion forms, respectively. These, like the Poisson's Laplacian, are commonly occurring industrial CFD solver elements. Use of the NASA CFL3D code to solve the Eikonal and Hamilton-Jacobi equations in advective-based forms is explored. The advection-based distance equations are found to have robust convergence. Geometries studied include single and two element airfoils, wing body and double delta configurations along with a complex electronics system. It is shown that for Eikonal accuracy, upwind metric differences are required. The Poisson approach is found effective and, since it does not require offset metric evaluations, easiest to implement. The sensitivity of flow solutions to wall distance assumptions is explored. Generally, results are not greatly affected by wall distance traits.

  6. Generalized semi-analytical solutions to multispecies transport equation coupled with sequential first-order reaction network with spatially or temporally variable transport and decay coefficients

    NASA Astrophysics Data System (ADS)

    Suk, Heejun

    2016-08-01

    This paper presents a semi-analytical procedure for solving coupled the multispecies reactive solute transport equations, with a sequential first-order reaction network on spatially or temporally varying flow velocities and dispersion coefficients involving distinct retardation factors. This proposed approach was developed to overcome the limitation reported by Suk (2013) regarding the identical retardation values for all reactive species, while maintaining the extensive capability of the previous Suk method involving spatially variable or temporally variable coefficients of transport, general initial conditions, and arbitrary temporal variable inlet concentration. The proposed approach sequentially calculates the concentration distributions of each species by employing only the generalized integral transform technique (GITT). Because the proposed solutions for each species' concentration distributions have separable forms in space and time, the solution for subsequent species (daughter species) can be obtained using only the GITT without the decomposition by change-of-variables method imposing the limitation of identical retardation values for all the reactive species by directly substituting solutions for the preceding species (parent species) into the transport equation of subsequent species (daughter species). The proposed solutions were compared with previously published analytical solutions or numerical solutions of the numerical code of the Two-Dimensional Subsurface Flow, Fate and Transport of Microbes and Chemicals (2DFATMIC) in three verification examples. In these examples, the proposed solutions were well matched with previous analytical solutions and the numerical solutions obtained by 2DFATMIC model. A hypothetical single-well push-pull test example and a scale-dependent dispersion example were designed to demonstrate the practical application of the proposed solution to a real field problem.

  7. Variational differential equations for engineering type trajectories close to a planet with an atmosphere

    NASA Technical Reports Server (NTRS)

    Dickmanns, E. D.

    1972-01-01

    The differential equations for the adjoint variables are derived and coded in FORTRAN. The program is written in a form to either take into account or neglect thrust, aerodynamic forces, planet rotation and oblateness, and altitude dependent winds.

  8. Comparison of solutions to bi-Maxwellian and Maxwellian transport equations for subsonic flows. [in terrestrial ionosphere

    NASA Technical Reports Server (NTRS)

    Demars, H. G.; Schunk, R. W.

    1987-01-01

    Conditions corresponding to the steady state subsonic flow of a fully ionized electron-proton plasma in the terrestrial ionosphere are presently characterized by systematically comparing the solutions to the bi-Maxwellian-based 16-moment and Maxwellian-based 13-moment transport equations. The former can account for large temperature anisotropies and the flow of both parallel and perpendicular thermal energy, while the latter account for small temperature anisotropies and only a total heat flow. The comparison is conducted for 2000-10,000 K lower boundary temperatures and 1-4-K/km temperature gradients, over the 1500-13,000-km altitude range.

  9. Generalized linear Boltzmann equation, describing non-classical particle transport, and related asymptotic solutions for small mean free paths

    NASA Astrophysics Data System (ADS)

    Rukolaine, Sergey A.

    2016-05-01

    In classical kinetic models a particle free path distribution is exponential, but this is more likely to be an exception than a rule. In this paper we derive a generalized linear Boltzmann equation (GLBE) for a general free path distribution in the framework of Alt's model. In the case that the free path distribution has at least first and second finite moments we construct an asymptotic solution to the initial value problem for the GLBE for small mean free paths. In the special case of the one-speed transport problem the asymptotic solution results in a diffusion approximation to the GLBE.

  10. A Piecewise Linear Discontinuous Finite Element Spatial Discretization of the Transport Equation in 2D Cylindrical Geometry

    SciTech Connect

    Bailey, T S; Adams, M L; Chang, J H

    2008-10-01

    We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional cylindrical (RZ) geometry for arbitrary polygonal meshes. This discretization is a discontinuous finite element method that utilizes the piecewise linear basis functions developed by Stone and Adams. We describe an asymptotic analysis that shows this method to be accurate for many problems in the thick diffusion limit on arbitrary polygons, allowing this method to be applied to radiative transfer problems with these types of meshes. We also present numerical results for multiple problems on quadrilateral grids and compare these results to the well-known bi-linear discontinuous finite element method.

  11. Transport properties and equation of state for HCNO mixtures in and beyond the warm dense matter regime

    SciTech Connect

    Ticknor, Christopher; Collins, Lee A.; Kress, Joel D.

    2015-08-04

    We present simulations of a four component mixture of HCNO with orbital free molecular dynamics (OFMD). These simulations were conducted for 5–200 eV with densities ranging between 0.184 and 36.8 g/cm3. We extract the equation of state from the simulations and compare to average atom models. We found that we only need to add a cold curve model to find excellent agreement. In addition, we studied mass transport properties. We present fits to the self-diffusion and shear viscosity that are able to reproduce the transport properties over the parameter range studied. We compare these OFMD results to models based on the Coulomb coupling parameter and one-component plasmas.

  12. Transport properties and equation of state for HCNO mixtures in and beyond the warm dense matter regime

    DOE PAGES

    Ticknor, Christopher; Collins, Lee A.; Kress, Joel D.

    2015-08-04

    We present simulations of a four component mixture of HCNO with orbital free molecular dynamics (OFMD). These simulations were conducted for 5–200 eV with densities ranging between 0.184 and 36.8 g/cm3. We extract the equation of state from the simulations and compare to average atom models. We found that we only need to add a cold curve model to find excellent agreement. In addition, we studied mass transport properties. We present fits to the self-diffusion and shear viscosity that are able to reproduce the transport properties over the parameter range studied. We compare these OFMD results to models based onmore » the Coulomb coupling parameter and one-component plasmas.« less

  13. Transport properties and equation of state for HCNO mixtures in and beyond the warm dense matter regime.

    PubMed

    Ticknor, Christopher; Collins, Lee A; Kress, Joel D

    2015-08-01

    We present simulations of a four-component mixture of HCNO with orbital free molecular dynamics (OFMD). These simulations were conducted for 5-200 eV with densities ranging between 0.184 and 36.8 g/cm3. We extract the equation of state from the simulations and compare to average atom models. We found that we only need to add a cold curve model to find excellent agreement. Additionally, we studied mass transport properties. We present fits to the self-diffusion and shear viscosity that are able to reproduce the transport properties over the parameter range studied. We compare these OFMD results to models based on the Coulomb coupling parameter and one-component plasmas.

  14. Sources and processes contributing to nitrogen deposition: an adjoint model analysis applied to biodiversity hotspots worldwide.

    PubMed

    Paulot, Fabien; Jacob, Daniel J; Henze, Daven K

    2013-04-01

    Anthropogenic enrichment of reactive nitrogen (Nr) deposition is an ecological concern. We use the adjoint of a global 3-D chemical transport model (GEOS-Chem) to identify the sources and processes that control Nr deposition to an ensemble of biodiversity hotspots worldwide and two U.S. national parks (Cuyahoga and Rocky Mountain). We find that anthropogenic sources dominate deposition at all continental sites and are mainly regional (less than 1000 km) in origin. In Hawaii, Nr supply is controlled by oceanic emissions of ammonia (50%) and anthropogenic sources (50%), with important contributions from Asia and North America. Nr deposition is also sensitive in complicated ways to emissions of SO2, which affect Nr gas-aerosol partitioning, and of volatile organic compounds (VOCs), which affect oxidant concentrations and produce organic nitrate reservoirs. For example, VOC emissions generally inhibit deposition of locally emitted NOx but significantly increase Nr deposition downwind. However, in polluted boreal regions, anthropogenic VOC emissions can promote Nr deposition in winter. Uncertainties in chemical rate constants for OH + NO2 and NO2 hydrolysis also complicate the determination of source-receptor relationships for polluted sites in winter. Application of our adjoint sensitivities to the representative concentration pathways (RCPs) scenarios for 2010-2050 indicates that future decreases in Nr deposition due to NOx emission controls will be offset by concurrent increases in ammonia emissions from agriculture.

  15. Seeking Energy System Pathways to Reduce Ozone Damage to Ecosystems through Adjoint-based Sensitivity Analysis

    NASA Astrophysics Data System (ADS)

    Capps, S. L.; Pinder, R. W.; Loughlin, D. H.; Bash, J. O.; Turner, M. D.; Henze, D. K.; Percell, P.; Zhao, S.; Russell, M. G.; Hakami, A.

    2014-12-01

    Tropospheric ozone (O3) affects the productivity of ecosystems in addition to degrading human health. Concentrations of this pollutant are significantly influenced by precursor gas emissions, many of which emanate from energy production and use processes. Energy system optimization models could inform policy decisions that are intended to reduce these harmful effects if the contribution of precursor gas emissions to human health and ecosystem degradation could be elucidated. Nevertheless, determining the degree to which precursor gas emissions harm ecosystems and human health is challenging because of the photochemical production of ozone and the distinct mechanisms by which ozone causes harm to different crops, tree species, and humans. Here, the adjoint of a regional chemical transport model is employed to efficiently calculate the relative influences of ozone precursor gas emissions on ecosystem and human health degradation, which informs an energy system optimization. Specifically, for the summer of 2007 the Community Multiscale Air Quality (CMAQ) model adjoint is used to calculate the location- and sector-specific influences of precursor gas emissions on potential productivity losses for the major crops and sensitive tree species as well as human mortality attributable to chronic ozone exposure in the continental U.S. The atmospheric concentrations are evaluated with 12-km horizontal resolution with crop production and timber biomass data gridded similarly. These location-specific factors inform the energy production and use technologies selected in the MARKet ALlocation (MARKAL) model.

  16. Adaptive mesh refinement and adjoint methods in geophysics simulations

    NASA Astrophysics Data System (ADS)

    Burstedde, Carsten

    2013-04-01

    required by human intervention and analysis. Specifying an objective functional that quantifies the misfit between the simulation outcome and known constraints and then minimizing it through numerical optimization can serve as an automated technique for parameter identification. As suggested by the similarity in formulation, the numerical algorithm is closely related to the one used for goal-oriented error estimation. One common point is that the so-called adjoint equation needs to be solved numerically. We will outline the derivation and implementation of these methods and discuss some of their pros and cons, supported by numerical results.

  17. Discontinuous Galerkin discretization of the Reynolds-averaged Navier-Stokes equations with the shear-stress transport model

    NASA Astrophysics Data System (ADS)

    Schoenawa, Stefan; Hartmann, Ralf

    2014-04-01

    In this article we consider the development of Discontinuous Galerkin (DG) methods for the numerical approximation of the Reynolds-averaged Navier-Stokes (RANS) equations with the shear-stress transport (SST) model by Menter. This turbulence model is based on a blending of the Wilcox k-ω model used near the wall and the k-ɛ model used in the rest of the domain where the blending functions depend on the distance to the nearest wall. For the computation of the distance of each quadrature point in the domain to the nearest of the curved, piecewise polynomial wall boundaries, we propose a stabilized continuous finite element (FE) discretization of the eikonal equation. Furthermore, we propose a new wall boundary condition for the dissipation rate ω based on the projection of the analytic near-wall behavior of ω onto the discrete ansatz space of the DG discretization. Finally, we introduce an artificial viscosity to the discretization of the turbulence kinetic energy (k-)equation to suppress oscillations of k near the underresolved boundary layer edge. The wall distance computation based on the continuous FE discretization of the eikonal equation is demonstrated for an internal and three external/aerodynamic flow geometries including a three-element high-lift configuration. The DG discretization of the RANS equations with the SST model is demonstrated for turbulent flows past a flat plate and the RAE2822 airfoil (Cases 9 and 10). The results are compared to the underlying k-ω model and experimental data.

  18. Kershaw closures for linear transport equations in slab geometry I: Model derivation

    NASA Astrophysics Data System (ADS)

    Schneider, Florian

    2016-10-01

    This paper provides a new class of moment models for linear kinetic equations in slab geometry. These models can be evaluated cheaply while preserving the important realizability property, that is the fact that the underlying closure is non-negative. Several comparisons with the (expensive) state-of-the-art minimum-entropy models are made, showing the similarity in approximation quality of the two classes.

  19. A solution of the monoenergetic neutral particle transport equation for adjacent half-spaces with anisotropic scattering

    NASA Astrophysics Data System (ADS)

    Ganapol, B. D.; Mostacci, D.; Previti, A.

    2016-07-01

    We present highly accurate solutions to the neutral particle transport equation in a half-space. While our initial motivation was in response to a recently published solution based on Chandrasekhar's H-function, the presentation to follow has taken on a more comprehensive tone. The solution by H-functions certainly did achieved high accuracy but was limited to isotropic scattering and emission from spatially uniform and linear sources. Moreover, the overly complicated nature of the H-function approach strongly suggests that its extension to anisotropic scattering and general sources is not at all practical. For this reason, an all encompassing theory for the determination of highly precise benchmarks, including anisotropic scattering for a variety of spatial source distributions, is presented for particle transport in a half-space. We illustrate the approach via a collection of cases including tables of 7-place flux benchmarks to guide transport methods developers. The solution presented can be applied to a considerable number of one and two half-space transport problems with variable sources and represents a state-of-the-art benchmark solution.

  20. Symmetries and nonlocal conservation laws of the general magma equation

    NASA Astrophysics Data System (ADS)

    Khamitova, Raisa

    2009-11-01

    In this paper the general magma equation modelling a melt flow in the Earth's mantle is discussed. Applying the new theorem on nonlocal conservation laws [Ibragimov NH. A new conservation theorem. J Math Anal Appl 2007;333(1):311-28] and using the symmetries of the model equation nonlocal conservation laws are computed. In accordance with Ibragimov [Ibragimov NH. Quasi-self-adjoint differential equations. Preprint in Archives of ALGA, vol. 4, BTH, Karlskrona, Sweden: Alga Publications; 2007. p. 55-60, ISSN: 1652-4934] it is shown that the general magma equation is quasi-self-adjoint for arbitrary m and n and self-adjoint for n = -m. These important properties are used for deriving local conservation laws.

  1. High-resolution mapping of sources contributing to urban air pollution using adjoint sensitivity analysis: benzene and diesel black carbon.

    PubMed

    Bastien, Lucas A J; McDonald, Brian C; Brown, Nancy J; Harley, Robert A

    2015-06-16

    The adjoint of the Community Multiscale Air Quality (CMAQ) model at 1 km horizontal resolution is used to map emissions that contribute to ambient concentrations of benzene and diesel black carbon (BC) in the San Francisco Bay area. Model responses of interest include population-weighted average concentrations for three highly polluted receptor areas and the entire air basin. We consider both summer (July) and winter (December) conditions. We introduce a novel approach to evaluate adjoint sensitivity calculations that complements existing methods. Adjoint sensitivities to emissions are found to be accurate to within a few percent, except at some locations associated with large sensitivities to emissions. Sensitivity of model responses to emissions is larger in winter, reflecting weaker atmospheric transport and mixing. The contribution of sources located within each receptor area to the same receptor's air pollution burden increases from 38-74% in summer to 56-85% in winter. The contribution of local sources is higher for diesel BC (62-85%) than for benzene (38-71%), reflecting the difference in these pollutants' atmospheric lifetimes. Morning (6-9am) and afternoon (4-7 pm) commuting-related emissions dominate region-wide benzene levels in winter (14 and 25% of the total response, respectively). In contrast, afternoon rush hour emissions do not contribute significantly in summer. Similar morning and afternoon peaks in sensitivity to emissions are observed for the BC response; these peaks are shifted toward midday because most diesel truck traffic occurs during off-peak hours. PMID:26001097

  2. High-resolution mapping of sources contributing to urban air pollution using adjoint sensitivity analysis: benzene and diesel black carbon.

    PubMed

    Bastien, Lucas A J; McDonald, Brian C; Brown, Nancy J; Harley, Robert A

    2015-06-16

    The adjoint of the Community Multiscale Air Quality (CMAQ) model at 1 km horizontal resolution is used to map emissions that contribute to ambient concentrations of benzene and diesel black carbon (BC) in the San Francisco Bay area. Model responses of interest include population-weighted average concentrations for three highly polluted receptor areas and the entire air basin. We consider both summer (July) and winter (December) conditions. We introduce a novel approach to evaluate adjoint sensitivity calculations that complements existing methods. Adjoint sensitivities to emissions are found to be accurate to within a few percent, except at some locations associated with large sensitivities to emissions. Sensitivity of model responses to emissions is larger in winter, reflecting weaker atmospheric transport and mixing. The contribution of sources located within each receptor area to the same receptor's air pollution burden increases from 38-74% in summer to 56-85% in winter. The contribution of local sources is higher for diesel BC (62-85%) than for benzene (38-71%), reflecting the difference in these pollutants' atmospheric lifetimes. Morning (6-9am) and afternoon (4-7 pm) commuting-related emissions dominate region-wide benzene levels in winter (14 and 25% of the total response, respectively). In contrast, afternoon rush hour emissions do not contribute significantly in summer. Similar morning and afternoon peaks in sensitivity to emissions are observed for the BC response; these peaks are shifted toward midday because most diesel truck traffic occurs during off-peak hours.

  3. Adjoint Method and Predictive Control for 1-D Flow in NASA Ames 11-Foot Transonic Wind Tunnel

    NASA Technical Reports Server (NTRS)

    Nguyen, Nhan; Ardema, Mark

    2006-01-01

    This paper describes a modeling method and a new optimal control approach to investigate a Mach number control problem for the NASA Ames 11-Foot Transonic Wind Tunnel. The flow in the wind tunnel is modeled by the 1-D unsteady Euler equations whose boundary conditions prescribe a controlling action by a compressor. The boundary control inputs to the compressor are in turn controlled by a drive motor system and an inlet guide vane system whose dynamics are modeled by ordinary differential equations. The resulting Euler equations are thus coupled to the ordinary differential equations via the boundary conditions. Optimality conditions are established by an adjoint method and are used to develop a model predictive linear-quadratic optimal control for regulating the Mach number due to a test model disturbance during a continuous pitch

  4. Hierarchical Equation of Motion Investigation of Decoherence and Relaxation Dynamics in Nonequilibrium Transport through Interacting Quantum Dots

    NASA Astrophysics Data System (ADS)

    Hartle, Rainer; Cohen, Guy; Reichman, David R.; Millis, Andrew J.

    2014-03-01

    A recently developed hierarchical quantum master equation approach is used to investigate nonequilibrium electron transport through an interacting double quantum dot system in the regime where the inter-dot coupling is weaker than the coupling to the electrodes. The corresponding eigenstates provide tunneling paths that may interfere constructively or destructively, depending on the energy of the tunneling electrons. Electron-electron interactions are shown to quench these interference effects in bias-voltage dependent ways, leading, in particular, to negative differential resistance, population inversion and an enhanced broadening of resonances in the respective transport characteristics. Relaxation times are found to be very long, and to be correlated with very slow dynamics of the inter-dot coherences (off diagonal density matrix elements). The ability of the hierarchical quantum master equation approach to access very long time scales is crucial for the study of this physics. This work is supported by the National Science Foundation (NSF DMR-1006282 and NSF CHE-1213247), the Yad Hanadiv-Rothschild Foundation (via a Rothschild Fellowship for GC) and the Alexander von Humboldt Foundation (via a Feodor Lynen fellowship for RH).

  5. Calculating Air Quality and Climate Co-Benefits Metrics from Adjoint Elasticities in Chemistry-Climate Models

    NASA Astrophysics Data System (ADS)

    Spak, S.; Henze, D. K.; Carmichael, G. R.

    2013-12-01

    The science and policy communities both need common metrics that clearly, comprehensively, and intuitively communicate the relative sensitivities of air quality and climate to emissions control strategies, include emissions and process uncertainties, and minimize the range of error that is transferred to the metric. This is particularly important because most emissions control policies impact multiple short-lived climate forcing agents, and non-linear climate and health responses in space and time limit the accuracy and policy value of simple emissions-based calculations. Here we describe and apply new second-order elasticity metrics to support the direct comparison of emissions control policies for air quality and health co-benefits analyses using adjoint chemical transport and chemistry-climate models. Borrowing an econometric concept, the simplest elasticities in the atmospheric system are the percentage changes in concentrations due to a percentage change in the emissions. We propose a second-order elasticity metric, the Emissions Reduction Efficiency, which supports comparison across compounds, to long-lived climate forcing agents like CO2, and to other air quality impacts, at any temporal or spatial scale. These adjoint-based metrics (1) possess a single uncertainty range; (2) allow for the inclusion of related health and other impacts effects within the same framework; (3) take advantage of adjoint and forward sensitivity models; and (4) are easily understood. Using global simulations with the adjoint of GEOS-Chem, we apply these metrics to identify spatial and sectoral variability in the climate and health co-benefits of sectoral emissions controls on black carbon, sulfur dioxide, and PM2.5. We find spatial gradients in optimal control strategies on every continent, along with differences among megacities.

  6. Estimates of black carbon emissions in the western United States using the GEOS-Chem adjoint model

    NASA Astrophysics Data System (ADS)

    Mao, Y. H.; Li, Q. B.; Henze, D. K.; Jiang, Z.; Jones, D. B. A.; Kopacz, M.; He, C.; Qi, L.; Gao, M.; Hao, W.-M.; Liou, K.-N.

    2015-07-01

    We estimate black carbon (BC) emissions in the western United States for July-September 2006 by inverting surface BC concentrations from the Interagency Monitoring of Protected Visual Environments (IMPROVE) network using a global chemical transport model (GEOS-Chem) and its adjoint. Our best estimate of the BC emissions is 49.9 Gg at 2° × 2.5° (a factor of 2.1 increase) and 47.3 Gg at 0.5° × 0.667° (1.9 times increase). Model results now capture the observed major fire episodes with substantial bias reductions ( 35 % at 2° × 2.5° and 15 % at 0.5° × 0.667°). The emissions are 20-50 % larger than those from our earlier analytical inversions (Mao et al., 2014). The discrepancy is especially drastic in the partitioning of anthropogenic versus biomass burning emissions. The August biomass burning BC emissions are 4.6-6.5 Gg and anthropogenic BC emissions 8.6-12.8 Gg, varying with the model resolution, error specifications, and subsets of observations used. On average both anthropogenic and biomass burning emissions in the adjoint inversions increase 2-fold relative to the respective {a priori} emissions, in distinct contrast to the halving of the anthropogenic and tripling of the biomass burning emissions in the analytical inversions. We attribute these discrepancies to the inability of the adjoint inversion system, with limited spatiotemporal coverage of the IMPROVE observations, to effectively distinguish collocated anthropogenic and biomass burning emissions on model grid scales. This calls for concurrent measurements of other tracers of biomass burning and fossil fuel combustion (e.g., carbon monoxide and carbon isotopes). We find that the adjoint inversion system as is has sufficient information content to constrain the total emissions of BC on the model grid scales.

  7. Aerodynamic Design Optimization on Unstructured Grids with a Continuous Adjoint Formulation

    NASA Technical Reports Server (NTRS)

    Anderson, W. Kyle; Venkatakrishnan, V.

    1997-01-01

    A continuous adjoint approach for obtaining sensitivity derivatives on unstructured grids is developed and analyzed. The derivation of the costate equations is presented, and a second-order accurate discretization method is described. The relationship between the continuous formulation and a discrete formulation is explored for inviscid, as well as for viscous flow. Several limitations in a strict adherence to the continuous approach are uncovered, and an approach that circumvents these difficulties is presented. The issue of grid sensitivities, which do not arise naturally in the continuous formulation, is investigated and is observed to be of importance when dealing with geometric singularities. A method is described for modifying inviscid and viscous meshes during the design cycle to accommodate changes in the surface shape. The accuracy of the sensitivity derivatives is established by comparing with finite-difference gradients and several design examples are presented.

  8. Self-adjoint extensions of the Dirac Hamiltonian in the magnetic-solenoid field and related exact solutions

    SciTech Connect

    Gavrilov, S.P.; Gitman, D.M.; Smirnov, A.A.

    2003-02-01

    We study solutions of Dirac equation in the field of Aharonov-Bohm solenoid and a collinear uniform magnetic field. On this base we construct self-adjoint extensions of the Dirac Hamiltonian using von Neumann's theory of deficiency indices. We reduce (3+1)-dimensional problem to (2+1)-dimensional one by a proper choice of spin operator. Then we study the problem doing a finite radius regularization of the solenoid field. We exploit solutions of the latter problem to specify boundary conditions in the singular case.

  9. On improving storm surge forecasting using an adjoint optimal technique

    NASA Astrophysics Data System (ADS)

    Li, Yineng; Peng, Shiqiu; Yan, Jing; Xie, Lian

    2013-12-01

    A three-dimensional ocean model and its adjoint model are used to simultaneously optimize the initial conditions (IC) and the wind stress drag coefficient (Cd) for improving storm surge forecasting. To demonstrate the effect of this proposed method, a number of identical twin experiments (ITEs) with a prescription of different error sources and two real data assimilation experiments are performed. Results from both the idealized and real data assimilation experiments show that adjusting IC and Cd simultaneously can achieve much more improvements in storm surge forecasting than adjusting IC or Cd only. A diagnosis on the dynamical balance indicates that adjusting IC only may introduce unrealistic oscillations out of the assimilation window, which can be suppressed by the adjustment of the wind stress when simultaneously adjusting IC and Cd. Therefore, it is recommended to simultaneously adjust IC and Cd to improve storm surge forecasting using an adjoint technique.

  10. A device adaptive inflow boundary condition for Wigner equations of quantum transport

    SciTech Connect

    Jiang, Haiyan; Lu, Tiao; Cai, Wei

    2014-02-01

    In this paper, an improved inflow boundary condition is proposed for Wigner equations in simulating a resonant tunneling diode (RTD), which takes into consideration the band structure of the device. The original Frensley inflow boundary condition prescribes the Wigner distribution function at the device boundary to be the semi-classical Fermi–Dirac distribution for free electrons in the device contacts without considering the effect of the quantum interaction inside the quantum device. The proposed device adaptive inflow boundary condition includes this effect by assigning the Wigner distribution to the value obtained from the Wigner transform of wave functions inside the device at zero external bias voltage, thus including the dominant effect on the electron distribution in the contacts due to the device internal band energy profile. Numerical results on computing the electron density inside the RTD under various incident waves and non-zero bias conditions show much improvement by the new boundary condition over the traditional Frensley inflow boundary condition.

  11. A device adaptive inflow boundary condition for Wigner equations of quantum transport

    NASA Astrophysics Data System (ADS)

    Jiang, Haiyan; Lu, Tiao; Cai, Wei

    2014-02-01

    In this paper, an improved inflow boundary condition is proposed for Wigner equations in simulating a resonant tunneling diode (RTD), which takes into consideration the band structure of the device. The original Frensley inflow boundary condition prescribes the Wigner distribution function at the device boundary to be the semi-classical Fermi-Dirac distribution for free electrons in the device contacts without considering the effect of the quantum interaction inside the quantum device. The proposed device adaptive inflow boundary condition includes this effect by assigning the Wigner distribution to the value obtained from the Wigner transform of wave functions inside the device at zero external bias voltage, thus including the dominant effect on the electron distribution in the contacts due to the device internal band energy profile. Numerical results on computing the electron density inside the RTD under various incident waves and non-zero bias conditions show much improvement by the new boundary condition over the traditional Frensley inflow boundary condition.

  12. A comparison of adjoint and data-centric verification techniques.

    SciTech Connect

    Wildey, Timothy Michael; Cyr, Eric C; Shadid, John N; Pawlowski, Roger P; Smith, Thomas Michael

    2013-03-01

    This document summarizes the results from a level 3 milestone study within the CASL VUQ effort. We compare the adjoint-based a posteriori error estimation approach with a recent variant of a data-centric verification technique. We provide a brief overview of each technique and then we discuss their relative advantages and disadvantages. We use Drekar::CFD to produce numerical results for steady-state Navier Stokes and SARANS approximations. 3

  13. Forward and adjoint sensitivity computation of chaotic dynamical systems

    SciTech Connect

    Wang, Qiqi

    2013-02-15

    This paper describes a forward algorithm and an adjoint algorithm for computing sensitivity derivatives in chaotic dynamical systems, such as the Lorenz attractor. The algorithms compute the derivative of long time averaged “statistical” quantities to infinitesimal perturbations of the system parameters. The algorithms are demonstrated on the Lorenz attractor. We show that sensitivity derivatives of statistical quantities can be accurately estimated using a single, short trajectory (over a time interval of 20) on the Lorenz attractor.

  14. Seismic Window Selection and Misfit Measurements for Global Adjoint Tomography

    NASA Astrophysics Data System (ADS)

    Lei, W.; Bozdag, E.; Lefebvre, M.; Podhorszki, N.; Smith, J. A.; Tromp, J.

    2013-12-01

    Global Adjoint Tomography requires fast parallel processing of large datasets. After obtaing the preprocessed observed and synthetic seismograms, we use the open source software packages FLEXWIN (Maggi et al. 2007) to select time windows and MEASURE_ADJ to make measurements. These measurements define adjoint sources for data assimilation. Previous versions of these tools work on a pair of SAC files---observed and synthetic seismic data for the same component and station, and loop over all seismic records associated with one earthquake. Given the large number of stations and earthquakes, the frequent read and write operations create severe I/O bottlenecks on modern computing platforms. We present new versions of these tools utilizing a new seismic data format, namely the Adaptive Seismic Data Format(ASDF). This new format shows superior scalability for applications on high-performance computers and accommodates various types of data, including earthquake, industry and seismic interferometry datasets. ASDF also provides user-friendly APIs, which can be easily integrated into the adjoint tomography workflow and combined with other data processing tools. In addition to solving the I/O bottleneck, we are making several improvements to these tools. For example, FLEXWIN is tuned to select windows for different types of earthquakes. To capture their distinct features, we categorize earthquakes by their depths and frequency bands. Moreover, instead of only picking phases between the first P arrival and the surface-wave arrivals, our aim is to select and assimilate many other later prominent phases in adjoint tomography. For example, in the body-wave band (17 s - 60 s), we include SKS, sSKS and their multiple, while in the surface-wave band (60 s - 120 s) we incorporate major-arc surface waves.

  15. Adjoint method for estimating Jiles-Atherton hysteresis model parameters

    NASA Astrophysics Data System (ADS)

    Zaman, Mohammad Asif; Hansen, Paul C.; Neustock, Lars T.; Padhy, Punnag; Hesselink, Lambertus

    2016-09-01

    A computationally efficient method for identifying the parameters of the Jiles-Atherton hysteresis model is presented. Adjoint analysis is used in conjecture with an accelerated gradient descent optimization algorithm. The proposed method is used to estimate the Jiles-Atherton model parameters of two different materials. The obtained results are found to be in good agreement with the reported values. By comparing with existing methods of model parameter estimation, the proposed method is found to be computationally efficient and fast converging.

  16. Source identification problem for an elliptic-hyperbolic equation

    NASA Astrophysics Data System (ADS)

    Ashyralyev, Allaberen; Tetikoglu, Fatma Songul Ozesenli; Kahraman, Tulay

    2016-08-01

    In the present paper, a boundary value problem for the differential equation with parameter in a Hilbert space with self-adjoint definite operator is investigated. The well-posedness of this problem is presented. The stability inequalities for the solution of source identification problem for elliptic-hyperbolic equations are given.

  17. Spectral monodromy of non-self-adjoint operators

    SciTech Connect

    Phan, Quang Sang

    2014-01-15

    In the present paper, we build a combinatorial invariant, called the “spectral monodromy” from the spectrum of a single (non-self-adjoint) h-pseudodifferential operator with two degrees of freedom in the semi-classical limit. Our inspiration comes from the quantum monodromy defined for the joint spectrum of an integrable system of n commuting self-adjoint h-pseudodifferential operators, given by S. Vu Ngoc [“Quantum monodromy in integrable systems,” Commun. Math. Phys. 203(2), 465–479 (1999)]. The first simple case that we treat in this work is a normal operator. In this case, the discrete spectrum can be identified with the joint spectrum of an integrable quantum system. The second more complex case we propose is a small perturbation of a self-adjoint operator with a classical integrability property. We show that the discrete spectrum (in a small band around the real axis) also has a combinatorial monodromy. The main difficulty in this case is that we do not know the description of the spectrum everywhere, but only in a Cantor type set. In addition, we also show that the corresponding monodromy can be identified with the classical monodromy, defined by J. Duistermaat [“On global action-angle coordinates,” Commun. Pure Appl. Math. 33(6), 687–706 (1980)].

  18. Orbit-averaged drift kinetic equation for the study of alpha-particle transport in tokamaks

    SciTech Connect

    Sager, G.T.; Miley, G.H. . Fusion Studies Lab.); Burrell, K.H. )

    1990-11-01

    Neoclassical transport of minority suprathermal alpha particles is investigated. This paper departs from previous investigations in that (a) the banana-width ordering parameter {rho}{sub {theta}}/L is not formally restricted to be a small parameter and (b) a linearized collision operator that retains the effects of pitch-angle scattering, electron and ion drag, and speed diffusion is used. A step model approximation for the large-aspect-ratio, circular-cross-section tokamak magnetic field is adopted to simplify the orbit-averaging procedure. Assuming that the suprathermal alphas are in the banana regime, an asymptotic expansion in {tau}{sub B}/{tau}{sub S} {much lt} l is carried out.

  19. Fast linear solver for radiative transport equation with multiple right hand sides in diffuse optical tomography

    NASA Astrophysics Data System (ADS)

    Jia, Jingfei; Kim, Hyun K.; Hielscher, Andreas H.

    2015-12-01

    It is well known that radiative transfer equation (RTE) provides more accurate tomographic results than its diffusion approximation (DA). However, RTE-based tomographic reconstruction codes have limited applicability in practice due to their high computational cost. In this article, we propose a new efficient method for solving the RTE forward problem with multiple light sources in an all-at-once manner instead of solving it for each source separately. To this end, we introduce here a novel linear solver called block biconjugate gradient stabilized method (block BiCGStab) that makes full use of the shared information between different right hand sides to accelerate solution convergence. Two parallelized block BiCGStab methods are proposed for additional acceleration under limited threads situation. We evaluate the performance of this algorithm with numerical simulation studies involving the Delta-Eddington approximation to the scattering phase function. The results show that the single threading block RTE solver proposed here reduces computation time by a factor of 1.5-3 as compared to the traditional sequential solution method and the parallel block solver by a factor of 1.5 as compared to the traditional parallel sequential method. This block linear solver is, moreover, independent of discretization schemes and preconditioners used; thus further acceleration and higher accuracy can be expected when combined with other existing discretization schemes or preconditioners.

  20. Equation of state and transport properties of warm dense helium via quantum molecular dynamics simulations

    NASA Astrophysics Data System (ADS)

    Li, Zhi-Guo; Cheng, Yan; Chen, Qi-Feng; Chen, Xiang-Rong

    2016-05-01

    The equation of state, self-diffusion, and viscosity coefficients of helium have been investigated by quantum molecular dynamics (QMD) simulations in the warm dense matter regime. Our simulations are validated through the comparison with the reliable experimental data. The calculated principal and reshock Hugoniots of liquid helium are in good agreement with the gas-gun data. On this basis, we revisit the issue for helium, i.e., the possibility of the instabilities predicted by chemical models at around 2000 GPa and 10 g/cm3 along the pressure isotherms of 6309, 15 849, and 31 623 K. Our calculations show no indications of instability in this pressure-temperature region, which reconfirm the predictions of previous QMD simulations. The self-diffusion and viscosity coefficients of warm dense helium have been systematically investigated by the QMD simulations. We carefully test the finite-size effects and convergences of statistics, and obtain numerically converged self-diffusion and viscosity coefficients by using the Kubo-Green formulas. The present results have been used to evaluate the existing one component plasma models. Finally, the validation of the Stokes-Einstein relationship for helium in the warm dense regime is discussed.

  1. A User's Manual for MASH V1.5 - A Monte Carlo Adjoint Shielding Code System

    SciTech Connect

    C. O. Slater; J. M. Barnes; J. O. Johnson; J.D. Drischler

    1998-10-01

    The Monte Carlo ~djoint ~ielding Code System, MASH, calculates neutron and gamma- ray environments and radiation protection factors for armored military vehicles, structures, trenches, and other shielding configurations by coupling a forward discrete ordinates air- over-ground transport calculation with an adjoint Monte Carlo treatment of the shielding geometry. Efficiency and optimum use of computer time are emphasized. The code system includes the GRTUNCL and DORT codes for air-over-ground transport calculations, the MORSE code with the GIFT5 combinatorial geometry package for adjoint shielding calculations, and several peripheral codes that perform the required data preparations, transformations, and coupling functions. The current version, MASH v 1.5, is the successor to the original MASH v 1.0 code system initially developed at Oak Ridge National Laboratory (ORNL). The discrete ordinates calculation determines the fluence on a coupling surface surrounding the shielding geometry due to an external neutron/gamma-ray source. The Monte Carlo calculation determines the effectiveness of the fluence at that surface in causing a response in a detector within the shielding geometry, i.e., the "dose importance" of the coupling surface fluence. A coupling code folds the fluence together with the dose importance, giving the desired dose response. The coupling code can determine the dose response as a function of the shielding geometry orientation relative to the source, distance from the source, and energy response of the detector. This user's manual includes a short description of each code, the input required to execute the code along with some helpful input data notes, and a representative sample problem.

  2. Fully automated, high speed, tomographic phase object reconstruction using the transport of intensity equation in transmission and reflection configurations.

    PubMed

    Nguyen, Thanh; Nehmetallah, George; Tran, Dat; Darudi, Ahmad; Soltani, Peyman

    2015-12-10

    While traditional transport of intensity equation (TIE) based phase retrieval of a phase object is performed through axial translation of the CCD, in this work a tunable lens TIE is employed in both transmission and reflection configurations. These configurations are extended to a 360° tomographic 3D reconstruction through multiple illuminations from different angles by a custom fabricated rotating assembly of the phase object. Synchronization circuitry is developed to control the CCD camera and the Arduino board, which in its turn controls the tunable lens and the stepper motor to automate the tomographic reconstruction process. Finally, a MATLAB based user friendly graphical user interface is developed to control the whole system and perform tomographic reconstruction using both multiplicative and inverse radon based techniques. PMID:26836869

  3. Phase retrieval with the transport-of-intensity equation in an arbitrarily-shaped aperture by iterative discrete cosine transforms

    DOE PAGES

    Huang, Lei; Zuo, Chao; Idir, Mourad; Qu, Weijuan; Asundi, Anand

    2015-04-21

    A novel transport-of-intensity equation (TIE) based phase retrieval method is proposed with putting an arbitrarily-shaped aperture into the optical wavefield. In this arbitrarily-shaped aperture, the TIE can be solved under non-uniform illuminations and even non-homogeneous boundary conditions by iterative discrete cosine transforms with a phase compensation mechanism. Simulation with arbitrary phase, arbitrary aperture shape, and non-uniform intensity distribution verifies the effective compensation and high accuracy of the proposed method. Experiment is also carried out to check the feasibility of the proposed method in real measurement. Comparing to the existing methods, the proposed method is applicable for any types of phasemore » distribution under non-uniform illumination and non-homogeneous boundary conditions within an arbitrarily-shaped aperture, which enables the technique of TIE with hard aperture become a more flexible phase retrieval tool in practical measurements.« less

  4. PHASE RETRIEVAL, SYMMETRIZATION RULE AND TRANSPORT OF INTENSITY EQUATION IN APPLICATION TO INDUCTION MAPPING OF MAGNETIC MATERIALS.

    SciTech Connect

    VOLKOV,V.V.; ZHU,Y.

    2002-08-04

    Recent progress in the field of noninterferometric phase retrieval brings the ordinary Fresnel microscopy to a new quantitative level, suitable for recovering both the amplitude and phase of the object, based on image intensity measurements of the object. We show that this is sufficient for in-plane component mapping of magnetic induction for small magnetic elements with known geometry ranging from micro- to few nanometers size. In present paper we re-examine some conservation principles used for the transport-of-intensity (TIE) equation derived by Teaque for application to phase retrieval in light and X-ray optics. In particular, we prove that the intensity conservation law should be replaced in general case with the energy-flow conservation law. This law describes the amplitude-phase balance of the partially coherent beam on its propagation along the optical path, valid both for light and electron optics. This substitution has at least two important fundamental consequences.

  5. Series integration of the diaphragm cell transport equation when the diffusion coefficient is a function of concentration

    NASA Technical Reports Server (NTRS)

    Cain, Judith B.; Baird, James K.

    1992-01-01

    An integral of the form, t = B0 + BL ln(Delta-c) + B1(Delta-c) + B2(Delta-c)-squared + ..., where t is the time and Delta-c is the concentration difference across the frit, is derived in the case of the diaphragm cell transport equation where the interdiffusion coefficient is a function of concentration. The coefficient, B0, is a constant of the integration, while the coefficients, BL, B1, B2,..., depend in general upon the constant, the compartment volumes, and the interdiffusion coefficient and various of its concentration derivatives evaluated at the mean concentration for the cell. Explicit formulas for BL, B1, B2,... are given.

  6. Gradient flipping algorithm: introducing non-convex constraints in wavefront reconstructions with the transport of intensity equation.

    PubMed

    Parvizi, A; Van den Broek, W; Koch, C T

    2016-04-18

    The transport of intensity equation (TIE) is widely applied for recovering wave fronts from an intensity measurement and a measurement of its variation along the direction of propagation. In order to get around the problem of non-uniqueness and ill-conditionedness of the solution of the TIE in the very common case of unspecified boundary conditions or noisy data, additional constraints to the solution are necessary. Although from a numerical optimization point of view, convex constraint as imposed to by total variation minimization is preferable, we will show that in many cases non-convex constraints are necessary to overcome the low-frequency artifacts so typical for convex constraints. We will provide simulated and experimental examples that demonstrate the superiority of solutions to the TIE obtained by our recently introduced gradient flipping algorithm over a total variation constrained solution. PMID:27137272

  7. Phase retrieval with the transport-of-intensity equation in an arbitrarily-shaped aperture by iterative discrete cosine transforms

    SciTech Connect

    Huang, Lei; Zuo, Chao; Idir, Mourad; Qu, Weijuan; Asundi, Anand

    2015-04-21

    A novel transport-of-intensity equation (TIE) based phase retrieval method is proposed with putting an arbitrarily-shaped aperture into the optical wavefield. In this arbitrarily-shaped aperture, the TIE can be solved under non-uniform illuminations and even non-homogeneous boundary conditions by iterative discrete cosine transforms with a phase compensation mechanism. Simulation with arbitrary phase, arbitrary aperture shape, and non-uniform intensity distribution verifies the effective compensation and high accuracy of the proposed method. Experiment is also carried out to check the feasibility of the proposed method in real measurement. Comparing to the existing methods, the proposed method is applicable for any types of phase distribution under non-uniform illumination and non-homogeneous boundary conditions within an arbitrarily-shaped aperture, which enables the technique of TIE with hard aperture become a more flexible phase retrieval tool in practical measurements.

  8. Fully automated, high speed, tomographic phase object reconstruction using the transport of intensity equation in transmission and reflection configurations.

    PubMed

    Nguyen, Thanh; Nehmetallah, George; Tran, Dat; Darudi, Ahmad; Soltani, Peyman

    2015-12-10

    While traditional transport of intensity equation (TIE) based phase retrieval of a phase object is performed through axial translation of the CCD, in this work a tunable lens TIE is employed in both transmission and reflection configurations. These configurations are extended to a 360° tomographic 3D reconstruction through multiple illuminations from different angles by a custom fabricated rotating assembly of the phase object. Synchronization circuitry is developed to control the CCD camera and the Arduino board, which in its turn controls the tunable lens and the stepper motor to automate the tomographic reconstruction process. Finally, a MATLAB based user friendly graphical user interface is developed to control the whole system and perform tomographic reconstruction using both multiplicative and inverse radon based techniques.

  9. Simultaneous resolution of the micromagnetic and spin transport equations applied to current-induced domain wall dynamics

    NASA Astrophysics Data System (ADS)

    Sturma, M.; Bellegarde, C.; Toussaint, J.-C.; Gusakova, D.

    2016-09-01

    In this paper, we use simulations to study current-induced domain wall dynamics by simultaneously resolving the spin transport and micromagnetic equations for a three-dimensional ferromagnetic strip. In contrast to local approaches, which neglect mutual interaction between spins and magnetic moments, our approach recalculates the spin distribution at each time step using the generalized drift diffusion model, which takes the transverse spin absorption phenomenon into account. We quantified the differences between a local approach and treatment based on a self-consistent method by plotting the domain wall velocity as a function of the domain wall width. We also characterized the domain wall velocity and the Walker breakdown condition as a function of the transverse spin absorption length l⊥, which plays a crucial role in domain wall dynamics.

  10. Neoclassical electron and ion transport in toroidally rotating plasmas

    SciTech Connect

    Sugama, H.; Horton, W.

    1997-06-01

    Neoclassical transport processes of electrons and ions are investigated in detail for toroidally rotating axisymmetric plasmas with large flow velocities on the order of the ion thermal speed. The Onsager relations for the flow-dependent neoclassical transport coefficients are derived from the symmetry properties of the drift kinetic equation with the self-adjoint collision operator. The complete neoclassical transport matrix with the Onsager symmetry is obtained for the rotating plasma consisting of electrons and single-species ions in the Pfirsch{endash}Schl{umlt u}ter and banana regimes. It is found that the inward banana fluxes of particles and toroidal momentum are driven by the parallel electric field, which are phenomena coupled through the Onsager symmetric off-diagonal coefficients to the parallel currents caused by the radial thermodynamic forces conjugate to the inward fluxes, respectively. {copyright} {ital 1997 American Institute of Physics.}

  11. Minimising the error in eigenvalue calculations involving the Boltzmann transport equation using goal-based adaptivity on unstructured meshes

    NASA Astrophysics Data System (ADS)

    Goffin, Mark A.; Baker, Christopher M. J.; Buchan, Andrew G.; Pain, Christopher C.; Eaton, Matthew D.; Smith, Paul N.

    2013-06-01

    This article presents a method for goal-based anisotropic adaptive methods for the finite element method applied to the Boltzmann transport equation. The neutron multiplication factor, k, is used as the goal of the adaptive procedure. The anisotropic adaptive algorithm requires error measures for k with directional dependence. General error estimators are derived for any given functional of the flux and applied to k to acquire the driving force for the adaptive procedure. The error estimators require the solution of an appropriately formed dual equation. Forward and dual error indicators are calculated by weighting the Hessian of each solution with the dual and forward residual respectively. The Hessian is used as an approximation of the interpolation error in the solution which gives rise to the directional dependence. The two indicators are combined to form a single error metric that is used to adapt the finite element mesh. The residual is approximated using a novel technique arising from the sub-grid scale finite element discretisation. Two adaptive routes are demonstrated: (i) a single mesh is used to solve all energy groups, and (ii) a different mesh is used to solve each energy group. The second method aims to capture the benefit from representing the flux from each energy group on a specifically optimised mesh. The k goal-based adaptive method was applied to three examples which illustrate the superior accuracy in criticality problems that can be obtained.

  12. Minimising the error in eigenvalue calculations involving the Boltzmann transport equation using goal-based adaptivity on unstructured meshes

    SciTech Connect

    Goffin, Mark A.; Baker, Christopher M.J.; Buchan, Andrew G.; Pain, Christopher C.; Eaton, Matthew D.; Smith, Paul N.

    2013-06-01

    This article presents a method for goal-based anisotropic adaptive methods for the finite element method applied to the Boltzmann transport equation. The neutron multiplication factor, k{sub eff}, is used as the goal of the adaptive procedure. The anisotropic adaptive algorithm requires error measures for k{sub eff} with directional dependence. General error estimators are derived for any given functional of the flux and applied to k{sub eff} to acquire the driving force for the adaptive procedure. The error estimators require the solution of an appropriately formed dual equation. Forward and dual error indicators are calculated by weighting the Hessian of each solution with the dual and forward residual respectively. The Hessian is used as an approximation of the interpolation error in the solution which gives rise to the directional dependence. The two indicators are combined to form a single error metric that is used to adapt the finite element mesh. The residual is approximated using a novel technique arising from the sub-grid scale finite element discretisation. Two adaptive routes are demonstrated: (i) a single mesh is used to solve all energy groups, and (ii) a different mesh is used to solve each energy group. The second method aims to capture the benefit from representing the flux from each energy group on a specifically optimised mesh. The k{sub eff} goal-based adaptive method was applied to three examples which illustrate the superior accuracy in criticality problems that can be obtained.

  13. Boundary-artifact-free phase retrieval with the transport of intensity equation: fast solution with use of discrete cosine transform.

    PubMed

    Zuo, Chao; Chen, Qian; Asundi, Anand

    2014-04-21

    The transport of intensity equation (TIE) is a two-dimensional second order elliptic partial differential equation that must be solved under appropriate boundary conditions. However, the boundary conditions are difficult to obtain in practice. The fast Fourier transform (FFT) based TIE solutions are widely adopted for its speed and simplicity. However, it implies periodic boundary conditions, which lead to significant boundary artifacts when the imposed assumption is violated. In this work, TIE phase retrieval is considered as an inhomogeneous Neumann boundary value problem with the boundary values experimentally measurable around a hard-edged aperture, without any assumption or prior knowledge about the test object and the setup. The analytic integral solution via Green's function is given, as well as a fast numerical implementation for a rectangular region using the discrete cosine transform. This approach is applicable for the case of non-uniform intensity distribution with no extra effort to extract the boundary values from the intensity derivative signals. Its efficiency and robustness have been verified by several numerical simulations even when the objects are complex and the intensity measurements are noisy. This method promises to be an effective fast TIE solver for quantitative phase imaging applications. PMID:24787811

  14. Modeling Finite Faults Using the Adjoint Wave Field

    NASA Astrophysics Data System (ADS)

    Hjörleifsdóttir, V.; Liu, Q.; Tromp, J.

    2004-12-01

    Time-reversal acoustics, a technique in which an acoustic signal is recorded by an array of transducers, time-reversed, and retransmitted, is used, e.g., in medical therapy to locate and destroy gallstones (for a review see Fink, 1997). As discussed by Tromp et al. (2004), time-reversal techniques for locating sources are closely linked to so-called `adjoint methods' (Talagrand and Courtier, 1987), which may be used to evaluate the gradient of a misfit function. Tromp et al. (2004) illustrate how a (finite) source inversion may be implemented based upon the adjoint wave field by writing the change in the misfit function, δ χ, due to a change in the moment-density tensor, δ m, as an integral of the adjoint strain field ɛ x,t) over the fault plane Σ : δ χ = ∫ 0T∫_Σ ɛ x,T-t) :δ m(x,t) d2xdt. We find that if the real fault plane is located at a distance δ h in the direction of the fault normal hat n, then to first order an additional factor of ∫ 0T∫_Σ δ h (x) ∂ n ɛ x,T-t):m(x,t) d2xdt is added to the change in the misfit function. The adjoint strain is computed by using the time-reversed difference between data and synthetics recorded at all receivers as simultaneous sources and recording the resulting strain on the fault plane. In accordance with time-reversal acoustics, all the resulting waves will constructively interfere at the position of the original source in space and time. The level of convergence will be deterimined by factors such as the source-receiver geometry, the frequency of the recorded data and synthetics, and the accuracy of the velocity structure used when back propagating the wave field. The terms ɛ x,T-t) and ∂ n ɛ x,T-t):m(x,t) can be viewed as sensitivity kernels for the moment density and the faultplane location respectively. By looking at these quantities we can make an educated choice of fault parametrization given the data in hand. The process can then be repeated to invert for the best source model, as

  15. A verification regime for the spatial discretization of the SN transport equations

    SciTech Connect

    Schunert, S.; Azmy, Y.

    2012-07-01

    The order-of-accuracy test in conjunction with the method of manufactured solutions is the current state of the art in computer code verification. In this work we investigate the application of a verification procedure including the order-of-accuracy test on a generic SN transport solver that implements the AHOTN spatial discretization. Different types of semantic errors, e.g. removal of a line of code or changing a single character, are introduced randomly into the previously verified S{sub N} code and the proposed verification procedure is used to identify the coding mistakes (if possible) and classify them. Itemized by error type we record the stage of the verification procedure where the error is detected and report the frequency with which the errors are correctly identified at various stages of the verification. Errors that remain undetected by the verification procedure are further scrutinized to determine the reason why the introduced coding mistake eluded the verification procedure. The result of this work is that the verification procedure based on an order-of-accuracy test finds almost all detectable coding mistakes but rarely, 1.44% of the time, and under certain circumstances can fail. (authors)

  16. Differential form of the Skornyakov-Ter-Martirosyan Equations

    SciTech Connect

    Pen'kov, F. M.; Sandhas, W.

    2005-12-15

    The Skornyakov-Ter-Martirosyan three-boson integral equations in momentum space are transformed into differential equations. This allows us to take into account quite directly the Danilov condition providing self-adjointness of the underlying three-body Hamiltonian with zero-range pair interactions. For the helium trimer the numerical solutions of the resulting differential equations are compared with those of the Faddeev-type AGS equations.

  17. Multigroup discrete ordinates solution of Boltzmann-Fokker-Planck equations and cross section library development of ion transport

    SciTech Connect

    Prinja, A.K.

    1995-08-01

    We have developed and successfully implemented a two-dimensional bilinear discontinuous in space and time, used in conjunction with the S{sub N} angular approximation, to numerically solve the time dependent, one-dimensional, one-speed, slab geometry, (ion) transport equation. Numerical results and comparison with analytical solutions have shown that the bilinear-discontinuous (BLD) scheme is third-order accurate in the space ad time dimensions independently. Comparison of the BLD results with diamond-difference methods indicate that the BLD method is both quantitavely and qualitatively superior to the DD scheme. We note that the form of the transport operator is such that these conclusions carry over to energy dependent problems that include the constant-slowing-down-approximation term, and to multiple space dimensions or combinations thereof. An optimized marching or inversion scheme or a parallel algorithm should be investigated to determine if the increased accuracy can compensate for the extra overhead required for a BLD solution, and then could be compared to other discretization methods such as nodal or characteristic schemes.

  18. Spectral-Element Simulations of Wave Propagation in Porous Media: Finite-Frequency Sensitivity Kernels Based Upon Adjoint Methods

    NASA Astrophysics Data System (ADS)

    Morency, C.; Tromp, J.

    2008-12-01

    successfully performed. We present finite-frequency sensitivity kernels for wave propagation in porous media based upon adjoint methods. We first show that the adjoint equations in porous media are similar to the regular Biot equations upon defining an appropriate adjoint source. Then we present finite-frequency kernels for seismic phases in porous media (e.g., fast P, slow P, and S). These kernels illustrate the sensitivity of seismic observables to structural parameters and form the basis of tomographic inversions. Finally, we show an application of this imaging technique related to the detection of buried landmines and unexploded ordnance (UXO) in porous environments.

  19. A local'' exponential transform method for global variance reduction in Monte Carlo transport problems

    SciTech Connect

    Baker, R.S. ); Larsen, E.W. . Dept. of Nuclear Engineering)

    1992-01-01

    Numerous variance reduction techniques, such as splitting/Russian roulette, weight windows, and the exponential transform exist for improving the efficiency of Monte Carlo transport calculations. Typically, however, these methods, while reducing the variance in the problem area of interest tend to increase the variance in other, presumably less important, regions. As such, these methods tend to be not as effective in Monte Carlo calculations which require the minimization of the variance everywhere. Recently, Local'' Exponential Transform (LET) methods have been developed as a means of approximating the zero-variance solution. A numerical solution to the adjoint diffusion equation is used, along with an exponential representation of the adjoint flux in each cell, to determine local'' biasing parameters. These parameters are then used to bias the forward Monte Carlo transport calculation in a manner similar to the conventional exponential transform, but such that the transform parameters are now local in space and energy, not global. Results have shown that the Local Exponential Transform often offers a significant improvement over conventional geometry splitting/Russian roulette with weight windows. Since the biasing parameters for the Local Exponential Transform were determined from a low-order solution to the adjoint transport problem, the LET has been applied in problems where it was desirable to minimize the variance in a detector region. The purpose of this paper is to show that by basing the LET method upon a low-order solution to the forward transport problem, one can instead obtain biasing parameters which will minimize the maximum variance in a Monte Carlo transport calculation.

  20. A ``local`` exponential transform method for global variance reduction in Monte Carlo transport problems

    SciTech Connect

    Baker, R.S.; Larsen, E.W.

    1992-08-01

    Numerous variance reduction techniques, such as splitting/Russian roulette, weight windows, and the exponential transform exist for improving the efficiency of Monte Carlo transport calculations. Typically, however, these methods, while reducing the variance in the problem area of interest tend to increase the variance in other, presumably less important, regions. As such, these methods tend to be not as effective in Monte Carlo calculations which require the minimization of the variance everywhere. Recently, ``Local`` Exponential Transform (LET) methods have been developed as a means of approximating the zero-variance solution. A numerical solution to the adjoint diffusion equation is used, along with an exponential representation of the adjoint flux in each cell, to determine ``local`` biasing parameters. These parameters are then used to bias the forward Monte Carlo transport calculation in a manner similar to the conventional exponential transform, but such that the transform parameters are now local in space and energy, not global. Results have shown that the Local Exponential Transform often offers a significant improvement over conventional geometry splitting/Russian roulette with weight windows. Since the biasing parameters for the Local Exponential Transform were determined from a low-order solution to the adjoint transport problem, the LET has been applied in problems where it was desirable to minimize the variance in a detector region. The purpose of this paper is to show that by basing the LET method upon a low-order solution to the forward transport problem, one can instead obtain biasing parameters which will minimize the maximum variance in a Monte Carlo transport calculation.

  1. A user`s manual for MASH 1.0: A Monte Carlo Adjoint Shielding Code System

    SciTech Connect

    Johnson, J.O.

    1992-03-01

    The Monte Carlo Adjoint Shielding Code System, MASH, calculates neutron and gamma-ray environments and radiation protection factors for armored military vehicles, structures, trenches, and other shielding configurations by coupling a forward discrete ordinates air-over-ground transport calculation with an adjoint Monte Carlo treatment of the shielding geometry. Efficiency and optimum use of computer time are emphasized. The code system include the GRTUNCL and DORT codes for air-over-ground transport calculations, the MORSE code with the GIFT5 combinatorial geometry package for adjoint shielding calculations, and several peripheral codes that perform the required data preparations, transformations, and coupling functions. MASH is the successor to the Vehicle Code System (VCS) initially developed at Oak Ridge National Laboratory (ORNL). The discrete ordinates calculation determines the fluence on a coupling surface surrounding the shielding geometry due to an external neutron/gamma-ray source. The Monte Carlo calculation determines the effectiveness of the fluence at that surface in causing a response in a detector within the shielding geometry, i.e., the ``dose importance`` of the coupling surface fluence. A coupling code folds the fluence together with the dose importance, giving the desired dose response. The coupling code can determine the dose response a a function of the shielding geometry orientation relative to the source, distance from the source, and energy response of the detector. This user`s manual includes a short description of each code, the input required to execute the code along with some helpful input data notes, and a representative sample problem (input data and selected output edits) for each code.

  2. Kinetic energy equations for the average-passage equation system

    NASA Technical Reports Server (NTRS)

    Johnson, Richard W.; Adamczyk, John J.

    1989-01-01

    Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.

  3. Finite difference numerical method for the superlattice Boltzmann transport equation and case comparison of CPU(C) and GPU(CUDA) implementations

    SciTech Connect

    Priimak, Dmitri

    2014-12-01

    We present a finite difference numerical algorithm for solving two dimensional spatially homogeneous Boltzmann transport equation which describes electron transport in a semiconductor superlattice subject to crossed time dependent electric and constant magnetic fields. The algorithm is implemented both in C language targeted to CPU and in CUDA C language targeted to commodity NVidia GPU. We compare performances and merits of one implementation versus another and discuss various software optimisation techniques.

  4. Adjoint-based optimization for understanding and suppressing jet noise

    NASA Astrophysics Data System (ADS)

    Freund, Jonathan B.

    2011-08-01

    Advanced simulation tools, particularly large-eddy simulation techniques, are becoming capable of making quality predictions of jet noise for realistic nozzle geometries and at engineering relevant flow conditions. Increasing computer resources will be a key factor in improving these predictions still further. Quality prediction, however, is only a necessary condition for the use of such simulations in design optimization. Predictions do not themselves lead to quieter designs. They must be interpreted or harnessed in some way that leads to design improvements. As yet, such simulations have not yielded any simplifying principals that offer general design guidance. The turbulence mechanisms leading to jet noise remain poorly described in their complexity. In this light, we have implemented and demonstrated an aeroacoustic adjoint-based optimization technique that automatically calculates gradients that point the direction in which to adjust controls in order to improve designs. This is done with only a single flow solutions and a solution of an adjoint system, which is solved at computational cost comparable to that for the flow. Optimization requires iterations, but having the gradient information provided via the adjoint accelerates convergence in a manner that is insensitive to the number of parameters to be optimized. This paper, which follows from a presentation at the 2010 IUTAM Symposium on Computational Aero-Acoustics for Aircraft Noise Prediction, reviews recent and ongoing efforts by the author and co-workers. It provides a new formulation of the basic approach and demonstrates the approach on a series of model flows, culminating with a preliminary result for a turbulent jet.

  5. Adjoint optimization of natural convection problems: differentially heated cavity

    NASA Astrophysics Data System (ADS)

    Saglietti, Clio; Schlatter, Philipp; Monokrousos, Antonios; Henningson, Dan S.

    2016-06-01

    Optimization of natural convection-driven flows may provide significant improvements to the performance of cooling devices, but a theoretical investigation of such flows has been rarely done. The present paper illustrates an efficient gradient-based optimization method for analyzing such systems. We consider numerically the natural convection-driven flow in a differentially heated cavity with three Prandtl numbers (Pr=0.15{-}7 ) at super-critical conditions. All results and implementations were done with the spectral element code Nek5000. The flow is analyzed using linear direct and adjoint computations about a nonlinear base flow, extracting in particular optimal initial conditions using power iteration and the solution of the full adjoint direct eigenproblem. The cost function for both temperature and velocity is based on the kinetic energy and the concept of entransy, which yields a quadratic functional. Results are presented as a function of Prandtl number, time horizons and weights between kinetic energy and entransy. In particular, it is shown that the maximum transient growth is achieved at time horizons on the order of 5 time units for all cases, whereas for larger time horizons the adjoint mode is recovered as optimal initial condition. For smaller time horizons, the influence of the weights leads either to a concentric temperature distribution or to an initial condition pattern that opposes the mean shear and grows according to the Orr mechanism. For specific cases, it could also been shown that the computation of optimal initial conditions leads to a degenerate problem, with a potential loss of symmetry. In these situations, it turns out that any initial condition lying in a specific span of the eigenfunctions will yield exactly the same transient amplification. As a consequence, the power iteration converges very slowly and fails to extract all possible optimal initial conditions. According to the authors' knowledge, this behavior is illustrated here

  6. Necessary Conditions for Optimal Control of Stochastic Evolution Equations in Hilbert Spaces

    SciTech Connect

    Al-Hussein, Abdul Rahman

    2011-06-15

    We consider a nonlinear stochastic optimal control problem associated with a stochastic evolution equation. This equation is driven by a continuous martingale in a separable Hilbert space and an unbounded time-dependent linear operator.We derive a stochastic maximum principle for this optimal control problem. Our results are achieved by using the adjoint backward stochastic partial differential equation.

  7. Direct Linearization and Adjoint Approaches to Evaluation of Atmospheric Weighting Functions and Surface Partial Derivatives: General Principles, Synergy and Areas of Application

    NASA Technical Reports Server (NTRS)

    Ustino, Eugene A.

    2006-01-01

    This slide presentation reviews the observable radiances as functions of atmospheric parameters and of surface parameters; the mathematics of atmospheric weighting functions (WFs) and surface partial derivatives (PDs) are presented; and the equation of the forward radiative transfer (RT) problem is presented. For non-scattering atmospheres this can be done analytically, and all WFs and PDs can be computed analytically using the direct linearization approach. For scattering atmospheres, in general case, the solution of the forward RT problem can be obtained only numerically, but we need only two numerical solutions: one of the forward RT problem and one of the adjoint RT problem to compute all WFs and PDs we can think of. In this presentation we discuss applications of both the linearization and adjoint approaches

  8. A self-adjoint decomposition of the radial momentum operator

    NASA Astrophysics Data System (ADS)

    Liu, Q. H.; Xiao, S. F.

    2015-12-01

    With acceptance of the Dirac's observation that the canonical quantization entails using Cartesian coordinates, we examine the operator erPr rather than Pr itself and demonstrate that there is a decomposition of erPr into a difference of two self-adjoint but noncommutative operators, in which one is the total momentum and another is the transverse one. This study renders the operator Pr indirectly measurable and physically meaningful, offering an explanation of why the mean value of Pr over a quantum mechanical state makes sense and supporting Dirac's claim that Pr "is real and is the true momentum conjugate to r".

  9. Advances in Global Adjoint Tomography -- Massive Data Assimilation

    NASA Astrophysics Data System (ADS)

    Ruan, Y.; Lei, W.; Bozdag, E.; Lefebvre, M. P.; Smith, J. A.; Krischer, L.; Tromp, J.

    2015-12-01

    Azimuthal anisotropy and anelasticity are key to understanding a myriad of processes in Earth's interior. Resolving these properties requires accurate simulations of seismic wave propagation in complex 3-D Earth models and an iterative inversion strategy. In the wake of successes in regional studies(e.g., Chen et al., 2007; Tape et al., 2009, 2010; Fichtner et al., 2009, 2010; Chen et al.,2010; Zhu et al., 2012, 2013; Chen et al., 2015), we are employing adjoint tomography based on a spectral-element method (Komatitsch & Tromp 1999, 2002) on a global scale using the supercomputer ''Titan'' at Oak Ridge National Laboratory. After 15 iterations, we have obtained a high-resolution transversely isotropic Earth model (M15) using traveltime data from 253 earthquakes. To obtain higher resolution images of the emerging new features and to prepare the inversion for azimuthal anisotropy and anelasticity, we expanded the original dataset with approximately 4,220 additional global earthquakes (Mw5.5-7.0) --occurring between 1995 and 2014-- and downloaded 300-minute-long time series for all available data archived at the IRIS Data Management Center, ORFEUS, and F-net. Ocean Bottom Seismograph data from the last decade are also included to maximize data coverage. In order to handle the huge dataset and solve the I/O bottleneck in global adjoint tomography, we implemented a python-based parallel data processing workflow based on the newly developed Adaptable Seismic Data Format (ASDF). With the help of the data selection tool MUSTANG developed by IRIS, we cleaned our dataset and assembled event-based ASDF files for parallel processing. We have started Centroid Moment Tensors (CMT) inversions for all 4,220 earthquakes with the latest model M15, and selected high-quality data for measurement. We will statistically investigate each channel using synthetic seismograms calculated in M15 for updated CMTs and identify problematic channels. In addition to data screening, we also modified

  10. A deterministic solution of the first order linear Boltzmann transport equation in the presence of external magnetic fields

    SciTech Connect

    St Aubin, J. Keyvanloo, A.; Fallone, B. G.; Vassiliev, O.

    2015-02-15

    Purpose: Accurate radiotherapy dose calculation algorithms are essential to any successful radiotherapy program, considering the high level of dose conformity and modulation in many of today’s treatment plans. As technology continues to progress, such as is the case with novel MRI-guided radiotherapy systems, the necessity for dose calculation algorithms to accurately predict delivered dose in increasingly challenging scenarios is vital. To this end, a novel deterministic solution has been developed to the first order linear Boltzmann transport equation which accurately calculates x-ray based radiotherapy doses in the presence of magnetic fields. Methods: The deterministic formalism discussed here with the inclusion of magnetic fields is outlined mathematically using a discrete ordinates angular discretization in an attempt to leverage existing deterministic codes. It is compared against the EGSnrc Monte Carlo code, utilizing the emf-macros addition which calculates the effects of electromagnetic fields. This comparison is performed in an inhomogeneous phantom that was designed to present a challenging calculation for deterministic calculations in 0, 0.6, and 3 T magnetic fields oriented parallel and perpendicular to the radiation beam. The accuracy of the formalism discussed here against Monte Carlo was evaluated with a gamma comparison using a standard 2%/2 mm and a more stringent 1%/1 mm criterion for a standard reference 10 × 10 cm{sup 2} field as well as a smaller 2 × 2 cm{sup 2} field. Results: Greater than 99.8% (94.8%) of all points analyzed passed a 2%/2 mm (1%/1 mm) gamma criterion for all magnetic field strengths and orientations investigated. All dosimetric changes resulting from the inclusion of magnetic fields were accurately calculated using the deterministic formalism. However, despite the algorithm’s high degree of accuracy, it is noticed that this formalism was not unconditionally stable using a discrete ordinate angular discretization

  11. Aerodynamic Design Optimization on Unstructured Meshes Using the Navier-Stokes Equations

    NASA Technical Reports Server (NTRS)

    Nielsen, Eric J.; Anderson, W. Kyle

    1998-01-01

    A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one-equation turbulence model. A discussion of the numerical implementation of the flow and adjoint equations is presented. Both compressible and incompressible solvers are differentiated and the accuracy of the sensitivity derivatives is verified by comparing with gradients obtained using finite differences. Several simplifying approximations to the complete linearization of the residual are also presented, and the resulting accuracy of the derivatives is examined. Demonstration optimizations for both compressible and incompressible flows are given.

  12. On rational R-matrices with adjoint SU(n) symmetry

    NASA Astrophysics Data System (ADS)

    Stronks, Laurens; van de Leur, Johan; Schuricht, Dirk

    2016-11-01

    Using the representation theory of Yangians we construct the rational R-matrix which takes values in the adjoint representation of SU(n). From this we derive an integrable SU(n) spin chain with lattice spins transforming under the adjoint representation. However, the resulting Hamiltonian is found to be non-Hermitian. Dedicated to the memory of Petr Petrovich Kulish.

  13. Comparison of the Monte Carlo adjoint-weighted and differential operator perturbation methods

    SciTech Connect

    Kiedrowski, Brian C; Brown, Forrest B

    2010-01-01

    Two perturbation theory methodologies are implemented for k-eigenvalue calculations in the continuous-energy Monte Carlo code, MCNP6. A comparison of the accuracy of these techniques, the differential operator and adjoint-weighted methods, is performed numerically and analytically. Typically, the adjoint-weighted method shows better performance over a larger range; however, there are exceptions.

  14. Ab initio simulations for matter deep in the interior of giant planets: equation of state data and transport coefficients

    NASA Astrophysics Data System (ADS)

    Redmer, Ronald; Becker, Andreas; Bethkenhagen, Mandy; French, Martin; Lorenzen, Winfried

    2014-05-01

    The behavior of warm dense matter (pressures of several Mbar and temperatures of several eV) is of paramount importance for interior and dynamo models of giant planets. However, the high-pressure phase diagram of even the simplest and most abundant elements hydrogen and helium as well as that of molecular systems (e.g. water, ammonia, methane and their mixtures) is not well known. The complexity of the behavior arises from metal-insulator transitions and demixing phenomena that occur at high pressures. New phases with exotic properties (e.g. superionic phases with proton conduction) have been predicted as well. These effects will have a strong impact on interior and dynamo models of solar and extrasolar giant planets. We apply ab initio molecular dynamics simulations based on finite-temperature density functional theory to calculate the equation of state data, the high-pressure phase diagram, and the transport properties (electrical and thermal conductivity, viscosity) for a wide range of densities and temperatures. We present new results for hydrogen-helium mixtures and for water, ammonia, and methane. We discuss implications for the interior and magnetic field structure of the gas giants Jupiter and Saturn and the ice giants Uranus and Neptune.

  15. Practical procedure for retrieval of quantitative phase map for two-phase interface using the transport of intensity equation.

    PubMed

    Zhang, Xiaobin; Oshima, Yoshifumi

    2015-11-01

    A practical procedure for retrieving quantitative phase distribution at the interface between a thin amorphous germanium (a-Ge) film and vacuum based on the transport of intensity equation is proposed. First, small regions were selected in transmission electron microscopy (TEM) images with three different focus settings in order to avoid phase modulation due to low frequency noise. Second, the selected TEM image and its three reflected images were combined for mirror-symmetry to meet the boundary requirements. However, in this symmetrization, extra phase modulation arose due to the discontinuous nature of Fresnel fringes at the boundaries among the four parts of the combined image. Third, a corrected phase map was obtained by subtracting a linear fit to the extra phase modulation. The phase shift for a thin a-Ge film was determined to be approximately 0.5 rad, indicating that the average inner potential was 18.3 V. The validity of the present phase retrieval is discussed using simple simulations. PMID:26177522

  16. Virtual Seismometer and Adjoint Methods for Induced Seismicity Monitoring

    NASA Astrophysics Data System (ADS)

    Morency, C.; Matzel, E.

    2014-12-01

    Induced seismicity is associated with subsurface fluid injection, and puts at risk efforts to develop geologic carbon sequestration and enhanced geothermal systems. We are developing methods to monitor the microseismically active zone so that we can identify faults at risk of slipping. We are using the Virtual Seismometer Method (VSM), which is an interferometric technique that is very sensitive to the source parameters (location, mechanism and magnitude) and to the earth structure in the source region. Given an ideal geometry, that is, when two quakes are roughly in line with a recording station, the correlation of their waveforms provide a precise estimate of the Green's function between them, modified by their source mechanisms. When measuring microseismicity, this geometry is rarely ideal and we need to account for variations in the geometry as well. In addition, we also investigate the adjoint method to calculate sensitivity kernels, which define the sensitivity of an observable to model parameters. Classically, adjoint tomography relies on the interaction between a forward waveform, from the source to the recording station, and a backpropagated waveform, from the recorded station to the source. By combining the two approaches we can focus on properties directly between induced micro events, and doing so, monitor the evolution of the seismicity and precisely image potential fault zones. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

  17. Essential self-adjointness of the graph-Laplacian

    NASA Astrophysics Data System (ADS)

    Jorgensen, Palle E. T.

    2008-07-01

    We study the operator theory associated with such infinite graphs G as occur in electrical networks, in fractals, in statistical mechanics, and even in internet search engines. Our emphasis is on the determination of spectral data for a natural Laplace operator associated with the graph in question. This operator Δ will depend not only on G but also on a prescribed positive real valued function c defined on the edges in G. In electrical network models, this function c will determine a conductance number for each edge. We show that the corresponding Laplace operator Δ is automatically essential self-adjoint. By this we mean that Δ is defined on the dense subspace D (of all the real valued functions on the set of vertices G0 with finite support) in the Hilbert space l2(G0). The conclusion is that the closure of the operator Δ is self-adjoint in l2(G0), and so, in particular, that it has a unique spectral resolution, determined by a projection valued measure on the Borel subsets of the infinite half-line. We prove that generically our graph Laplace operator Δ =Δc will have continuous spectrum. For a given infinite graph G with conductance function c, we set up a system of finite graphs with periodic boundary conditions such the finite spectra, for an ascending family of finite graphs, will have the Laplace operator for G as its limit.

  18. The coupling of the neutron transport application RATTLESNAKE to the nuclear fuels performance application BISON under the MOOSE framework

    SciTech Connect

    Gleicher, Frederick N.; Williamson, Richard L.; Ortensi, Javier; Wang, Yaqi; Spencer, Benjamin W.; Novascone, Stephen R.; Hales, Jason D.; Martineau, Richard C.

    2014-10-01

    The MOOSE neutron transport application RATTLESNAKE was coupled to the fuels performance application BISON to provide a higher fidelity tool for fuel performance simulation. This project is motivated by the desire to couple a high fidelity core analysis program (based on the self-adjoint angular flux equations) to a high fidelity fuel performance program, both of which can simulate on unstructured meshes. RATTLESNAKE solves self-adjoint angular flux transport equation and provides a sub-pin level resolution of the multigroup neutron flux with resonance treatment during burnup or a fast transient. BISON solves the coupled thermomechanical equations for the fuel on a sub-millimeter scale. Both applications are able to solve their respective systems on aligned and unaligned unstructured finite element meshes. The power density and local burnup was transferred from RATTLESNAKE to BISON with the MOOSE Multiapp transfer system. Multiple depletion cases were run with one-way data transfer from RATTLESNAKE to BISON. The eigenvalues are shown to agree well with values obtained from the lattice physics code DRAGON. The one-way data transfer of power density is shown to agree with the power density obtained from an internal Lassman-style model in BISON.

  19. Semi-analytical solution to the frequency-dependent Boltzmann transport equation for cross-plane heat conduction in thin films

    SciTech Connect

    Hua, Chengyun; Minnich, Austin J.

    2015-05-07

    Cross-plane heat transport in thin films with thicknesses comparable to the phonon mean free paths is of both fundamental and practical interest for applications such as light-emitting diodes and quantum well lasers. However, physical insight is difficult to obtain for the cross-plane geometry due to the challenge of solving the Boltzmann equation in a finite domain. Here, we present a semi-analytical series expansion method to solve the transient, frequency-dependent Boltzmann transport equation that is valid from the diffusive to ballistic transport regimes and rigorously includes the frequency-dependence of phonon properties. Further, our method is more than three orders of magnitude faster than prior numerical methods and provides a simple analytical expression for the thermal conductivity as a function of film thickness. Our result enables a straightforward physical understanding of cross-plane heat conduction in thin films.

  20. The diffusion approximation versus the telegraph equation for modeling solar energetic particle transport with adiabatic focusing. I. Isotropic pitch-angle scattering

    SciTech Connect

    Effenberger, Frederic; Litvinenko, Yuri E.

    2014-03-01

    The diffusion approximation to the Fokker-Planck equation is commonly used to model the transport of solar energetic particles in interplanetary space. In this study, we present exact analytical predictions of a higher order telegraph approximation for particle transport and compare them with the corresponding predictions of the diffusion approximation and numerical solutions of the full Fokker-Planck equation. We specifically investigate the role of the adiabatic focusing effect of a spatially varying magnetic field on an evolving particle distribution. Comparison of the analytical and numerical results shows that the telegraph approximation reproduces the particle intensity profiles much more accurately than does the diffusion approximation, especially when the focusing is strong. However, the telegraph approximation appears to offer no significant advantage over the diffusion approximation for calculating the particle anisotropy. The telegraph approximation can be a useful tool for describing both diffusive and wave-like aspects of the cosmic-ray transport.

  1. STOMP Subsurface Transport Over Multiple Phases Version 1.0 Addendum: ECKEChem Equilibrium-Conservation-Kinetic Equation Chemistry and Reactive Transport

    SciTech Connect

    White, Mark D.; McGrail, B. Peter

    2005-12-01

    flow and transport simulator, STOMP (Subsurface Transport Over Multiple Phases). Prior to these code development activities, the STOMP simulator included sequential and scalable implementations for numerically simulating the injection of supercritical CO2 into deep saline aquifers. Additionally, the sequential implementations included operational modes that considered nonisothermal conditions and kinetic dissolution of CO2 into the saline aqueous phase. This addendum documents the advancement of these numerical simulation capabilities to include reactive transport in the STOMP simulator through the inclusion of the recently PNNL developed batch geochemistry solution module ECKEChem (Equilibrium-Conservation-Kinetic Equation Chemistry). Potential geologic reservoirs for sequestering CO2 include deep saline aquifers, hydrate-bearing formations, depleted or partially depleted natural gas and petroleum reservoirs, and coal beds. The mechanisms for sequestering carbon dioxide in geologic reservoirs include physical trapping, dissolution in the reservoir fluids, hydraulic trapping (hysteretic entrapment of nonwetting fluids), and chemical reaction. This document and the associated code development and verification work are concerned with the chemistry of injecting CO2 into geologic reservoirs. As geologic sequestration of CO2 via chemical reaction, namely precipitation reactions, are most dominate in deep saline aquifers, the principal focus of this document is the numerical simulation of CO2 injection, migration, and geochemical reaction in deep saline aquifers. The ECKEChem batch chemistry module was developed in a fashion that would allow its implementation into all operational modes of the STOMP simulator, making it a more versatile chemistry component. Additionally, this approach allows for verification of the ECKEChem module against more classical reactive transport problems involving aqueous systems.

  2. Squared eigenfunctions for the Sasa-Satsuma equation

    NASA Astrophysics Data System (ADS)

    Yang, Jianke; Kaup, D. J.

    2009-02-01

    Squared eigenfunctions are quadratic combinations of Jost functions and adjoint Jost functions which satisfy the linearized equation of an integrable equation. They are needed for various studies related to integrable equations, such as the development of its soliton perturbation theory. In this article, squared eigenfunctions are derived for the Sasa-Satsuma equation whose spectral operator is a 3×3 system, while its linearized operator is a 2×2 system. It is shown that these squared eigenfunctions are sums of two terms, where each term is a product of a Jost function and an adjoint Jost function. The procedure of this derivation consists of two steps: First is to calculate the variations of the potentials via variations of the scattering data by the Riemann-Hilbert method. The second one is to calculate the variations of the scattering data via the variations of the potentials through elementary calculations. While this procedure has been used before on other integrable equations, it is shown here, for the first time, that for a general integrable equation, the functions appearing in these variation relations are precisely the squared eigenfunctions and adjoint squared eigenfunctions satisfying, respectively, the linearized equation and the adjoint linearized equation of the integrable system. This proof clarifies this procedure and provides a unified explanation for previous results of squared eigenfunctions on individual integrable equations. This procedure uses primarily the spectral operator of the Lax pair. Thus two equations in the same integrable hierarchy will share the same squared eigenfunctions (except for a time-dependent factor). In the Appendix, the squared eigenfunctions are presented for the Manakov equations whose spectral operator is closely related to that of the Sasa-Satsuma equation.

  3. Exact Solutions and Conservation Laws for a New Integrable Equation

    SciTech Connect

    Gandarias, M. L.; Bruzon, M. S.

    2010-09-30

    In this work we study a generalization of an integrable equation proposed by Qiao and Liu from the point of view of the theory of symmetry reductions in partial differential equations. Among the solutions we obtain a travelling wave with decaying velocity and a smooth soliton solution. We determine the subclass of these equations which are quasi-self-adjoint and we get a nontrivial conservation law.

  4. Local error estimates for discontinuous solutions of nonlinear hyperbolic equations

    NASA Technical Reports Server (NTRS)

    Tadmor, Eitan

    1989-01-01

    Let u(x,t) be the possibly discontinuous entropy solution of a nonlinear scalar conservation law with smooth initial data. Suppose u sub epsilon(x,t) is the solution of an approximate viscosity regularization, where epsilon greater than 0 is the small viscosity amplitude. It is shown that by post-processing the small viscosity approximation u sub epsilon, pointwise values of u and its derivatives can be recovered with an error as close to epsilon as desired. The analysis relies on the adjoint problem of the forward error equation, which in this case amounts to a backward linear transport with discontinuous coefficients. The novelty of this approach is to use a (generalized) E-condition of the forward problem in order to deduce a W(exp 1,infinity) energy estimate for the discontinuous backward transport equation; this, in turn, leads one to an epsilon-uniform estimate on moments of the error u(sub epsilon) - u. This approach does not follow the characteristics and, therefore, applies mutatis mutandis to other approximate solutions such as E-difference schemes.

  5. Mass anomalous dimension in SU(2) with two adjoint fermions

    SciTech Connect

    Bursa, Francis; Del Debbio, Luigi; Keegan, Liam; Pica, Claudio; Pickup, Thomas

    2010-01-01

    We study SU(2) lattice gauge theory with two flavors of Dirac fermions in the adjoint representation. We measure the running of the coupling in the Schroedinger functional scheme and find it is consistent with existing results. We discuss how systematic errors affect the evidence for an infrared fixed point (IRFP). We present the first measurement of the running of the mass in the Schroedinger functional scheme. The anomalous dimension of the chiral condensate, which is relevant for phenomenological applications, can be easily extracted from the running of the mass, under the assumption that the theory has an IRFP. At the current level of accuracy, we can estimate 0.05<{gamma}<0.56 at the IRFP.

  6. Optimizing spectral wave estimates with adjoint-based sensitivity maps

    NASA Astrophysics Data System (ADS)

    Orzech, Mark; Veeramony, Jay; Flampouris, Stylianos

    2014-04-01

    A discrete numerical adjoint has recently been developed for the stochastic wave model SWAN. In the present study, this adjoint code is used to construct spectral sensitivity maps for two nearshore domains. The maps display the correlations of spectral energy levels throughout the domain with the observed energy levels at a selected location or region of interest (LOI/ROI), providing a full spectrum of values at all locations in the domain. We investigate the effectiveness of sensitivity maps based on significant wave height ( H s ) in determining alternate offshore instrument deployment sites when a chosen nearshore location or region is inaccessible. Wave and bathymetry datasets are employed from one shallower, small-scale domain (Duck, NC) and one deeper, larger-scale domain (San Diego, CA). The effects of seasonal changes in wave climate, errors in bathymetry, and multiple assimilation points on sensitivity map shapes and model performance are investigated. Model accuracy is evaluated by comparing spectral statistics as well as with an RMS skill score, which estimates a mean model-data error across all spectral bins. Results indicate that data assimilation from identified high-sensitivity alternate locations consistently improves model performance at nearshore LOIs, while assimilation from low-sensitivity locations results in lesser or no improvement. Use of sub-sampled or alongshore-averaged bathymetry has a domain-specific effect on model performance when assimilating from a high-sensitivity alternate location. When multiple alternate assimilation locations are used from areas of lower sensitivity, model performance may be worse than with a single, high-sensitivity assimilation point.

  7. Trajectory Optimization Using Adjoint Method and Chebyshev Polynomial Approximation for Minimizing Fuel Consumption During Climb

    NASA Technical Reports Server (NTRS)

    Nguyen, Nhan T.; Hornby, Gregory; Ishihara, Abe

    2013-01-01

    This paper describes two methods of trajectory optimization to obtain an optimal trajectory of minimum-fuel- to-climb for an aircraft. The first method is based on the adjoint method, and the second method is based on a direct trajectory optimization method using a Chebyshev polynomial approximation and cubic spine approximation. The approximate optimal trajectory will be compared with the adjoint-based optimal trajectory which is considered as the true optimal solution of the trajectory optimization problem. The adjoint-based optimization problem leads to a singular optimal control solution which results in a bang-singular-bang optimal control.

  8. Numerical Solution of 3D Poisson-Nernst-Planck Equations Coupled with Classical Density Functional Theory for Modeling Ion and Electron Transport in a Confined Environment

    SciTech Connect

    Meng, Da; Zheng, Bin; Lin, Guang; Sushko, Maria L.

    2014-08-29

    We have developed efficient numerical algorithms for the solution of 3D steady-state Poisson-Nernst-Planck equations (PNP) with excess chemical potentials described by the classical density functional theory (cDFT). The coupled PNP equations are discretized by finite difference scheme and solved iteratively by Gummel method with relaxation. The Nernst-Planck equations are transformed into Laplace equations through the Slotboom transformation. Algebraic multigrid method is then applied to efficiently solve the Poisson equation and the transformed Nernst-Planck equations. A novel strategy for calculating excess chemical potentials through fast Fourier transforms is proposed which reduces computational complexity from O(N2) to O(NlogN) where N is the number of grid points. Integrals involving Dirac delta function are evaluated directly by coordinate transformation which yields more accurate result compared to applying numerical quadrature to an approximated delta function. Numerical results for ion and electron transport in solid electrolyte for Li ion batteries are shown to be in good agreement with the experimental data and the results from previous studies.

  9. Integrability of BKP and Odderon equations

    NASA Astrophysics Data System (ADS)

    Lipatov, L. N.

    2013-04-01

    In QCD the gluon is reggeized. The Pomeron is a composite state of two reggeized gluons. Its wave function satisfies the BFKL equation. The BFKL Hamiltonian in LLA is invariant under the Möbius transformations. The wave function of the Odderon and other multi-gluon composite states satisfies the BKP equation. The corresponding Hamiltonian in the multi-color limit has the properties of the Möbius invariance, holomorphic separability, duality and integrability. We discuss various approaches applied to the solution of the BKP equation for the singlet and adjoint representations of the gauge group.

  10. Adjoint-Based, Three-Dimensional Error Prediction and Grid Adaptation

    NASA Technical Reports Server (NTRS)

    Park, Michael A.

    2002-01-01

    Engineering computational fluid dynamics (CFD) analysis and design applications focus on output functions (e.g., lift, drag). Errors in these output functions are generally unknown and conservatively accurate solutions may be computed. Computable error estimates can offer the possibility to minimize computational work for a prescribed error tolerance. Such an estimate can be computed by solving the flow equations and the linear adjoint problem for the functional of interest. The computational mesh can be modified to minimize the uncertainty of a computed error estimate. This robust mesh-adaptation procedure automatically terminates when the simulation is within a user specified error tolerance. This procedure for estimating and adapting to error in a functional is demonstrated for three-dimensional Euler problems. An adaptive mesh procedure that links to a Computer Aided Design (CAD) surface representation is demonstrated for wing, wing-body, and extruded high lift airfoil configurations. The error estimation and adaptation procedure yielded corrected functions that are as accurate as functions calculated on uniformly refined grids with ten times as many grid points.

  11. Acoustic wave-equation-based earthquake location

    NASA Astrophysics Data System (ADS)

    Tong, Ping; Yang, Dinghui; Liu, Qinya; Yang, Xu; Harris, Jerry

    2016-04-01

    We present a novel earthquake location method using acoustic wave-equation-based traveltime inversion. The linear relationship between the location perturbation (δt0, δxs) and the resulting traveltime residual δt of a particular seismic phase, represented by the traveltime sensitivity kernel K(t0, xs) with respect to the earthquake location (t0, xs), is theoretically derived based on the adjoint method. Traveltime sensitivity kernel K(t0, xs) is formulated as a convolution between the forward and adjoint wavefields, which are calculated by numerically solving two acoustic wave equations. The advantage of this newly derived traveltime kernel is that it not only takes into account the earthquake-receiver geometry but also accurately honours the complexity of the velocity model. The earthquake location is obtained by solving a regularized least-squares problem. In 3-D realistic applications, it is computationally expensive to conduct full wave simulations. Therefore, we propose a 2.5-D approach which assumes the forward and adjoint wave simulations within a 2-D vertical plane passing through the earthquake and receiver. Various synthetic examples show the accuracy of this acoustic wave-equation-based earthquake location method. The accuracy and efficiency of the 2.5-D approach for 3-D earthquake location are further verified by its application to the 2004 Big Bear earthquake in Southern California.

  12. Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates

    SciTech Connect

    Jakeman, J.D. Wildey, T.

    2015-01-01

    In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the physical discretization error and the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity of the sparse grid. Utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchical surplus based strategies. Throughout this paper we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.

  13. Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates

    DOE PAGES

    Jakeman, J. D.; Wildey, T.

    2015-01-01

    In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity. We show that utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchical surplus based strategies. Throughout this papermore » we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.« less

  14. Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates

    SciTech Connect

    Jakeman, J. D.; Wildey, T.

    2015-01-01

    In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity. We show that utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchical surplus based strategies. Throughout this paper we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.

  15. MS S4.03.002 - Adjoint-Based Design for Configuration Shaping

    NASA Technical Reports Server (NTRS)

    Nemec, Marian; Aftosmis, Michael J.

    2009-01-01

    This slide presentation discusses a method of inverse design for low sonic boom using adjoint-based gradient computations. It outlines a method for shaping a configuration in order to match a prescribed near-field signature.

  16. Application of Adjoint Methodology in Various Aspects of Sonic Boom Design

    NASA Technical Reports Server (NTRS)

    Rallabhandi, Sriram K.

    2014-01-01

    One of the advances in computational design has been the development of adjoint methods allowing efficient calculation of sensitivities in gradient-based shape optimization. This paper discusses two new applications of adjoint methodology that have been developed to aid in sonic boom mitigation exercises. In the first, equivalent area targets are generated using adjoint sensitivities of selected boom metrics. These targets may then be used to drive the vehicle shape during optimization. The second application is the computation of adjoint sensitivities of boom metrics on the ground with respect to parameters such as flight conditions, propagation sampling rate, and selected inputs to the propagation algorithms. These sensitivities enable the designer to make more informed selections of flight conditions at which the chosen cost functionals are less sensitive.

  17. Comparison of the adjoint and adjoint-free 4dVar assimilation of the hydrographic and velocity observations in the Adriatic Sea

    NASA Astrophysics Data System (ADS)

    Yaremchuk, Max; Martin, Paul; Koch, Andrey; Beattie, Christopher

    2016-01-01

    Performance of the adjoint and adjoint-free 4-dimensional variational (4dVar) data assimilation techniques is compared in application to the hydrographic surveys and velocity observations collected in the Adriatic Sea in 2006. Assimilating the data into the Navy Coastal Ocean Model (NCOM) has shown that both methods deliver similar reduction of the cost function and demonstrate comparable forecast skill at approximately the same computational expense. The obtained optimal states were, however, significantly different in terms of distance from the background state: application of the adjoint method resulted in a 30-40% larger departure, mostly due to the excessive level of ageostrophic motions in the southern basin of the Sea that was not covered by observations.

  18. Entropy production and Onsager symmetry in neoclassical transport processes of toroidal plasmas

    SciTech Connect

    Sugama, H.; Horton, W.

    1996-01-01

    Entropy production and Onsager symmetry in neoclassical transport processes of magnetically confined plasmas are studied in detail for general toroidal systems, including nonaxisymmetric configurations. It is found that the flux surface average of the entropy production defined from the linearized collision operator and the gyroangle-averaged distribution function coincides with the sum of the inner products of the thermodynamic forces and the conjugate fluxes consisting of the Pfirsch-Schlueter, banana-plateau, nonaxisymmetric parts of the neoclassical radial fluxes and the parallel current. It is proved from the self-adjointness of the linearized collision operator that the Onsager symmetry is robustly valid for the neoclassical transport equations in the cases of general toroidal plasmas consisting of electrons and multi-species ions with arbitrary collision frequencies. It is shown that the Onsager symmetry holds whether or not the ambipolarity condition is used to reduce the number of the conjugate pairs of the transport fluxes and the thermodynamic forces. The full transport coefficients for the banana-plateau and nonaxisymmetric parts are separately derived, and their symmetry properties are investigated. The nonaxisymmetric transport equations are obtained for arbitrary collision frequencies in the Pfirsch{endash}Schlueter and plateau regimes, and it is directly confirmed that the total banana-plateau and nonaxisymmetric transport equations satisfy the Onsager symmetry. {copyright} {ital 1996 American Institute of Physics.}

  19. Comparison of Ensemble and Adjoint Approaches to Variational Optimization of Observational Arrays

    NASA Astrophysics Data System (ADS)

    Nechaev, D.; Panteleev, G.; Yaremchuk, M.

    2015-12-01

    Comprehensive monitoring of the circulation in the Chukchi Sea and Bering Strait is one of the key prerequisites of the successful long-term forecast of the Arctic Ocean state. Since the number of continuously maintained observational platforms is restricted by logistical and political constraints, the configuration of such an observing system should be guided by an objective strategy that optimizes the observing system coverage, design, and the expenses of monitoring. The presented study addresses optimization of system consisting of a limited number of observational platforms with respect to reduction of the uncertainties in monitoring the volume/freshwater/heat transports through a set of key sections in the Chukchi Sea and Bering Strait. Variational algorithms for optimization of observational arrays are verified in the test bed of the set of 4Dvar optimized summer-fall circulations in the Pacific sector of the Arctic Ocean. The results of an optimization approach based on low-dimensional ensemble of model solutions is compared against a more conventional algorithm involving application of the tangent linear and adjoint models. Special attention is paid to the computational efficiency and portability of the optimization procedure.

  20. Estimates of Asian dust sources using the adjoint of GEOS-Chem

    NASA Astrophysics Data System (ADS)

    Jeong, J.; Park, R.; Ku, B.

    2011-12-01

    Soil dust aerosols, typically originated from northern China, southern Mongolia, and the Taklamakan desert in spring, have large impacts on human health, local visibility, air quality, and climate in Asia. Large uncertainty, however, exists in estimates of dust emissions in 3-D models. We develop the adjoint of dust modeling in a global chemical transport model, GEOS-Chem, using a four-dimensional variational method and apply it to obtain optimized dust sources over East Asia in April 2001 together with surface PM10 aerosol measurements from the Chinese ambient air pollution index, the Korean Ministry of Environment, and the Acid Deposition Monitoring Network. The optimized dust sources from the assimilation show a large decrease in dust emissions over the Gobi Desert. To evaluate the assimilated results, we compare simulated dust aerosol optical depths (AODs) using the optimized sources with the Total Ozone Mapping Spectrometer aerosol index and the Multi-angle Imaging Spectrometer AOD data. We find that the optimized sources result in much better agreement with the observations, especially in the context of improved the spatial distribution of the simulated AOD compared with the observation over East Asia.

  1. Preliminary Results from the Application of Automated Adjoint Code Generation to CFL3D

    NASA Technical Reports Server (NTRS)

    Carle, Alan; Fagan, Mike; Green, Lawrence L.

    1998-01-01

    This report describes preliminary results obtained using an automated adjoint code generator for Fortran to augment a widely-used computational fluid dynamics flow solver to compute derivatives. These preliminary results with this augmented code suggest that, even in its infancy, the automated adjoint code generator can accurately and efficiently deliver derivatives for use in transonic Euler-based aerodynamic shape optimization problems with hundreds to thousands of independent design variables.

  2. Combined rate equation and Monte Carlo studies of electron transport in a GaAs/Al0.45Ga0.55As quantum-cascade laser

    NASA Astrophysics Data System (ADS)

    Borowik, Piotr; Thobel, Jean-Luc; Adamowicz, Leszek

    2012-11-01

    Comparison of the Monte Carlo and rate equation methods as applied to the study of electron transport in a mid-infrared quantum cascade laser structure initially proposed by Page et al (2001 Appl. Phys. Lett. 78 3529) is presented for a range of realistic injector doping levels. An analysis of the difference between these two methods is given. It is suggested that justified approximations of the rate equation method, originated by imposing Fermi-Dirac statistics and the same electron effective temperature for each of the energy sub-bands, can be interpreted as partial inclusion of electron-electron interactions. Results of the rate equation method may be used as good initial conditions for a more precise Monte Carlo simulation. An algorithm combining rate equation and Monte Carlo simulations is examined. A reasonable agreement between the introduced method and a fully self-consistent resolution of Monte Carlo and Schrödinger coupled with Poisson equations is demonstrated. The computation time may be reduced when the combined algorithm is used.

  3. Amplitude Equation for Instabilities Driven at Deformable Surfaces - Rosensweig Instability

    NASA Astrophysics Data System (ADS)

    Pleiner, Harald; Bohlius, Stefan; Brand, Helmut R.

    2008-11-01

    The derivation of amplitude equations from basic hydro-, magneto-, or electrodynamic equations requires the knowledge of the set of adjoint linear eigenvectors. This poses a particular problem for the case of a free and deformable surface, where the adjoint boundary conditions are generally non-trivial. In addition, when the driving force acts on the system via the deformable surface, not only Fredholm's alternative in the bulk, but also the proper boundary conditions are required to get amplitude equations. This is explained and demonstrated for the normal field (or Rosensweig) instability in ferrofluids as well as in ferrogels. An important aspect of the problem is its intrinsic dynamic nature, although at the end the instability is stationary. The resulting amplitude equation contains cubic and quadratic nonlinearities as well as first and (in the gel case) second order time derivatives. Spatial variations of the amplitudes cannot be obtained by using simply Newell's method in the bulk.

  4. Plumes, Hotspot & Slabs Imaged by Global Adjoint Tomography

    NASA Astrophysics Data System (ADS)

    Bozdag, E.; Lefebvre, M. P.; Lei, W.; Peter, D. B.; Smith, J. A.; Komatitsch, D.; Tromp, J.

    2015-12-01

    We present the "first generation" global adjoint tomography model based on 3D wave simulations, which is the result of 15 conjugate-gradient iterations with confined transverse isotropy to the upper mantle. Our starting model is the 3D mantle and crustal models S362ANI (Kustowski et al. 2008) and Crust2.0 (Bassin et al. 2000), respectively. We take into account the full nonlinearity of wave propagation in numerical simulations including attenuation (both in forward and adjoint simulations), topography/bathymetry, etc., using the GPU version of the SPECFEM3D_GLOBE package. We invert for crust and mantle together without crustal corrections to avoid any bias in mantle structure. We started with an initial selection of 253 global CMT events within the magnitude range 5.8 ≤ Mw ≤ 7.0 with numerical simulations having resolution down to 27 s combining 30-s body and 60-s surface waves. After the 12th iteration we increased the resolution to 17 s, including higher-frequency body waves as well as going down to 45 s in surface-wave measurements. We run 180-min seismograms and assimilate all minor- and major-arc body and surface waves. Our 15th iteration model update shows a tantalisingly enhanced image of the Tahiti plume as well as various other plumes and hotspots, such as Caroline, Galapagos, Yellowstone, Erebus, etc. Furthermore, we see clear improvements in slab resolution along the Hellenic and Japan Arcs, as well as subduction along the East of Scotia Plate, which does not exist in the initial model. Point-spread function tests (Fichtner & Trampert 2011) suggest that we are close to the resolution of continental-scale studies in our global inversions and able to confidently map features, for instance, at the scale of the Yellowstone hotspot. This is a clear consequence of our multi-scale smoothing strategy, in which we define our smoothing operator as a function of the approximate Hessian kernel and smooth our gradients less wherever we have good ray coverage

  5. Big Data Challenges in Global Seismic 'Adjoint Tomography' (Invited)

    NASA Astrophysics Data System (ADS)

    Tromp, J.; Bozdag, E.; Krischer, L.; Lefebvre, M.; Lei, W.; Smith, J.

    2013-12-01

    The challenge of imaging Earth's interior on a global scale is closely linked to the challenge of handling large data sets. The related iterative workflow involves five distinct phases, namely, 1) data gathering and culling, 2) synthetic seismogram calculations, 3) pre-processing (time-series analysis and time-window selection), 4) data assimilation and adjoint calculations, 5) post-processing (pre-conditioning, regularization, model update). In order to implement this workflow on modern high-performance computing systems, a new seismic data format is being developed. The Adaptable Seismic Data Format (ASDF) is designed to replace currently used data formats with a more flexible format that allows for fast parallel I/O. The metadata is divided into abstract categories, such as "source" and "receiver", along with provenance information for complete reproducibility. The structure of ASDF is designed keeping in mind three distinct applications: earthquake seismology, seismic interferometry, and exploration seismology. Existing time-series analysis tool kits, such as SAC and ObsPy, can be easily interfaced with ASDF so that seismologists can use robust, previously developed software packages. ASDF accommodates an automated, efficient workflow for global adjoint tomography. Manually managing the large number of simulations associated with the workflow can rapidly become a burden, especially with increasing numbers of earthquakes and stations. Therefore, it is of importance to investigate the possibility of automating the entire workflow. Scientific Workflow Management Software (SWfMS) allows users to execute workflows almost routinely. SWfMS provides additional advantages. In particular, it is possible to group independent simulations in a single job to fit the available computational resources. They also give a basic level of fault resilience as the workflow can be resumed at the correct state preceding a failure. Some of the best candidates for our particular workflow

  6. Lagrange Multipliers, Adjoint Equations, the Pontryagin Maximum Principle and Heuristic Proofs

    ERIC Educational Resources Information Center

    Ollerton, Richard L.

    2013-01-01

    Deeper understanding of important mathematical concepts by students may be promoted through the (initial) use of heuristic proofs, especially when the concepts are also related back to previously encountered mathematical ideas or tools. The approach is illustrated by use of the Pontryagin maximum principle which is then illuminated by reference to…

  7. Multigrid methods for bifurcation problems: The self adjoint case

    NASA Technical Reports Server (NTRS)

    Taasan, Shlomo

    1987-01-01

    This paper deals with multigrid methods for computational problems that arise in the theory of bifurcation and is restricted to the self adjoint case. The basic problem is to solve for arcs of solutions, a task that is done successfully with an arc length continuation method. Other important issues are, for example, detecting and locating singular points as part of the continuation process, switching branches at bifurcation points, etc. Multigrid methods have been applied to continuation problems. These methods work well at regular points and at limit points, while they may encounter difficulties in the vicinity of bifurcation points. A new continuation method that is very efficient also near bifurcation points is presented here. The other issues mentioned above are also treated very efficiently with appropriate multigrid algorithms. For example, it is shown that limit points and bifurcation points can be solved for directly by a multigrid algorithm. Moreover, the algorithms presented here solve the corresponding problems in just a few work units (about 10 or less), where a work unit is the work involved in one local relaxation on the finest grid.

  8. Skyrmions in Yang-Mills theories with massless adjoint quarks

    SciTech Connect

    Auzzi, R.; Bolognesi, S.; Shifman, M.

    2008-06-15

    Dynamics of SU(N{sub c}) Yang-Mills theories with N{sub f} adjoint Weyl fermions is quite different from that of SU(N{sub c}) gauge theories with fundamental quarks. The symmetry breaking pattern is SU(N{sub f}){yields}SO(N{sub f}). The corresponding sigma model supports Skyrmions whose microscopic identification is not immediately clear. We address this issue as well as the issue of the Skyrmion stability. The case of N{sub f}=2 had been considered previously. Here we discuss N{sub f}{>=}3. We discuss the coupling between the massless Goldstone bosons and massive composite fermions [with mass O(N{sub c}{sup 0})] from the standpoint of the low-energy chiral sigma model. We derive the Wess-Zumino-Novikov-Witten term and then determine Skyrmion statistics. We also determine their fermion number (mod 2) and observe an abnormal relation between the statistics and the fermion number. This explains the Skyrmion stability. In addition, we consider another microscopic theory--SO(N{sub c}) Yang-Mills with N{sub f} Weyl fermions in the vectorial representation--which has the same chiral symmetry breaking pattern and the same chiral Lagrangian. We discuss distinctive features of these two scenarios.

  9. Group classification and conservation laws of anisotropic wave equations with a source

    NASA Astrophysics Data System (ADS)

    Ibragimov, N. H.; Gandarias, M. L.; Galiakberova, L. R.; Bruzon, M. S.; Avdonina, E. D.

    2016-08-01

    Linear and nonlinear waves in anisotropic media are useful in investigating complex materials in physics, biomechanics, biomedical acoustics, etc. The present paper is devoted to investigation of symmetries and conservation laws for nonlinear anisotropic wave equations with specific external sources when the equations in question are nonlinearly self-adjoint. These equations involve two arbitrary functions. Construction of conservation laws associated with symmetries is based on the generalized conservation theorem for nonlinearly self-adjoint partial differential equations. First we calculate the conservation laws for the basic equation without any restrictions on the arbitrary functions. Then we make the group classification of the basic equation in order to specify all possible values of the arbitrary functions when the equation has additional symmetries and construct the additional conservation laws.

  10. Weak second-order splitting schemes for Lagrangian Monte Carlo particle methods for the composition PDF/FDF transport equations

    SciTech Connect

    Wang Haifeng Popov, Pavel P.; Pope, Stephen B.

    2010-03-01

    We study a class of methods for the numerical solution of the system of stochastic differential equations (SDEs) that arises in the modeling of turbulent combustion, specifically in the Monte Carlo particle method for the solution of the model equations for the composition probability density function (PDF) and the filtered density function (FDF). This system consists of an SDE for particle position and a random differential equation for particle composition. The numerical methods considered advance the solution in time with (weak) second-order accuracy with respect to the time step size. The four primary contributions of the paper are: (i) establishing that the coefficients in the particle equations can be frozen at the mid-time (while preserving second-order accuracy), (ii) examining the performance of three existing schemes for integrating the SDEs, (iii) developing and evaluating different splitting schemes (which treat particle motion, reaction and mixing on different sub-steps), and (iv) developing the method of manufactured solutions (MMS) to assess the convergence of Monte Carlo particle methods. Tests using MMS confirm the second-order accuracy of the schemes. In general, the use of frozen coefficients reduces the numerical errors. Otherwise no significant differences are observed in the performance of the different SDE schemes and splitting schemes.

  11. Mesh adaptation on the sphere using optimal transport and the numerical solution of a Monge-Ampère type equation

    NASA Astrophysics Data System (ADS)

    Weller, Hilary; Browne, Philip; Budd, Chris; Cullen, Mike

    2016-03-01

    An equation of Monge-Ampère type has, for the first time, been solved numerically on the surface of the sphere in order to generate optimally transported (OT) meshes, equidistributed with respect to a monitor function. Optimal transport generates meshes that keep the same connectivity as the original mesh, making them suitable for r-adaptive simulations, in which the equations of motion can be solved in a moving frame of reference in order to avoid mapping the solution between old and new meshes and to avoid load balancing problems on parallel computers. The semi-implicit solution of the Monge-Ampère type equation involves a new linearisation of the Hessian term, and exponential maps are used to map from old to new meshes on the sphere. The determinant of the Hessian is evaluated as the change in volume between old and new mesh cells, rather than using numerical approximations to the gradients. OT meshes are generated to compare with centroidal Voronoi tessellations on the sphere and are found to have advantages and disadvantages; OT equidistribution is more accurate, the number of iterations to convergence is independent of the mesh size, face skewness is reduced and the connectivity does not change. However anisotropy is higher and the OT meshes are non-orthogonal. It is shown that optimal transport on the sphere leads to meshes that do not tangle. However, tangling can be introduced by numerical errors in calculating the gradient of the mesh potential. Methods for alleviating this problem are explored. Finally, OT meshes are generated using observed precipitation as a monitor function, in order to demonstrate the potential power of the technique.

  12. Stochastic uncertainty analysis for solute transport in randomly heterogeneous media using a Karhunen-Loève-based moment equation approach

    USGS Publications Warehouse

    Liu, Gaisheng; Lu, Zhiming; Zhang, Dongxiao

    2007-01-01

    A new approach has been developed for solving solute transport problems in randomly heterogeneous media using the Karhunen-Loève-based moment equation (KLME) technique proposed by Zhang and Lu (2004). The KLME approach combines the Karhunen-Loève decomposition of the underlying random conductivity field and the perturbative and polynomial expansions of dependent variables including the hydraulic head, flow velocity, dispersion coefficient, and solute concentration. The equations obtained in this approach are sequential, and their structure is formulated in the same form as the original governing equations such that any existing simulator, such as Modular Three-Dimensional Multispecies Transport Model for Simulation of Advection, Dispersion, and Chemical Reactions of Contaminants in Groundwater Systems (MT3DMS), can be directly applied as the solver. Through a series of two-dimensional examples, the validity of the KLME approach is evaluated against the classical Monte Carlo simulations. Results indicate that under the flow and transport conditions examined in this work, the KLME approach provides an accurate representation of the mean concentration. For the concentration variance, the accuracy of the KLME approach is good when the conductivity variance is 0.5. As the conductivity variance increases up to 1.0, the mismatch on the concentration variance becomes large, although the mean concentration can still be accurately reproduced by the KLME approach. Our results also indicate that when the conductivity variance is relatively large, neglecting the effects of the cross terms between velocity fluctuations and local dispersivities, as done in some previous studies, can produce noticeable errors, and a rigorous treatment of the dispersion terms becomes more appropriate.

  13. A hybrid (Monte Carlo/deterministic) approach for multi-dimensional radiation transport

    SciTech Connect

    Bal, Guillaume; Davis, Anthony B.; Langmore, Ian

    2011-08-20

    Highlights: {yields} We introduce a variance reduction scheme for Monte Carlo (MC) transport. {yields} The primary application is atmospheric remote sensing. {yields} The technique first solves the adjoint problem using a deterministic solver. {yields} Next, the adjoint solution is used as an importance function for the MC solver. {yields} The adjoint problem is solved quickly since it ignores the volume. - Abstract: A novel hybrid Monte Carlo transport scheme is demonstrated in a scene with solar illumination, scattering and absorbing 2D atmosphere, a textured reflecting mountain, and a small detector located in the sky (mounted on a satellite or a airplane). It uses a deterministic approximation of an adjoint transport solution to reduce variance, computed quickly by ignoring atmospheric interactions. This allows significant variance and computational cost reductions when the atmospheric scattering and absorption coefficient are small. When combined with an atmospheric photon-redirection scheme, significant variance reduction (equivalently acceleration) is achieved in the presence of atmospheric interactions.

  14. Towards magnetic sounding of the Earth's core by an adjoint method

    NASA Astrophysics Data System (ADS)

    Li, K.; Jackson, A.; Livermore, P. W.

    2013-12-01

    Earth's magnetic field is generated and sustained by the so called geodynamo system in the core. Measurements of the geomagnetic field taken at the surface, downwards continued through the electrically insulating mantle to the core-mantle boundary (CMB), provide important constraints on the time evolution of the velocity, magnetic field and temperature anomaly in the fluid outer core. The aim of any study in data assimilation applied to the Earth's core is to produce a time-dependent model consistent with these observations [1]. Snapshots of these ``tuned" models provide a window through which the inner workings of the Earth's core, usually hidden from view, can be probed. We apply a variational data assimilation framework to an inertia-free magnetohydrodynamic system (MHD) [2]. Such a model is close to magnetostrophic balance [3], to which we have added viscosity to the dominant forces of Coriolis, pressure, Lorentz and buoyancy, believed to be a good approximation of the Earth's dynamo in the convective time scale. We chose to study the MHD system driven by a static temperature anomaly to mimic the actual inner working of Earth's dynamo system, avoiding at this stage the further complication of solving for the time dependent temperature field. At the heart of the models is a time-dependent magnetic field to which the core-flow is enslaved. In previous work we laid the foundation of the adjoint methodology, applied to a subset of the full equations [4]. As an intermediate step towards our ultimate vision of applying the techniques to a fully dynamic mode of the Earth's core tuned to geomagnetic observations, we present the intermediate step of applying the adjoint technique to the inertia-free Navier-Stokes equation in continuous form. We use synthetic observations derived from evolving a geophysically-reasonable magnetic field profile as the initial condition of our MHD system. Based on our study, we also propose several different strategies for accurately

  15. Parallelization of the Red-Black Algorithm on Solving the Second-Order PN Transport Equation with the Hybrid Finite Element Method

    SciTech Connect

    Yaqi Wang; Cristian Rabiti; Giuseppe Palmiotti

    2011-06-01

    The Red-Black algorithm has been successfully applied on solving the second-order parity transport equation with the PN approximation in angle and the Hybrid Finite Element Method (HFEM) in space, i.e., the Variational Nodal Method (VNM) [1,2,3,4,5]. Any transport solving techniques, including the Red-Black algorithm, need to be parallelized in order to take the advantage of the development of supercomputers with multiple processors for the advanced modeling and simulation. To our knowledge, an attempt [6] was done to parallelize it, but it was devoted only to the z axis plans in three-dimensional calculations. General parallelization of the Red-Black algorithm with the spatial domain decomposition has not been reported in the literature. In this summary, we present our implementation of the parallelization of the Red-Black algorithm and its efficiency results.

  16. Towards magnetic sounding of the Earth's core by an adjoint method

    NASA Astrophysics Data System (ADS)

    Li, K.; Jackson, A.; Livermore, P. W.

    2012-12-01

    Earth's magnetic field is generated and sustained by the so called geodynamo system in the core. Measurements of the geomagnetic field taken at the surface, downwards continued through the electrically insulating mantle to the core-mantle boundary (CMB), provide important constraints on the time evolution of the velocity, magnetic field and temperature anomaly in the fluid outer core. The aim of any study in data assimilation applied to the Earth's core is to produce a time-dependent model consistent with these observations [1]. Snapshots of these ``tuned" models provide a window through which the inner workings of the Earth's core, usually hidden from view, can be probed. We apply a variational data assimilation framework to an inertia-free magnetohydrodynamic system (MHD) [2]. Such a model is close to magnetostrophic balance [4], to which we have added viscosity to the dominant forces of Coriolis, pressure, Lorentz and buoyancy, believed to be a good approximation of the Earth's dynamo. As a starting point, we have chosen to neglect the buoyancy force, this being another unknown and, at this stage, an unnecessary complication. At the heart of the models is a time-dependent magnetic field which is interacting with the core flow (itself slaved to the magnetic field). Based on the methodology developed in Li et al. (2011) [3], we show further developments in which we apply the adjoint technique to our version of the Navier-Stokes equation in continuous form. In this talk, we present the initial results using perfect synthetic data without any observation error, performing closed-loop tests to demonstrate the ability of our model for retrieving the 3D structure of the velocity and the magnetic fields at the same time.

  17. Dirac lattices, zero-range potentials, and self-adjoint extension

    NASA Astrophysics Data System (ADS)

    Bordag, M.; Muñoz-Castañeda, J. M.

    2015-03-01

    We consider the electromagnetic field in the presence of polarizable point dipoles. In the corresponding effective Maxwell equation these dipoles are described by three dimensional delta function potentials. We review the approaches handling these: the self-adjoint extension, regularization/renormalization and the zero range potential methods. Their close interrelations are discussed in detail and compared with the electrostatic approach which drops the contributions from the self fields. For a homogeneous two dimensional lattice of dipoles we write down the complete solutions, which allow, for example, for an easy numerical treatment of the scattering of the electromagnetic field on the lattice or for investigating plasmons. Using these formulas, we consider the limiting case of vanishing lattice spacing, i.e., the transition to a continuous sheet. For a scalar field and for the TE polarization of the electromagnetic field this transition is smooth and results in the results known from the continuous sheet. Especially for the TE polarization, we reproduce the results known from the hydrodynamic model describing a two dimensional electron gas. For the TM polarization, for polarizability parallel and perpendicular to the lattice, in both cases, the transition is singular. For the parallel polarizability this is surprising and different from the hydrodynamic model. For perpendicular polarizability this is what was known in literature. We also investigate the case when the transition is done with dipoles described by smeared delta function, i.e., keeping a regularization. Here, for TM polarization for parallel polarizability, when subsequently doing the limit of vanishing lattice spacing, we reproduce the result known from the hydrodynamic model. In case of perpendicular polarizability we need an additional renormalization to reproduce the result obtained previously by stepping back from the dipole approximation.

  18. Adjoint-based airfoil shape optimization in transonic flow

    NASA Astrophysics Data System (ADS)

    Gramanzini, Joe-Ray

    The primary focus of this work is efficient aerodynamic shape optimization in transonic flow. Adjoint-based optimization techniques are employed on airfoil sections and evaluated in terms of computational accuracy as well as efficiency. This study examines two test cases proposed by the AIAA Aerodynamic Design Optimization Discussion Group. The first is a two-dimensional, transonic, inviscid, non-lifting optimization of a Modified-NACA 0012 airfoil. The second is a two-dimensional, transonic, viscous optimization problem using a RAE 2822 airfoil. The FUN3D CFD code of NASA Langley Research Center is used as the ow solver for the gradient-based optimization cases. Two shape parameterization techniques are employed to study their effect and the number of design variables on the final optimized shape: Multidisciplinary Aerodynamic-Structural Shape Optimization Using Deformation (MASSOUD) and the BandAids free-form deformation technique. For the two airfoil cases, angle of attack is treated as a global design variable. The thickness and camber distributions are the local design variables for MASSOUD, and selected airfoil surface grid points are the local design variables for BandAids. Using the MASSOUD technique, a drag reduction of 72.14% is achieved for the NACA 0012 case, reducing the total number of drag counts from 473.91 to 130.59. Employing the BandAids technique yields a 78.67% drag reduction, from 473.91 to 99.98. The RAE 2822 case exhibited a drag reduction from 217.79 to 132.79 counts, a 39.05% decrease using BandAids.

  19. A non-linear discontinuous Petrov-Galerkin method for removing oscillations in the solution of the time-dependent transport equation

    SciTech Connect

    Merton, S. R.; Smedley-Stevenson, R. P.; Pain, C. C.

    2012-07-01

    This paper describes a Non-Linear Discontinuous Petrov-Galerkin method and its application to the one-speed Boltzmann Transport Equation (BTE) for space-time problems. The purpose of the method is to remove unwanted oscillations in the transport solution which occur in the vicinity of sharp flux gradients, while improving computational efficiency and numerical accuracy. This is achieved by applying artificial dissipation in the solution gradient direction, internal to an element using a novel finite element (FE) Riemann approach. The added dissipation is calculated at each node of the finite element mesh based on local behaviour of the transport solution on both the spatial and temporal axes of the problem. Thus a different dissipation is used in different elements. The magnitude of dissipation that is used is obtained from a gradient-informed scaling of the advection velocities in the stabilisation term. This makes the method in its most general form non-linear. The method is implemented within a very general finite element Riemann framework. This makes it completely independent of choice of angular basis function allowing one to use different descriptions of the angular variation. Results show the non-linear scheme performs consistently well in demanding time-dependent multi-dimensional neutron transport problems. (authors)

  20. Assessing the Impact of Observations on Numerical Weather Forecasts Using the Adjoint Method

    NASA Technical Reports Server (NTRS)

    Gelaro, Ronald

    2012-01-01

    The adjoint of a data assimilation system provides a flexible and efficient tool for estimating observation impacts on short-range weather forecasts. The impacts of any or all observations can be estimated simultaneously based on a single execution of the adjoint system. The results can be easily aggregated according to data type, location, channel, etc., making this technique especially attractive for examining the impacts of new hyper-spectral satellite instruments and for conducting regular, even near-real time, monitoring of the entire observing system. This talk provides a general overview of the adjoint method, including the theoretical basis and practical implementation of the technique. Results are presented from the adjoint-based observation impact monitoring tool in NASA's GEOS-5 global atmospheric data assimilation and forecast system. When performed in conjunction with standard observing system experiments (OSEs), the adjoint results reveal both redundancies and dependencies between observing system impacts as observations are added or removed from the assimilation system. Understanding these dependencies may be important for optimizing the use of the current observational network and defining requirements for future observing systems