Discrete conservation laws and the convergence of long time simulations of the mkdv equation

NASA Astrophysics Data System (ADS)

Gorria, C.; Alejo, M. A.; Vega, L.

2013-02-01

Pseudospectral collocation methods and finite difference methods have been used for approximating an important family of soliton like solutions of the mKdV equation. These solutions present a structural instability which make difficult to approximate their evolution in long time intervals with enough accuracy. The standard numerical methods do not guarantee the convergence to the proper solution of the initial value problem and often fail by approaching solutions associated to different initial conditions. In this frame the numerical schemes that preserve the discrete invariants related to some conservation laws of this equation produce better results than the methods which only take care of a high consistency order. Pseudospectral spatial discretization appear as the most robust of the numerical methods, but finite difference schemes are useful in order to analyze the rule played by the conservation of the invariants in the convergence.

A conservative finite difference algorithm for the unsteady transonic potential equation in generalized coordinates

NASA Technical Reports Server (NTRS)

Bridgeman, J. O.; Steger, J. L.; Caradonna, F. X.

1982-01-01

An implicit, approximate-factorization, finite-difference algorithm has been developed for the computation of unsteady, inviscid transonic flows in two and three dimensions. The computer program solves the full-potential equation in generalized coordinates in conservation-law form in order to properly capture shock-wave position and speed. A body-fitted coordinate system is employed for the simple and accurate treatment of boundary conditions on the body surface. The time-accurate algorithm is modified to a conventional ADI relaxation scheme for steady-state computations. Results from two- and three-dimensional steady and two-dimensional unsteady calculations are compared with existing methods.

Finite difference methods for the solution of unsteady potential flows

NASA Technical Reports Server (NTRS)

Caradonna, F. X.

1982-01-01

Various problems which are confronted in the development of an unsteady finite difference potential code are reviewed mainly in the context of what is done for a typical small disturbance and full potential method. The issues discussed include choice of equations, linearization and conservation, differencing schemes, and algorithm development. A number of applications, including unsteady three dimensional rotor calculations, are demonstrated.

Parallel, adaptive finite element methods for conservation laws

NASA Technical Reports Server (NTRS)

Biswas, Rupak; Devine, Karen D.; Flaherty, Joseph E.

1994-01-01

We construct parallel finite element methods for the solution of hyperbolic conservation laws in one and two dimensions. Spatial discretization is performed by a discontinuous Galerkin finite element method using a basis of piecewise Legendre polynomials. Temporal discretization utilizes a Runge-Kutta method. Dissipative fluxes and projection limiting prevent oscillations near solution discontinuities. A posteriori estimates of spatial errors are obtained by a p-refinement technique using superconvergence at Radau points. The resulting method is of high order and may be parallelized efficiently on MIMD computers. We compare results using different limiting schemes and demonstrate parallel efficiency through computations on an NCUBE/2 hypercube. We also present results using adaptive h- and p-refinement to reduce the computational cost of the method.

Second-order accurate nonoscillatory schemes for scalar conservation laws

NASA Technical Reports Server (NTRS)

Huynh, Hung T.

1989-01-01

Explicit finite difference schemes for the computation of weak solutions of nonlinear scalar conservation laws is presented and analyzed. These schemes are uniformly second-order accurate and nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time.

A Novel Finite-Sum Inequality-Based Method for Robust H∞ Control of Uncertain Discrete-Time Takagi-Sugeno Fuzzy Systems With Interval-Like Time-Varying Delays.

PubMed

Zhang, Xian-Ming; Han, Qing-Long; Ge, Xiaohua

2017-09-22

This paper is concerned with the problem of robust H∞ control of an uncertain discrete-time Takagi-Sugeno fuzzy system with an interval-like time-varying delay. A novel finite-sum inequality-based method is proposed to provide a tighter estimation on the forward difference of certain Lyapunov functional, leading to a less conservative result. First, an auxiliary vector function is used to establish two finite-sum inequalities, which can produce tighter bounds for the finite-sum terms appearing in the forward difference of the Lyapunov functional. Second, a matrix-based quadratic convex approach is employed to equivalently convert the original matrix inequality including a quadratic polynomial on the time-varying delay into two boundary matrix inequalities, which delivers a less conservative bounded real lemma (BRL) for the resultant closed-loop system. Third, based on the BRL, a novel sufficient condition on the existence of suitable robust H∞ fuzzy controllers is derived. Finally, two numerical examples and a computer-simulated truck-trailer system are provided to show the effectiveness of the obtained results.

The P1-RKDG method for two-dimensional Euler equations of gas dynamics

NASA Technical Reports Server (NTRS)

Cockburn, Bernardo; Shu, Chi-Wang

1991-01-01

A class of nonlinearly stable Runge-Kutta local projection discontinuous Galerkin (RKDG) finite element methods for conservation laws is investigated. Two dimensional Euler equations for gas dynamics are solved using P1 elements. The generalization of the local projections, which for scalar nonlinear conservation laws was designed to satisfy a local maximum principle, to systems of conservation laws such as the Euler equations of gas dynamics using local characteristic decompositions is discussed. Numerical examples include the standard regular shock reflection problem, the forward facing step problem, and the double Mach reflection problem. These preliminary numerical examples are chosen to show the capacity of the approach to obtain nonlinearly stable results comparable with the modern nonoscillatory finite difference methods.

Finite difference methods for the solution of unsteady potential flows

NASA Technical Reports Server (NTRS)

Caradonna, F. X.

1985-01-01

A brief review is presented of various problems which are confronted in the development of an unsteady finite difference potential code. This review is conducted mainly in the context of what is done for a typical small disturbance and full potential methods. The issues discussed include choice of equation, linearization and conservation, differencing schemes, and algorithm development. A number of applications including unsteady three-dimensional rotor calculation, are demonstrated.

HEMP 3D: A finite difference program for calculating elastic-plastic flow, appendix B

NASA Astrophysics Data System (ADS)

Wilkins, Mark L.

1993-05-01

The HEMP 3D program can be used to solve problems in solid mechanics involving dynamic plasticity and time dependent material behavior and problems in gas dynamics. The equations of motion, the conservation equations, and the constitutive relations listed below are solved by finite difference methods following the format of the HEMP computer simulation program formulated in two space dimensions and time.

Numerical Simulation of a Solar Domestic Hot Water System

NASA Astrophysics Data System (ADS)

Mongibello, L.; Bianco, N.; Di Somma, M.; Graditi, G.; Naso, V.

2014-11-01

An innovative transient numerical model is presented for the simulation of a solar Domestic Hot Water (DHW) system. The solar collectors have been simulated by using a zerodimensional analytical model. The temperature distributions in the heat transfer fluid and in the water inside the tank have been evaluated by one-dimensional models. The reversion elimination algorithm has been used to include the effects of natural convection among the water layers at different heights in the tank on the thermal stratification. A finite difference implicit scheme has been implemented to solve the energy conservation equation in the coil heat exchanger, and the energy conservation equation in the tank has been solved by using the finite difference Euler implicit scheme. Energy conservation equations for the solar DHW components models have been coupled by means of a home-made implicit algorithm. Results of the simulation performed using as input data the experimental values of the ambient temperature and the solar irradiance in a summer day are presented and discussed.

Mass-corrections for the conservative coupling of flow and transport on collocated meshes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Waluga, Christian, E-mail: waluga@ma.tum.de; Wohlmuth, Barbara; Rüde, Ulrich

2016-01-15

Buoyancy-driven flow models demand a careful treatment of the mass-balance equation to avoid spurious source and sink terms in the non-linear coupling between flow and transport. In the context of finite-elements, it is therefore commonly proposed to employ sufficiently rich pressure spaces, containing piecewise constant shape functions to obtain local or even strong mass-conservation. In three-dimensional computations, this usually requires nonconforming approaches, special meshes or higher order velocities, which make these schemes prohibitively expensive for some applications and complicate the implementation into legacy code. In this paper, we therefore propose a lean and conservatively coupled scheme based on standard stabilizedmore » linear equal-order finite elements for the Stokes part and vertex-centered finite volumes for the energy equation. We show that in a weak mass-balance it is possible to recover exact conservation properties by a local flux-correction which can be computed efficiently on the control volume boundaries of the transport mesh. We discuss implementation aspects and demonstrate the effectiveness of the flux-correction by different two- and three-dimensional examples which are motivated by geophysical applications.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghosh, Debojyoti; Constantinescu, Emil M.

The numerical simulation of meso-, convective-, and microscale atmospheric flows requires the solution of the Euler or the Navier-Stokes equations. Nonhydrostatic weather prediction algorithms often solve the equations in terms of derived quantities such as Exner pressure and potential temperature (and are thus not conservative) and/or as perturbations to the hydrostatically balanced equilibrium state. This paper presents a well-balanced, conservative finite difference formulation for the Euler equations with a gravitational source term, where the governing equations are solved as conservation laws for mass, momentum, and energy. Preservation of the hydrostatic balance to machine precision by the discretized equations is essentialmore » because atmospheric phenomena are often small perturbations to this balance. The proposed algorithm uses the weighted essentially nonoscillatory and compact-reconstruction weighted essentially nonoscillatory schemes for spatial discretization that yields high-order accurate solutions for smooth flows and is essentially nonoscillatory across strong gradients; however, the well-balanced formulation may be used with other conservative finite difference methods. The performance of the algorithm is demonstrated on test problems as well as benchmark atmospheric flow problems, and the results are verified with those in the literature.« less

Numerical Simulation of Combustion and Rotor-Stator Interaction in a Turbine Combustor

DOE PAGES

Isvoranu, Dragos D.; Cizmas, Paul G. A.

2003-01-01

This article presents the development of a numerical algorithm for the computation of flow and combustion in a turbine combustor. The flow and combustion are modeled by the Reynolds-averaged Navier-Stokes equations coupled with the species-conservation equations. The chemistry model used herein is a two-step, global, finite-rate combustion model for methane and combustion gases. The governing equations are written in the strong conservation form and solved using a fully implicit, finite-difference approximation. The gas dynamics and chemistry equations are fully decoupled. A correction technique has been developed to enforce the conservation of mass fractions. The numerical algorithm developed herein has beenmore » used to investigate the flow and combustion in a one-stage turbine combustor.« less

Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method

NASA Astrophysics Data System (ADS)

Lai, Wencong; Khan, Abdul A.

2018-04-01

A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of Saint-Venant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.

Nonlinear truncation error analysis of finite difference schemes for the Euler equations

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Mcrae, D. S.

1983-01-01

It is pointed out that, in general, dissipative finite difference integration schemes have been found to be quite robust when applied to the Euler equations of gas dynamics. The present investigation considers a modified equation analysis of both implicit and explicit finite difference techniques as applied to the Euler equations. The analysis is used to identify those error terms which contribute most to the observed solution errors. A technique for analytically removing the dominant error terms is demonstrated, resulting in a greatly improved solution for the explicit Lax-Wendroff schemes. It is shown that the nonlinear truncation errors are quite large and distributed quite differently for each of the three conservation equations as applied to a one-dimensional shock tube problem.

On a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws. I - Nonstiff strongly dynamic problems

NASA Technical Reports Server (NTRS)

Harten, A.; Tal-Ezer, H.

1981-01-01

An implicit finite difference method of fourth order accuracy in space and time is introduced for the numerical solution of one-dimensional systems of hyperbolic conservation laws. The basic form of the method is a two-level scheme which is unconditionally stable and nondissipative. The scheme uses only three mesh points at level t and three mesh points at level t + delta t. The dissipative version of the basic method given is conditionally stable under the CFL (Courant-Friedrichs-Lewy) condition. This version is particularly useful for the numerical solution of problems with strong but nonstiff dynamic features, where the CFL restriction is reasonable on accuracy grounds. Numerical results are provided to illustrate properties of the proposed method.

Arbitrary-Order Conservative and Consistent Remapping and a Theory of Linear Maps: Part II

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ullrich, Paul A.; Devendran, Dharshi; Johansen, Hans

2016-04-01

The focus on this series of articles is on the generation of accurate, conservative, consistent, and (optionally) monotone linear offline maps. This paper is the second in the series. It extends on the first part by describing four examples of 2D linear maps that can be constructed in accordance with the theory of the earlier work. The focus is again on spherical geometry, although these techniques can be readily extended to arbitrary manifolds. The four maps include conservative, consistent, and (optionally) monotone linear maps (i) between two finite-volume meshes, (ii) from finite-volume to finite-element meshes using a projection-type approach, (iii)more » from finite-volume to finite-element meshes using volumetric integration, and (iv) between two finite-element meshes. Arbitrary order of accuracy is supported for each of the described nonmonotone maps.« less

Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids II: Extension to Two Dimensional Scalar Equation

NASA Technical Reports Server (NTRS)

Wang, Z. J.; Liu, Yen; Kwak, Dochan (Technical Monitor)

2002-01-01

The framework for constructing a high-order, conservative Spectral (Finite) Volume (SV) method is presented for two-dimensional scalar hyperbolic conservation laws on unstructured triangular grids. Each triangular grid cell forms a spectral volume (SV), and the SV is further subdivided into polygonal control volumes (CVs) to supported high-order data reconstructions. Cell-averaged solutions from these CVs are used to reconstruct a high order polynomial approximation in the SV. Each CV is then updated independently with a Godunov-type finite volume method and a high-order Runge-Kutta time integration scheme. A universal reconstruction is obtained by partitioning all SVs in a geometrically similar manner. The convergence of the SV method is shown to depend on how a SV is partitioned. A criterion based on the Lebesgue constant has been developed and used successfully to determine the quality of various partitions. Symmetric, stable, and convergent linear, quadratic, and cubic SVs have been obtained, and many different types of partitions have been evaluated. The SV method is tested for both linear and non-linear model problems with and without discontinuities.

A mass-conservative adaptive FAS multigrid solver for cell-centered finite difference methods on block-structured, locally-cartesian grids

NASA Astrophysics Data System (ADS)

Feng, Wenqiang; Guo, Zhenlin; Lowengrub, John S.; Wise, Steven M.

2018-01-01

We present a mass-conservative full approximation storage (FAS) multigrid solver for cell-centered finite difference methods on block-structured, locally cartesian grids. The algorithm is essentially a standard adaptive FAS (AFAS) scheme, but with a simple modification that comes in the form of a mass-conservative correction to the coarse-level force. This correction is facilitated by the creation of a zombie variable, analogous to a ghost variable, but defined on the coarse grid and lying under the fine grid refinement patch. We show that a number of different types of fine-level ghost cell interpolation strategies could be used in our framework, including low-order linear interpolation. In our approach, the smoother, prolongation, and restriction operations need never be aware of the mass conservation conditions at the coarse-fine interface. To maintain global mass conservation, we need only modify the usual FAS algorithm by correcting the coarse-level force function at points adjacent to the coarse-fine interface. We demonstrate through simulations that the solver converges geometrically, at a rate that is h-independent, and we show the generality of the solver, applying it to several nonlinear, time-dependent, and multi-dimensional problems. In several tests, we show that second-order asymptotic (h → 0) convergence is observed for the discretizations, provided that (1) at least linear interpolation of the ghost variables is employed, and (2) the mass conservation corrections are applied to the coarse-level force term.

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.

The Finite-Surface Method for incompressible flow: a step beyond staggered grid

NASA Astrophysics Data System (ADS)

Hokpunna, Arpiruk; Misaka, Takashi; Obayashi, Shigeru

2017-11-01

We present a newly developed higher-order finite surface method for the incompressible Navier-Stokes equations (NSE). This method defines the velocities as a surface-averaged value on the surfaces of the pressure cells. Consequently, the mass conservation on the pressure cells becomes an exact equation. The only things left to approximate is the momentum equation and the pressure at the new time step. At certain conditions, the exact mass conservation enables the explicit n-th order accurate NSE solver to be used with the pressure treatment that is two or four order less accurate without loosing the apparent convergence rate. This feature was not possible with finite volume of finite difference methods. We use Fourier analysis with a model spectrum to determine the condition and found that the range covers standard boundary layer flows. The formal convergence and the performance of the proposed scheme is compared with a sixth-order finite volume method. Finally, the accuracy and performance of the method is evaluated in turbulent channel flows. This work is partially funded by a research colloaboration from IFS, Tohoku university and ASEAN+3 funding scheme from CMUIC, Chiang Mai University.

Conservative discretization of the Landau collision integral

DOE PAGES

Hirvijoki, E.; Adams, M. F.

2017-03-28

Here we describe a density, momentum-, and energy-conserving discretization of the nonlinear Landau collision integral. The method is suitable for both the finite-element and discontinuous Galerkin methods and does not require structured meshes. The conservation laws for the discretization are proven algebraically and demonstrated numerically for an axially symmetric nonlinear relaxation problem using a finite-element implementation.

Second order accurate finite difference approximations for the transonic small disturbance equation and the full potential equation

NASA Technical Reports Server (NTRS)

Mostrel, M. M.

1988-01-01

New shock-capturing finite difference approximations for solving two scalar conservation law nonlinear partial differential equations describing inviscid, isentropic, compressible flows of aerodynamics at transonic speeds are presented. A global linear stability theorem is applied to these schemes in order to derive a necessary and sufficient condition for the finite element method. A technique is proposed to render the described approximations total variation-stable by applying the flux limiters to the nonlinear terms of the difference equation dimension by dimension. An entropy theorem applying to the approximations is proved, and an implicit, forward Euler-type time discretization of the approximation is presented. Results of some numerical experiments using the approximations are reported.

Newton's method applied to finite-difference approximations for the steady-state compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Bailey, Harry E.; Beam, Richard M.

1991-01-01

Finite-difference approximations for steady-state compressible Navier-Stokes equations, whose two spatial dimensions are written in generalized curvilinear coordinates and strong conservation-law form, are presently solved by means of Newton's method in order to obtain a lifting-airfoil flow field under subsonic and transonnic conditions. In addition to ascertaining the computational requirements of an initial guess ensuring convergence and the degree of computational efficiency obtainable via the approximate Newton method's freezing of the Jacobian matrices, attention is given to the need for auxiliary methods assessing the temporal stability of steady-state solutions. It is demonstrated that nonunique solutions of the finite-difference equations are obtainable by Newton's method in conjunction with a continuation method.

An improved flux-split algorithm applied to hypersonic flows in chemical equilibrium

NASA Technical Reports Server (NTRS)

Palmer, Grant

1988-01-01

An explicit, finite-difference, shock-capturing numerical algorithm is presented and applied to hypersonic flows assumed to be in thermochemical equilibrium. Real-gas chemistry is either loosely coupled to the gasdynamics by way of a Gibbs free energy minimization package or fully coupled using species mass conservation equations with finite-rate chemical reactions. A scheme is developed that maintains stability in the explicit, finite-rate formulation while allowing relatively high time steps. The codes use flux vector splitting to difference the inviscid fluxes and employ real-gas corrections to viscosity and thermal conductivity. Numerical results are compared against existing ballistic range and flight data. Flows about complex geometries are also computed.

Ion-Conserving Modified Poisson-Boltzmann Theory Considering a Steric Effect in an Electrolyte

NASA Astrophysics Data System (ADS)

Sugioka, Hideyuki

2016-12-01

The modified Poisson-Nernst-Planck (MPNP) and modified Poisson-Boltzmann (MPB) equations are well known as fundamental equations that consider a steric effect, which prevents unphysical ion concentrations. However, it is unclear whether they are equivalent or not. To clarify this problem, we propose an improved free energy formulation that considers a steric limit with an ion-conserving condition and successfully derive the ion-conserving modified Poisson-Boltzmann (IC-MPB) equations that are equivalent to the MPNP equations. Furthermore, we numerically examine the equivalence by comparing between the IC-MPB solutions obtained by the Newton method and the steady MPNP solutions obtained by the finite-element finite-volume method. A surprising aspect of our finding is that the MPB solutions are much different from the MPNP (IC-MPB) solutions in a confined space. We consider that our findings will significantly contribute to understanding the surface science between solids and liquids.

High-resolution schemes for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Harten, A.

1982-01-01

A class of new explicit second order accurate finite difference schemes for the computation of weak solutions of hyperbolic conservation laws is presented. These highly nonlinear schemes are obtained by applying a nonoscillatory first order accurae scheme to an appropriately modified flux function. The so derived second order accurate schemes achieve high resolution while preserving the robustness of the original nonoscillatory first order accurate scheme.

Involution and Difference Schemes for the Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.; Blinkov, Yuri A.

In the present paper we consider the Navier-Stokes equations for the two-dimensional viscous incompressible fluid flows and apply to these equations our earlier designed general algorithmic approach to generation of finite-difference schemes. In doing so, we complete first the Navier-Stokes equations to involution by computing their Janet basis and discretize this basis by its conversion into the integral conservation law form. Then we again complete the obtained difference system to involution with eliminating the partial derivatives and extracting the minimal Gröbner basis from the Janet basis. The elements in the obtained difference Gröbner basis that do not contain partial derivatives of the dependent variables compose a conservative difference scheme. By exploiting arbitrariness in the numerical integration approximation we derive two finite-difference schemes that are similar to the classical scheme by Harlow and Welch. Each of the two schemes is characterized by a 5×5 stencil on an orthogonal and uniform grid. We also demonstrate how an inconsistent difference scheme with a 3×3 stencil is generated by an inappropriate numerical approximation of the underlying integrals.

High-Order Entropy Stable Formulations for Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Fisher, Travis C.

2013-01-01

A systematic approach is presented for developing entropy stable (SS) formulations of any order for the Navier-Stokes equations. These SS formulations discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality. They are valid for smooth as well as discontinuous flows provided sufficient dissipation is added at shocks and discontinuities. Entropy stable formulations exist for all diagonal norm, summation-by-parts (SBP) operators, including all centered finite-difference operators, Legendre collocation finite-element operators, and certain finite-volume operators. Examples are presented using various entropy stable formulations that demonstrate the current state-of-the-art of these schemes.

A locally conservative non-negative finite element formulation for anisotropic advective-diffusive-reactive systems

NASA Astrophysics Data System (ADS)

Mudunuru, M. K.; Shabouei, M.; Nakshatrala, K.

2015-12-01

Advection-diffusion-reaction (ADR) equations appear in various areas of life sciences, hydrogeological systems, and contaminant transport. Obtaining stable and accurate numerical solutions can be challenging as the underlying equations are coupled, nonlinear, and non-self-adjoint. Currently, there is neither a robust computational framework available nor a reliable commercial package known that can handle various complex situations. Herein, the objective of this poster presentation is to present a novel locally conservative non-negative finite element formulation that preserves the underlying physical and mathematical properties of a general linear transient anisotropic ADR equation. In continuous setting, governing equations for ADR systems possess various important properties. In general, all these properties are not inherited during finite difference, finite volume, and finite element discretizations. The objective of this poster presentation is two fold: First, we analyze whether the existing numerical formulations (such as SUPG and GLS) and commercial packages provide physically meaningful values for the concentration of the chemical species for various realistic benchmark problems. Furthermore, we also quantify the errors incurred in satisfying the local and global species balance for two popular chemical kinetics schemes: CDIMA (chlorine dioxide-iodine-malonic acid) and BZ (Belousov--Zhabotinsky). Based on these numerical simulations, we show that SUPG and GLS produce unphysical values for concentration of chemical species due to the violation of the non-negative constraint, contain spurious node-to-node oscillations, and have large errors in local and global species balance. Second, we proposed a novel finite element formulation to overcome the above difficulties. The proposed locally conservative non-negative computational framework based on low-order least-squares finite elements is able to preserve these underlying physical and mathematical properties. Several representative numerical examples are discussed to illustrate the importance of the proposed numerical formulations to accurately describe various aspects of mixing process in chaotic flows and to simulate transport in highly heterogeneous anisotropic media.

GEMPIC: geometric electromagnetic particle-in-cell methods

NASA Astrophysics Data System (ADS)

Kraus, Michael; Kormann, Katharina; Morrison, Philip J.; Sonnendrücker, Eric

2017-08-01

We present a novel framework for finite element particle-in-cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov-Maxwell system. We derive a semi-discrete Poisson bracket, which retains the defining properties of a bracket, anti-symmetry and the Jacobi identity, as well as conservation of its Casimir invariants, implying that the semi-discrete system is still a Hamiltonian system. In order to obtain a fully discrete Poisson integrator, the semi-discrete bracket is used in conjunction with Hamiltonian splitting methods for integration in time. Techniques from finite element exterior calculus ensure conservation of the divergence of the magnetic field and Gauss' law as well as stability of the field solver. The resulting methods are gauge invariant, feature exact charge conservation and show excellent long-time energy and momentum behaviour. Due to the generality of our framework, these conservation properties are guaranteed independently of a particular choice of the finite element basis, as long as the corresponding finite element spaces satisfy certain compatibility conditions.

Numerical solution of nonlinear partial differential equations of mixed type. [finite difference approximation

NASA Technical Reports Server (NTRS)

Jameson, A.

1976-01-01

A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.

Chiral anomaly and anomalous finite-size conductivity in graphene

NASA Astrophysics Data System (ADS)

Shen, Shun-Qing; Li, Chang-An; Niu, Qian

2017-09-01

Graphene is a monolayer of carbon atoms packed into a hexagon lattice to host two spin degenerate pairs of massless two-dimensional Dirac fermions with different chirality. It is known that the existence of non-zero electric polarization in reduced momentum space which is associated with a hidden chiral symmetry will lead to the zero-energy flat band of a zigzag nanoribbon and some anomalous transport properties. Here it is proposed that the Adler-Bell-Jackiw chiral anomaly or non-conservation of chiral charges of Dirac fermions at different valleys can be realized in a confined ribbon of finite width, even in the absence of a magnetic field. In the laterally diffusive regime, the finite-size correction to conductivity is always positive and is inversely proportional to the square of the lateral dimension W, which is different from the finite-size correction inversely proportional to W from the boundary modes. This anomalous finite-size conductivity reveals the signature of the chiral anomaly in graphene, and it is measurable experimentally. This finding provides an alternative platform to explore the purely quantum mechanical effect in graphene.

New developments in the method of space-time conservation element and solution element: Applications to the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

1993-01-01

A new numerical framework for solving conservation laws is being developed. This new approach differs substantially in both concept and methodology from the well-established methods--i.e., finite difference, finite volume, finite element, and spectral methods. It is conceptually simple and designed to avoid several key limitations to the above traditional methods. An explicit model scheme for solving a simple 1-D unsteady convection-diffusion equation is constructed and used to illuminate major differences between the current method and those mentioned above. Unexpectedly, its amplification factors for the pure convection and pure diffusion cases are identical to those of the Leapfrog and the DuFort-Frankel schemes, respectively. Also, this explicit scheme and its Navier-Stokes extension have the unusual property that their stabilities are limited only by the CFL condition. Moreover, despite the fact that it does not use any flux-limiter or slope-limiter, the Navier-Stokes solver is capable of generating highly accurate shock tube solutions with shock discontinuities being resolved within one mesh interval. An accurate Euler solver also is constructed through another extension. It has many unusual properties, e.g., numerical diffusion at all mesh points can be controlled by a set of local parameters.

A semi-implicit finite difference model for three-dimensional tidal circulation,

USGS Publications Warehouse

Casulli, V.; Cheng, R.T.

1992-01-01

A semi-implicit finite difference formulation for the numerical solution of three-dimensional tidal circulation is presented. The governing equations are the three-dimensional Reynolds equations in which the pressure is assumed to be hydrostatic. A minimal degree of implicitness has been introduced in the finite difference formula so that in the absence of horizontal viscosity the resulting algorithm is unconditionally stable at a minimal computational cost. When only one vertical layer is specified this method reduces, as a particular case, to a semi-implicit scheme for the solutions of the corresponding two-dimensional shallow water equations. The resulting two- and three-dimensional algorithm is fast, accurate and mass conservative. This formulation includes the simulation of flooding and drying of tidal flats, and is fully vectorizable for an efficient implementation on modern vector computers.

Flux vector splitting of the inviscid equations with application to finite difference methods

NASA Technical Reports Server (NTRS)

Steger, J. L.; Warming, R. F.

1979-01-01

The conservation-law form of the inviscid gasdynamic equations has the remarkable property that the nonlinear flux vectors are homogeneous functions of degree one. This property readily permits the splitting of flux vectors into subvectors by similarity transformations so that each subvector has associated with it a specified eigenvalue spectrum. As a consequence of flux vector splitting, new explicit and implicit dissipative finite-difference schemes are developed for first-order hyperbolic systems of equations. Appropriate one-sided spatial differences for each split flux vector are used throughout the computational field even if the flow is locally subsonic. The results of some preliminary numerical computations are included.

Mass Conservation in Modeling Moisture Diffusion in Multi-Layer Carbon Composite Structures

NASA Technical Reports Server (NTRS)

Nurge, Mark A.; Youngquist, Robert C.; Starr, Stanley O.

2009-01-01

Moisture diffusion in multi-layer carbon composite structures is difficult to model using finite difference methods due to the discontinuity in concentrations between adjacent layers of differing materials. Applying a mass conserving approach at these boundaries proved to be effective at accurately predicting moisture uptake for a sample exposed to a fixed temperature and relative humidity. Details of the model developed are presented and compared with actual moisture uptake data gathered over 130 days from a graphite epoxy composite sandwich coupon with a Rohacell foam core.

Rotordynamic coefficients for labyrinth seals calculated by means of a finite difference technique

NASA Technical Reports Server (NTRS)

Nordmann, R.; Weiser, P.

1989-01-01

The compressible, turbulent, time dependent and three dimensional flow in a labyrinth seal can be described by the Navier-Stokes equations in conjunction with a turbulence model. Additionally, equations for mass and energy conservation and an equation of state are required. To solve these equations, a perturbation analysis is performed yielding zeroth order equations for centric shaft position and first order equations describing the flow field for small motions around the seal center. For numerical solution a finite difference method is applied to the zeroth and first order equations resulting in leakage and dynamic seal coefficients respectively.

Heat and mass transfer in a dissociated laminar boundary layer of air with consideration of the finite rate of chemical reaction

NASA Technical Reports Server (NTRS)

Oyegbesan, A. O.; Algermissen, J.

1986-01-01

A numerical investigation of heat and mass transfer in a dissociated laminar boundary layer of air on an isothermal flat plate is carried out for different degrees of cooling of the wall. A finite-difference chemical model is used to study elementary reactions involving NO2 and N2O. The analysis is based on equations of continuity, momentum, energy, conservation and state for the two-dimensional viscous flow of a reacting multicomponent mixtures. Attention is given to the effects of both catalyticity and noncatalyticity of the wall.

On the construction and application of implicit factored schemes for conservation laws. [in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Warming, R. F.; Beam, R. M.

1978-01-01

Efficient, noniterative, implicit finite difference algorithms are systematically developed for nonlinear conservation laws including purely hyperbolic systems and mixed hyperbolic parabolic systems. Utilization of a rational fraction or Pade time differencing formulas, yields a direct and natural derivation of an implicit scheme in a delta form. Attention is given to advantages of the delta formation and to various properties of one- and two-dimensional algorithms.

Fluctuations and correlations of conserved charges in QCD at finite temperature with effective models

NASA Astrophysics Data System (ADS)

Fu, Wei-Jie; Liu, Yu-Xin; Wu, Yue-Liang

2010-01-01

We study fluctuations of conserved charges including baryon number, electric charge, and strangeness as well as the correlations among these conserved charges in the 2+1 flavor Polyakov-Nambu-Jona-Lasinio model at finite temperature. The calculated results are compared with those obtained from recent lattice calculations performed with an improved staggered fermion action at two values of the lattice cutoff with almost physical up and down quark masses and a physical value for the strange quark mass. We find that our calculated results are well consistent with those obtained in lattice calculations except for some quantitative differences for fluctuations related with strange quarks. Our calculations indicate that there is a pronounced cusp in the ratio of the quartic to quadratic fluctuations of baryon number, i.e. χ4B/χ2B, at the critical temperature during the phase transition, which confirms that χ4B/χ2B is a useful probe of the deconfinement and chiral phase transition.

High Order Finite Difference Methods with Subcell Resolution for 2D Detonation Waves

NASA Technical Reports Server (NTRS)

Wang, W.; Shu, C. W.; Yee, H. C.; Sjogreen, B.

2012-01-01

In simulating hyperbolic conservation laws in conjunction with an inhomogeneous stiff source term, if the solution is discontinuous, spurious numerical results may be produced due to different time scales of the transport part and the source term. This numerical issue often arises in combustion and high speed chemical reacting flows.

Lagrangian continuum dynamics in ALEGRA.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wong, Michael K. W.; Love, Edward

Alegra is an ALE (Arbitrary Lagrangian-Eulerian) multi-material finite element code that emphasizes large deformations and strong shock physics. The Lagrangian continuum dynamics package in Alegra uses a Galerkin finite element spatial discretization and an explicit central-difference stepping method in time. The goal of this report is to describe in detail the characteristics of this algorithm, including the conservation and stability properties. The details provided should help both researchers and analysts understand the underlying theory and numerical implementation of the Alegra continuum hydrodynamics algorithm.

An energy and potential enstrophy conserving scheme for the shallow water equations. [orography effects on atmospheric circulation

NASA Technical Reports Server (NTRS)

Arakawa, A.; Lamb, V. R.

1979-01-01

A three-dimensional finite difference scheme for the solution of the shallow water momentum equations which accounts for the conservation of potential enstrophy in the flow of a homogeneous incompressible shallow atmosphere over steep topography as well as for total energy conservation is presented. The scheme is derived to be consistent with a reasonable scheme for potential vorticity advection in a long-term integration for a general flow with divergent mass flux. Numerical comparisons of the characteristics of the present potential enstrophy-conserving scheme with those of a scheme that conserves potential enstrophy only for purely horizontal nondivergent flow are presented which demonstrate the reduction of computational noise in the wind field with the enstrophy-conserving scheme and its convergence even in relatively coarse grids.

Semi-discrete approximations to nonlinear systems of conservation laws; consistency and L(infinity)-stability imply convergence

NASA Technical Reports Server (NTRS)

Tadmor, Eitan

1988-01-01

A convergence theory for semi-discrete approximations to nonlinear systems of conservation laws is developed. It is shown, by a series of scalar counter-examples, that consistency with the conservation law alone does not guarantee convergence. Instead, a notion of consistency which takes into account both the conservation law and its augmenting entropy condition is introduced. In this context it is concluded that consistency and L(infinity)-stability guarantee for a relevant class of admissible entropy functions, that their entropy production rate belongs to a compact subset of H(loc)sup -1 (x,t). One can now use compensated compactness arguments in order to turn this conclusion into a convergence proof. The current state of the art for these arguments includes the scalar and a wide class of 2 x 2 systems of conservation laws. The general framework of the vanishing viscosity method is studied as an effective way to meet the consistency and L(infinity)-stability requirements. How this method is utilized to enforce consistency and stability for scalar conservation laws is shown. In this context we prove, under the appropriate assumptions, the convergence of finite difference approximations (e.g., the high resolution TVD and UNO methods), finite element approximations (e.g., the Streamline-Diffusion methods) and spectral and pseudospectral approximations (e.g., the Spectral Viscosity methods).

Semi-discrete approximations to nonlinear systems of conservation laws; consistency and L(infinity)-stability imply convergence. Final report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tadmor, E.

1988-07-01

A convergence theory for semi-discrete approximations to nonlinear systems of conservation laws is developed. It is shown, by a series of scalar counter-examples, that consistency with the conservation law alone does not guarantee convergence. Instead, a notion of consistency which takes into account both the conservation law and its augmenting entropy condition is introduced. In this context it is concluded that consistency and L(infinity)-stability guarantee for a relevant class of admissible entropy functions, that their entropy production rate belongs to a compact subset of H(loc)sup -1 (x,t). One can now use compensated compactness arguments in order to turn this conclusionmore » into a convergence proof. The current state of the art for these arguments includes the scalar and a wide class of 2 x 2 systems of conservation laws. The general framework of the vanishing viscosity method is studied as an effective way to meet the consistency and L(infinity)-stability requirements. How this method is utilized to enforce consistency and stability for scalar conservation laws is shown. In this context we prove, under the appropriate assumptions, the convergence of finite difference approximations (e.g., the high resolution TVD and UNO methods), finite element approximations (e.g., the Streamline-Diffusion methods) and spectral and pseudospectral approximations (e.g., the Spectral Viscosity methods).« less

Conservation laws shape dissipation

NASA Astrophysics Data System (ADS)

Rao, Riccardo; Esposito, Massimiliano

2018-02-01

Starting from the most general formulation of stochastic thermodynamics—i.e. a thermodynamically consistent nonautonomous stochastic dynamics describing systems in contact with several reservoirs—we define a procedure to identify the conservative and the minimal set of nonconservative contributions in the entropy production. The former is expressed as the difference between changes caused by time-dependent drivings and a generalized potential difference. The latter is a sum over the minimal set of flux-force contributions controlling the dissipative flows across the system. When the system is initially prepared at equilibrium (e.g. by turning off drivings and forces), a finite-time detailed fluctuation theorem holds for the different contributions. Our approach relies on identifying the complete set of conserved quantities and can be viewed as the extension of the theory of generalized Gibbs ensembles to nonequilibrium situations.

Single-cone finite-difference schemes for the (2+1)-dimensional Dirac equation in general electromagnetic textures

NASA Astrophysics Data System (ADS)

Pötz, Walter

2017-11-01

A single-cone finite-difference lattice scheme is developed for the (2+1)-dimensional Dirac equation in presence of general electromagnetic textures. The latter is represented on a (2+1)-dimensional staggered grid using a second-order-accurate finite difference scheme. A Peierls-Schwinger substitution to the wave function is used to introduce the electromagnetic (vector) potential into the Dirac equation. Thereby, the single-cone energy dispersion and gauge invariance are carried over from the continuum to the lattice formulation. Conservation laws and stability properties of the formal scheme are identified by comparison with the scheme for zero vector potential. The placement of magnetization terms is inferred from consistency with the one for the vector potential. Based on this formal scheme, several numerical schemes are proposed and tested. Elementary examples for single-fermion transport in the presence of in-plane magnetization are given, using material parameters typical for topological insulator surfaces.

Verlet scheme non-conservativeness for simulation of spherical particles collisional dynamics and method of its compensation

NASA Astrophysics Data System (ADS)

Savin, Andrei V.; Smirnov, Petr G.

2018-05-01

Simulation of collisional dynamics of a large ensemble of monodisperse particles by the method of discrete elements is considered. Verle scheme is used for integration of the equations of motion. Non-conservativeness of the finite-difference scheme is discovered depending on the time step, which is equivalent to a pure-numerical energy source appearance in the process of collision. Compensation method for the source is proposed and tested.

A 3D finite element ALE method using an approximate Riemann solution

DOE PAGES

Chiravalle, V. P.; Morgan, N. R.

2016-08-09

Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann-like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann-like problem. Here, two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well-known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problemmore » results are presented.« less

A 3D finite element ALE method using an approximate Riemann solution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chiravalle, V. P.; Morgan, N. R.

Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann-like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann-like problem. Here, two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well-known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problemmore » results are presented.« less

Divergence preserving discrete surface integral methods for Maxwell's curl equations using non-orthogonal unstructured grids

NASA Technical Reports Server (NTRS)

Madsen, Niel K.

1992-01-01

Several new discrete surface integral (DSI) methods for solving Maxwell's equations in the time-domain are presented. These methods, which allow the use of general nonorthogonal mixed-polyhedral unstructured grids, are direct generalizations of the canonical staggered-grid finite difference method. These methods are conservative in that they locally preserve divergence or charge. Employing mixed polyhedral cells, (hexahedral, tetrahedral, etc.) these methods allow more accurate modeling of non-rectangular structures and objects because the traditional stair-stepped boundary approximations associated with the orthogonal grid based finite difference methods can be avoided. Numerical results demonstrating the accuracy of these new methods are presented.

Proliferative lifespan is conserved after nuclear transfer.

PubMed

Clark, A John; Ferrier, Patricia; Aslam, Samena; Burl, Sarah; Denning, Chris; Wylie, Diana; Ross, Arlene; de Sousa, Paul; Wilmut, Ian; Cui, Wei

2003-06-01

Cultured primary cells exhibit a finite proliferative lifespan, termed the Hayflick limit. Cloning by nuclear transfer can reverse this cellular ageing process and can be accomplished with cultured cells nearing senescence. Here we describe nuclear transfer experiments in which donor cell lines at different ages and with different proliferative capacities were used to clone foetuses and animals from which new primary cell lines were generated. The rederived lines had the same proliferative capacity and rate of telomere shortening as the donor cell lines, suggesting that these are innate, genetically determined, properties that are conserved by nuclear transfer.

Finite Volume Methods: Foundation and Analysis

NASA Technical Reports Server (NTRS)

Barth, Timothy; Ohlberger, Mario

2003-01-01

Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems. They are extensively used in fluid mechanics, porous media flow, meteorology, electromagnetics, models of biological processes, semi-conductor device simulation and many other engineering areas governed by conservative systems that can be written in integral control volume form. This article reviews elements of the foundation and analysis of modern finite volume methods. The primary advantages of these methods are numerical robustness through the obtention of discrete maximum (minimum) principles, applicability on very general unstructured meshes, and the intrinsic local conservation properties of the resulting schemes. Throughout this article, specific attention is given to scalar nonlinear hyperbolic conservation laws and the development of high order accurate schemes for discretizing them. A key tool in the design and analysis of finite volume schemes suitable for non-oscillatory discontinuity capturing is discrete maximum principle analysis. A number of building blocks used in the development of numerical schemes possessing local discrete maximum principles are reviewed in one and several space dimensions, e.g. monotone fluxes, E-fluxes, TVD discretization, non-oscillatory reconstruction, slope limiters, positive coefficient schemes, etc. When available, theoretical results concerning a priori and a posteriori error estimates are given. Further advanced topics are then considered such as high order time integration, discretization of diffusion terms and the extension to systems of nonlinear conservation laws.

Grid generation about complex three-dimensional aircraft configurations

NASA Technical Reports Server (NTRS)

Klopfer, Goetz H.

1991-01-01

The problem of obtaining three dimensional grids with sufficient resolution to resolve all the flow or other physical features of interest is addressed. The generation of a computational grid involves a series of compromises to resolve several conflicting requirements. On one hand, one would like the grid to be fine enough and not too skewed to reduce the numerical errors and to adequately resolve the pertinent physical features of the flow field about the aircraft. On the other hand, the capabilities of present or even future supercomputers are finite and the number of mesh points must be limited to a reasonable number: one which is usually much less than desired for numerical accuracy. One technique to overcome this limitation is the 'zonal' grid approach. In this method, the overall field is subdivided into smaller zones or blocks in each of which an independent grid is generated with enough grid density to resolve the flow features in that zone. The zonal boundaries or interfaces require special boundary conditions such that the conservation properties of the governing equations are observed. Much work was done in 3-D zonal approaches with nonconservative zonal interfaces. A 3-D zonal conservative interfacing method that is efficient and easy to implement was developed during the past year. During the course of the work, it became apparent that it would be much more feasible to do the conservative interfacing with cell-centered finite volume codes instead of the originally planned finite difference codes. Accordingly, the CNS code was converted to finite volume form. This new version of the code is named CNSFV. The original multi-zonal interfacing capability of the CNS code was enhanced by generalizing the procedure to allow for completely arbitrarily shaped zones with no mesh continuity between the zones. While this zoning capability works well for most flow situations, it is, however, still nonconservative. The conservative interface algorithm was also implemented but was not completely validated.

A locally conservative stabilized continuous Galerkin finite element method for two-phase flow in poroelastic subsurfaces

NASA Astrophysics Data System (ADS)

Deng, Q.; Ginting, V.; McCaskill, B.; Torsu, P.

2017-10-01

We study the application of a stabilized continuous Galerkin finite element method (CGFEM) in the simulation of multiphase flow in poroelastic subsurfaces. The system involves a nonlinear coupling between the fluid pressure, subsurface's deformation, and the fluid phase saturation, and as such, we represent this coupling through an iterative procedure. Spatial discretization of the poroelastic system employs the standard linear finite element in combination with a numerical diffusion term to maintain stability of the algebraic system. Furthermore, direct calculation of the normal velocities from pressure and deformation does not entail a locally conservative field. To alleviate this drawback, we propose an element based post-processing technique through which local conservation can be established. The performance of the method is validated through several examples illustrating the convergence of the method, the effectivity of the stabilization term, and the ability to achieve locally conservative normal velocities. Finally, the efficacy of the method is demonstrated through simulations of realistic multiphase flow in poroelastic subsurfaces.

Efficient conservative ADER schemes based on WENO reconstruction and space-time predictor in primitive variables

NASA Astrophysics Data System (ADS)

Zanotti, Olindo; Dumbser, Michael

2016-01-01

We present a new version of conservative ADER-WENO finite volume schemes, in which both the high order spatial reconstruction as well as the time evolution of the reconstruction polynomials in the local space-time predictor stage are performed in primitive variables, rather than in conserved ones. To obtain a conservative method, the underlying finite volume scheme is still written in terms of the cell averages of the conserved quantities. Therefore, our new approach performs the spatial WENO reconstruction twice: the first WENO reconstruction is carried out on the known cell averages of the conservative variables. The WENO polynomials are then used at the cell centers to compute point values of the conserved variables, which are subsequently converted into point values of the primitive variables. This is the only place where the conversion from conservative to primitive variables is needed in the new scheme. Then, a second WENO reconstruction is performed on the point values of the primitive variables to obtain piecewise high order reconstruction polynomials of the primitive variables. The reconstruction polynomials are subsequently evolved in time with a novel space-time finite element predictor that is directly applied to the governing PDE written in primitive form. The resulting space-time polynomials of the primitive variables can then be directly used as input for the numerical fluxes at the cell boundaries in the underlying conservative finite volume scheme. Hence, the number of necessary conversions from the conserved to the primitive variables is reduced to just one single conversion at each cell center. We have verified the validity of the new approach over a wide range of hyperbolic systems, including the classical Euler equations of gas dynamics, the special relativistic hydrodynamics (RHD) and ideal magnetohydrodynamics (RMHD) equations, as well as the Baer-Nunziato model for compressible two-phase flows. In all cases we have noticed that the new ADER schemes provide less oscillatory solutions when compared to ADER finite volume schemes based on the reconstruction in conserved variables, especially for the RMHD and the Baer-Nunziato equations. For the RHD and RMHD equations, the overall accuracy is improved and the CPU time is reduced by about 25 %. Because of its increased accuracy and due to the reduced computational cost, we recommend to use this version of ADER as the standard one in the relativistic framework. At the end of the paper, the new approach has also been extended to ADER-DG schemes on space-time adaptive grids (AMR).

Documentation of the Fourth Order Band Model

NASA Technical Reports Server (NTRS)

Kalnay-Rivas, E.; Hoitsma, D.

1979-01-01

A general circulation model is presented which uses quadratically conservative, fourth order horizontal space differences on an unstaggered grid and second order vertical space differences with a forward-backward or a smooth leap frog time scheme to solve the primitive equations of motion. The dynamic equations for motion, finite difference equations, a discussion of the structure and flow chart of the program code, a program listing, and three relevent papers are given.

Optimal performance of generalized heat engines with finite-size baths of arbitrary multiple conserved quantities beyond independent-and-identical-distribution scaling

NASA Astrophysics Data System (ADS)

Ito, Kosuke; Hayashi, Masahito

2018-01-01

In quantum thermodynamics, effects of finiteness of the baths have been less considered. In particular, there is no general theory which focuses on finiteness of the baths of multiple conserved quantities. Then, we investigate how the optimal performance of generalized heat engines with multiple conserved quantities alters in response to the size of the baths. In the context of general theories of quantum thermodynamics, the size of the baths has been given in terms of the number of identical copies of a system, which does not cover even such a natural scaling as the volume. In consideration of the asymptotic extensivity, we deal with a generic scaling of the baths to naturally include the volume scaling. Based on it, we derive a bound for the performance of generalized heat engines reflecting finite-size effects of the baths, which we call fine-grained generalized Carnot bound. We also construct a protocol to achieve the optimal performance of the engine given by this bound. Finally, applying the obtained general theory, we deal with simple examples of generalized heat engines. As for an example of non-independent-and-identical-distribution scaling and multiple conserved quantities, we investigate a heat engine with two baths composed of an ideal gas exchanging particles, where the volume scaling is applied. The result implies that the mass of the particle explicitly affects the performance of this engine with finite-size baths.

Finite element solution for energy conservation using a highly stable explicit integration algorithm

NASA Technical Reports Server (NTRS)

Baker, A. J.; Manhardt, P. D.

1972-01-01

Theoretical derivation of a finite element solution algorithm for the transient energy conservation equation in multidimensional, stationary multi-media continua with irregular solution domain closure is considered. The complete finite element matrix forms for arbitrarily irregular discretizations are established, using natural coordinate function representations. The algorithm is embodied into a user-oriented computer program (COMOC) which obtains transient temperature distributions at the node points of the finite element discretization using a highly stable explicit integration procedure with automatic error control features. The finite element algorithm is shown to posses convergence with discretization for a transient sample problem. The condensed form for the specific heat element matrix is shown to be preferable to the consistent form. Computed results for diverse problems illustrate the versatility of COMOC, and easily prepared output subroutines are shown to allow quick engineering assessment of solution behavior.

Improved finite difference schemes for transonic potential calculations

NASA Technical Reports Server (NTRS)

Hafez, M.; Osher, S.; Whitlow, W., Jr.

1984-01-01

Engquist and Osher (1980) have introduced a finite difference scheme for solving the transonic small disturbance equation, taking into account cases in which only compression shocks are admitted. Osher et al. (1983) studied a class of schemes for the full potential equation. It is proved that these schemes satisfy a new discrete 'entropy inequality' which rules out expansion shocks. However, the conducted analysis is restricted to steady two-dimensional flows. The present investigation is concerned with the adoption of a heuristic approach. The full potential equation in conservation form is solved with the aid of a modified artificial density method, based on flux biasing. It is shown that, with the current scheme, expansion shocks are not possible.

Least-squares finite element methods for compressible Euler equations

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Carey, G. F.

1990-01-01

A method based on backward finite differencing in time and a least-squares finite element scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L-sq-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L-sq method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.

Revisiting and Extending Interface Penalties for Multi-Domain Summation-by-Parts Operators

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Nordstrom, Jan; Gottlieb, David

2007-01-01

General interface coupling conditions are presented for multi-domain collocation methods, which satisfy the summation-by-parts (SBP) spatial discretization convention. The combined interior/interface operators are proven to be L2 stable, pointwise stable, and conservative, while maintaining the underlying accuracy of the interior SBP operator. The new interface conditions resemble (and were motivated by) those used in the discontinuous Galerkin finite element community, and maintain many of the same properties. Extensive validation studies are presented using two classes of high-order SBP operators: 1) central finite difference, and 2) Legendre spectral collocation.

An overlapped grid method for multigrid, finite volume/difference flow solvers: MaGGiE

NASA Technical Reports Server (NTRS)

Baysal, Oktay; Lessard, Victor R.

1990-01-01

The objective is to develop a domain decomposition method via overlapping/embedding the component grids, which is to be used by upwind, multi-grid, finite volume solution algorithms. A computer code, given the name MaGGiE (Multi-Geometry Grid Embedder) is developed to meet this objective. MaGGiE takes independently generated component grids as input, and automatically constructs the composite mesh and interpolation data, which can be used by the finite volume solution methods with or without multigrid convergence acceleration. Six demonstrative examples showing various aspects of the overlap technique are presented and discussed. These cases are used for developing the procedure for overlapping grids of different topologies, and to evaluate the grid connection and interpolation data for finite volume calculations on a composite mesh. Time fluxes are transferred between mesh interfaces using a trilinear interpolation procedure. Conservation losses are minimal at the interfaces using this method. The multi-grid solution algorithm, using the coaser grid connections, improves the convergence time history as compared to the solution on composite mesh without multi-gridding.

Finite plateau in spectral gap of polychromatic constrained random networks

NASA Astrophysics Data System (ADS)

Avetisov, V.; Gorsky, A.; Nechaev, S.; Valba, O.

2017-12-01

We consider critical behavior in the ensemble of polychromatic Erdős-Rényi networks and regular random graphs, where network vertices are painted in different colors. The links can be randomly removed and added to the network subject to the condition of the vertex degree conservation. In these constrained graphs we run the Metropolis procedure, which favors the connected unicolor triads of nodes. Changing the chemical potential, μ , of such triads, for some wide region of μ , we find the formation of a finite plateau in the number of intercolor links, which exactly matches the finite plateau in the network algebraic connectivity (the value of the first nonvanishing eigenvalue of the Laplacian matrix, λ2). We claim that at the plateau the spontaneously broken Z2 symmetry is restored by the mechanism of modes collectivization in clusters of different colors. The phenomena of a finite plateau formation holds also for polychromatic networks with M ≥2 colors. The behavior of polychromatic networks is analyzed via the spectral properties of their adjacency and Laplacian matrices.

A fully consistent and conservative vertically adaptive coordinate system for SLIM 3D v0.4 with an application to the thermocline oscillations of Lake Tanganyika

NASA Astrophysics Data System (ADS)

Delandmeter, Philippe; Lambrechts, Jonathan; Legat, Vincent; Vallaeys, Valentin; Naithani, Jaya; Thiery, Wim; Remacle, Jean-François; Deleersnijder, Eric

2018-03-01

The discontinuous Galerkin (DG) finite element method is well suited for the modelling, with a relatively small number of elements, of three-dimensional flows exhibiting strong velocity or density gradients. Its performance can be highly enhanced by having recourse to r-adaptivity. Here, a vertical adaptive mesh method is developed for DG finite elements. This method, originally designed for finite difference schemes, is based on the vertical diffusion of the mesh nodes, with the diffusivity controlled by the density jumps at the mesh element interfaces. The mesh vertical movement is determined by means of a conservative arbitrary Lagrangian-Eulerian (ALE) formulation. Though conservativity is naturally achieved, tracer consistency is obtained by a suitable construction of the mesh vertical velocity field, which is defined in such a way that it is fully compatible with the tracer and continuity equations at a discrete level. The vertically adaptive mesh approach is implemented in the three-dimensional version of the geophysical and environmental flow Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM 3D; www.climate.be/slim). Idealised benchmarks, aimed at simulating the oscillations of a sharp thermocline, are dealt with. Then, the relevance of the vertical adaptivity technique is assessed by simulating thermocline oscillations of Lake Tanganyika. The results are compared to measured vertical profiles of temperature, showing similar stratification and outcropping events.

Effects of using a posteriori methods for the conservation of integral invariants. [for weather forecasting

NASA Technical Reports Server (NTRS)

Takacs, Lawrence L.

1988-01-01

The nature and effect of using a posteriori adjustments to nonconservative finite-difference schemes to enforce integral invariants of the corresponding analytic system are examined. The method of a posteriori integral constraint restoration is analyzed for the case of linear advection, and the harmonic response associated with the a posteriori adjustments is examined in detail. The conservative properties of the shallow water system are reviewed, and the constraint restoration algorithm applied to the shallow water equations are described. A comparison is made between forecasts obtained using implicit and a posteriori methods for the conservation of mass, energy, and potential enstrophy in the complete nonlinear shallow-water system.

Direct numerical simulations of fluid flow, heat transfer and phase changes

NASA Technical Reports Server (NTRS)

Juric, D.; Tryggvason, G.; Han, J.

1997-01-01

Direct numerical simulations of fluid flow, heat transfer, and phase changes are presented. The simulations are made possible by a recently developed finite difference/front tracking method based on the one-field formulation of the governing equations where a single set of conservation equations is written for all the phases involved. The conservation equations are solved on a fixed rectangular grid, but the phase boundaries are kept sharp by tracking them explicitly by a moving grid of lower dimension. The method is discussed and applications to boiling heat transfer and the solidification of drops colliding with a wall are shown.

Algorithm For Hypersonic Flow In Chemical Equilibrium

NASA Technical Reports Server (NTRS)

Palmer, Grant

1989-01-01

Implicit, finite-difference, shock-capturing algorithm calculates inviscid, hypersonic flows in chemical equilibrium. Implicit formulation chosen because overcomes limitation on mathematical stability encountered in explicit formulations. For dynamical portion of problem, Euler equations written in conservation-law form in Cartesian coordinate system for two-dimensional or axisymmetric flow. For chemical portion of problem, equilibrium state of gas at each point in computational grid determined by minimizing local Gibbs free energy, subject to local conservation of molecules, atoms, ions, and total enthalpy. Major advantage: resulting algorithm naturally stable and captures strong shocks without help of artificial-dissipation terms to damp out spurious numerical oscillations.

Extinction and survival in two-species annihilation

NASA Astrophysics Data System (ADS)

Amar, J. G.; Ben-Naim, E.; Davis, S. M.; Krapivsky, P. L.

2018-02-01

We study diffusion-controlled two-species annihilation with a finite number of particles. In this stochastic process, particles move diffusively, and when two particles of opposite type come into contact, the two annihilate. We focus on the behavior in three spatial dimensions and for initial conditions where particles are confined to a compact domain. Generally, one species outnumbers the other, and we find that the difference between the number of majority and minority species, which is a conserved quantity, controls the behavior. When the number difference exceeds a critical value, the minority becomes extinct and a finite number of majority particles survive, while below this critical difference, a finite number of particles of both species survive. The critical difference Δc grows algebraically with the total initial number of particles N , and when N ≫1 , the critical difference scales as Δc˜N1 /3 . Furthermore, when the initial concentrations of the two species are equal, the average number of surviving majority and minority particles, M+ and M-, exhibit two distinct scaling behaviors, M+˜N1 /2 and M-˜N1 /6 . In contrast, when the initial populations are equal, these two quantities are comparable M+˜M-˜N1 /3 .

Finite area method for nonlinear conical flows

NASA Technical Reports Server (NTRS)

Sritharan, S. S.; Seebass, A. R.

1982-01-01

A fully conservative finite area method for the computation of steady inviscid flow about general conical bodies at incidence is described. The procedure utilizes the potential approximation and implements a body conforming mesh generator. The conical potential is assumed to have its best linear variation inside each mesh cell and a secondary interlocking cell system is used to establish the flux balance required to conserve mass. In the supersonic regions the scheme is desymmetrized by adding appropriate artificial viscosity in conservation form. The algorithm is nearly an order of a magnitude faster than present Euler methods and predicts known results accurately and qualitative features such as nodal point lift off correctly. Results are compared with those of other investigations.

Relaxation and Preconditioning for High Order Discontinuous Galerkin Methods with Applications to Aeroacoustics and High Speed Flows

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

2004-01-01

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. Other related issues in high order WENO finite difference and finite volume methods have also been investigated. methods are two classes of high order, high resolution methods suitable for convection dominated simulations with possible discontinuous or sharp gradient solutions. In [18], we first review these two classes of methods, pointing out their similarities and differences in algorithm formulation, theoretical properties, implementation issues, applicability, and relative advantages. We then present some quantitative comparisons of the third order finite volume WENO methods and discontinuous Galerkin methods for a series of test problems to assess their relative merits in accuracy and CPU timing. In [3], we review the development of the Runge-Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge-Kutta time discretizations, that allows the method to be non-linearly stable regardless of its accuracy, with a finite element space discretization by discontinuous approximations, that incorporates the ideas of numerical fluxes and slope limiters coined during the remarkable development of the high-resolution finite difference and finite volume schemes. The resulting RKDG methods are stable, high-order accurate, and highly parallelizable schemes that can easily handle complicated geometries and boundary conditions. We review the theoretical and algorithmic aspects of these methods and show several applications including nonlinear conservation laws, the compressible and incompressible Navier-Stokes equations, and Hamilton-Jacobi-like equations.

Stabilised finite-element methods for solving the level set equation with mass conservation

NASA Astrophysics Data System (ADS)

Kabirou Touré, Mamadou; Fahsi, Adil; Soulaïmani, Azzeddine

2016-01-01

Finite-element methods are studied for solving moving interface flow problems using the level set approach and a stabilised variational formulation proposed in Touré and Soulaïmani (2012; Touré and Soulaïmani To appear in 2016), coupled with a level set correction method. The level set correction is intended to enhance the mass conservation satisfaction property. The stabilised variational formulation (Touré and Soulaïmani 2012; Touré and Soulaïmani, To appear in 2016) constrains the level set function to remain close to the signed distance function, while the mass conservation is a correction step which enforces the mass balance. The eXtended finite-element method (XFEM) is used to take into account the discontinuities of the properties within an element. XFEM is applied to solve the Navier-Stokes equations for two-phase flows. The numerical methods are numerically evaluated on several test cases such as time-reversed vortex flow, a rigid-body rotation of Zalesak's disc, sloshing flow in a tank, a dam-break over a bed, and a rising bubble subjected to buoyancy. The numerical results show the importance of satisfying global mass conservation to accurately capture the interface position.

High-order centered difference methods with sharp shock resolution

NASA Technical Reports Server (NTRS)

Gustafsson, Bertil; Olsson, Pelle

1994-01-01

In this paper we consider high-order centered finite difference approximations of hyperbolic conservation laws. We propose different ways of adding artificial viscosity to obtain sharp shock resolution. For the Riemann problem we give simple explicit formulas for obtaining stationary one and two-point shocks. This can be done for any order of accuracy. It is shown that the addition of artificial viscosity is equivalent to ensuring the Lax k-shock condition. We also show numerical experiments that verify the theoretical results.

Metriplectic integrators for the Landau collision operator

DOE PAGES

Kraus, Michael; Hirvijoki, Eero

2017-10-02

Here, we present a novel framework for addressing the nonlinear Landau collision integral in terms of finite element and other subspace projection methods. We employ the underlying metriplectic structure of the Landau collision integral and, using a Galerkin discretization for the velocity space, we transform the infinite-dimensional system into a finite-dimensional, time-continuous metriplectic system. Temporal discretization is accomplished using the concept of discrete gradients. The conservation of energy, momentum, and particle densities, as well as the production of entropy is demonstrated algebraically for the fully discrete system. Due to the generality of our approach, the conservation properties and the monotonicmore » behavior of entropy are guaranteed for finite element discretizations, in general, independently of the mesh configuration.« less

CMS-Wave

DTIC Science & Technology

2015-10-30

Coastal Inlets Research Program CMS -Wave CMS -Wave is a two-dimensional spectral wind-wave generation and transformation model that employs a forward...marching, finite-difference method to solve the wave action conservation equation. Capabilities of CMS -Wave include wave shoaling, refraction... CMS -Wave can be used in either on a half- or full-plane mode, with primary waves propagating from the seaward boundary toward shore. It can

Mass-conservative reconstruction of Galerkin velocity fields for transport simulations

NASA Astrophysics Data System (ADS)

Scudeler, C.; Putti, M.; Paniconi, C.

2016-08-01

Accurate calculation of mass-conservative velocity fields from numerical solutions of Richards' equation is central to reliable surface-subsurface flow and transport modeling, for example in long-term tracer simulations to determine catchment residence time distributions. In this study we assess the performance of a local Larson-Niklasson (LN) post-processing procedure for reconstructing mass-conservative velocities from a linear (P1) Galerkin finite element solution of Richards' equation. This approach, originally proposed for a-posteriori error estimation, modifies the standard finite element velocities by imposing local conservation on element patches. The resulting reconstructed flow field is characterized by continuous fluxes on element edges that can be efficiently used to drive a second order finite volume advective transport model. Through a series of tests of increasing complexity that compare results from the LN scheme to those using velocity fields derived directly from the P1 Galerkin solution, we show that a locally mass-conservative velocity field is necessary to obtain accurate transport results. We also show that the accuracy of the LN reconstruction procedure is comparable to that of the inherently conservative mixed finite element approach, taken as a reference solution, but that the LN scheme has much lower computational costs. The numerical tests examine steady and unsteady, saturated and variably saturated, and homogeneous and heterogeneous cases along with initial and boundary conditions that include dry soil infiltration, alternating solute and water injection, and seepage face outflow. Typical problems that arise with velocities derived from P1 Galerkin solutions include outgoing solute flux from no-flow boundaries, solute entrapment in zones of low hydraulic conductivity, and occurrences of anomalous sources and sinks. In addition to inducing significant mass balance errors, such manifestations often lead to oscillations in concentration values that can moreover cause the numerical solution to explode. These problems do not occur when using LN post-processed velocities.

Constructing space difference schemes which satisfy a cell entropy inequality

NASA Technical Reports Server (NTRS)

Merriam, Marshal L.

1989-01-01

A numerical methodology for solving convection problems is presented, using finite difference schemes which satisfy the second law of thermodynamics on a cell-by-cell basis in addition to the usual conservation laws. It is shown that satisfaction of a cell entropy inequality is sufficient, in some cases, to guarantee nonlinear stability. Some details are given for several one-dimensional problems, including the quasi-one-dimensional Euler equations applied to flow in a nozzle.

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Bart, Timothy J.; Kutler, Paul (Technical Monitor)

1998-01-01

Chapter 1 briefly reviews several related topics associated with the symmetrization of systems of conservation laws and quasi-conservation laws: (1) Basic Entropy Symmetrization Theory; (2) Symmetrization and eigenvector scaling; (3) Symmetrization of the compressible Navier-Stokes equations; and (4) Symmetrization of the quasi-conservative form of the magnetohydrodynamic (MHD) equations. Chapter 2 describes one of the best known tools employed in the study of differential equations, the maximum principle: any function f(x) which satisfies the inequality f(double prime)>0 on the interval [a,b] attains its maximum value at one of the endpoints on the interval. Chapter three examines the upwind finite volume schemes for scalar and system conservation laws. The basic tasks in the upwind finite volume approach have already been presented: reconstruction, flux evaluation, and evolution. By far, the most difficult task in this process is the reconstruction step.

A direct Primitive Variable Recovery Scheme for hyperbolic conservative equations: The case of relativistic hydrodynamics.

PubMed

Aguayo-Ortiz, A; Mendoza, S; Olvera, D

2018-01-01

In this article we develop a Primitive Variable Recovery Scheme (PVRS) to solve any system of coupled differential conservative equations. This method obtains directly the primitive variables applying the chain rule to the time term of the conservative equations. With this, a traditional finite volume method for the flux is applied in order avoid violation of both, the entropy and "Rankine-Hugoniot" jump conditions. The time evolution is then computed using a forward finite difference scheme. This numerical technique evades the recovery of the primitive vector by solving an algebraic system of equations as it is often used and so, it generalises standard techniques to solve these kind of coupled systems. The article is presented bearing in mind special relativistic hydrodynamic numerical schemes with an added pedagogical view in the appendix section in order to easily comprehend the PVRS. We present the convergence of the method for standard shock-tube problems of special relativistic hydrodynamics and a graphical visualisation of the errors using the fluctuations of the numerical values with respect to exact analytic solutions. The PVRS circumvents the sometimes arduous computation that arises from standard numerical methods techniques, which obtain the desired primitive vector solution through an algebraic polynomial of the charges.

A direct Primitive Variable Recovery Scheme for hyperbolic conservative equations: The case of relativistic hydrodynamics

PubMed Central

Mendoza, S.; Olvera, D.

2018-01-01

In this article we develop a Primitive Variable Recovery Scheme (PVRS) to solve any system of coupled differential conservative equations. This method obtains directly the primitive variables applying the chain rule to the time term of the conservative equations. With this, a traditional finite volume method for the flux is applied in order avoid violation of both, the entropy and “Rankine-Hugoniot” jump conditions. The time evolution is then computed using a forward finite difference scheme. This numerical technique evades the recovery of the primitive vector by solving an algebraic system of equations as it is often used and so, it generalises standard techniques to solve these kind of coupled systems. The article is presented bearing in mind special relativistic hydrodynamic numerical schemes with an added pedagogical view in the appendix section in order to easily comprehend the PVRS. We present the convergence of the method for standard shock-tube problems of special relativistic hydrodynamics and a graphical visualisation of the errors using the fluctuations of the numerical values with respect to exact analytic solutions. The PVRS circumvents the sometimes arduous computation that arises from standard numerical methods techniques, which obtain the desired primitive vector solution through an algebraic polynomial of the charges. PMID:29659602

Domain decomposition methods for systems of conservation laws: Spectral collocation approximations

NASA Technical Reports Server (NTRS)

Quarteroni, Alfio

1989-01-01

Hyperbolic systems of conversation laws are considered which are discretized in space by spectral collocation methods and advanced in time by finite difference schemes. At any time-level a domain deposition method based on an iteration by subdomain procedure was introduced yielding at each step a sequence of independent subproblems (one for each subdomain) that can be solved simultaneously. The method is set for a general nonlinear problem in several space variables. The convergence analysis, however, is carried out only for a linear one-dimensional system with continuous solutions. A precise form of the error reduction factor at each iteration is derived. Although the method is applied here to the case of spectral collocation approximation only, the idea is fairly general and can be used in a different context as well. For instance, its application to space discretization by finite differences is straight forward.

Modeling highly transient flow, mass, and heat transport in the Chattahoochee River near Atlanta, Georgia

USGS Publications Warehouse

Jobson, Harvey E.; Keefer, Thomas N.

1979-01-01

A coupled flow-temperature model has been developed and verified for a 27.9-km reach of the Chattahoochee River between Buford Dam and Norcross, Ga. Flow in this reach of the Chattahoochee is continuous but highly regulated by Buford Dam, a flood-control and hydroelectric facility located near Buford, Ga. Calibration and verification utilized two sets of data collected under highly unsteady discharge conditions. Existing solution techniques, with certain minor improvements, were applied to verify the existing technology of flow and transport modeling. A linear, implicit finite-difference flow model was coupled with implicit, finite-difference transport and temperature models. Both the conservative and nonconservative forms of the transport equation were solved, and the difference in the predicted concentrations of dye were found to be insignificant. The temperature model, therefore, was based on the simpler nonconservative form of the transport equation. (Woodard-USGS)

Developments in the Gung Ho dynamical core

NASA Astrophysics Data System (ADS)

Melvin, Thomas

2017-04-01

Gung Ho is the new dynamical core being developed for the next generation Met Office weather and climate model, suitable for meeting the exascale challenge on emerging computer architectures. It builds upon the earlier collaborative project between the Met Office, NERC and STFC Daresbury of the same name to investigate suitable numerical methods for dynamical cores. A mixed-finite element approach is used, where different finite element spaces are used to represent various fields. This method provides a number of beneficial improvements over the current model, such a compatibility and inherent conservation on quasi-uniform unstructured meshes, whilst maintaining the accuracy and good dispersion properties of the staggered grid currently used. Furthermore, the mixed finite element approach allows a large degree of flexibility in the type of mesh, order of approximation and discretisation, providing a simple way to test alternative options to obtain the best model possible.

Robust non-fragile finite-frequency H∞ static output-feedback control for active suspension systems

NASA Astrophysics Data System (ADS)

Wang, Gang; Chen, Changzheng; Yu, Shenbo

2017-07-01

This paper deals with the problem of non-fragile H∞ static output-feedback control of vehicle active suspension systems with finite-frequency constraint. The control objective is to improve ride comfort within the given frequency range and ensure the hard constraints in the time-domain. Moreover, in order to enhance the robustness of the controller, the control gain perturbation is also considered in controller synthesis. Firstly, a new non-fragile H∞ finite-frequency control condition is established by using generalized Kalman-Yakubovich-Popov (GKYP) lemma. Secondly, the static output-feedback control gain is directly derived by using a non-iteration algorithm. Different from the existing iteration LMI results, the static output-feedback design is simple and less conservative. Finally, the proposed control algorithm is applied to a quarter-car active suspension model with actuator dynamics, numerical results are made to show the effectiveness and merits of the proposed method.

Numerical investigation of sixth order Boussinesq equation

NASA Astrophysics Data System (ADS)

Kolkovska, N.; Vucheva, V.

2017-10-01

We propose a family of conservative finite difference schemes for the Boussinesq equation with sixth order dispersion terms. The schemes are of second order of approximation. The method is conditionally stable with a mild restriction τ = O(h) on the step sizes. Numerical tests are performed for quadratic and cubic nonlinearities. The numerical experiments show second order of convergence of the discrete solution to the exact one.

Investigation of shock-induced combustion past blunt projectiles

NASA Technical Reports Server (NTRS)

Ahuja, J. K.; Tiwari, S. N.

1996-01-01

A numerical study is conducted to simulate shock-induced combustion in premixed hydrogen-air mixtures at various free-stream conditions and parameters. Two-dimensional axisymmetric, reacting viscous flow over blunt projectiles is computed to study shock-induced combustion at Mach 5.11 and Mach 6.46 in hydrogen-air mixture. A seven-species, seven reactions finite rate hydrogen-air chemical reaction mechanism is used combined with a finite-difference, shock-fitting method to solve the complete set of Navier-Stokes and species conservation equations. The study has allowed an improved understanding of the physics of shock-induced combustion over blunt projectiles and the numerical results can now be explained more readily with one-dimensional wave-interaction model.

Free stream capturing in fluid conservation law for moving coordinates in three dimensions

NASA Technical Reports Server (NTRS)

Obayashi, Shigeru

1991-01-01

The free-stream capturing technique for both the finite-volume (FV) and finite-difference (FD) framework is summarized. For an arbitrary motion of the grid, the FV analysis shows that volumes swept by all six surfaces of the cell have to be computed correctly. This means that the free-stream capturing time-metric terms should be calculated not only from a surface vector of a cell at a single time level, but also from a volume swept by the cell surface in space and time. The FV free-stream capturing formulation is applicable to the FD formulation by proper translation from an FV cell to an FD mesh.

Numerical methods for systems of conservation laws of mixed type using flux splitting

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

1990-01-01

The essentially non-oscillatory (ENO) finite difference scheme is applied to systems of conservation laws of mixed hyperbolic-elliptic type. A flux splitting, with the corresponding Jacobi matrices having real and positive/negative eigenvalues, is used. The hyperbolic ENO operator is applied separately. The scheme is numerically tested on the van der Waals equation in fluid dynamics. Convergence was observed with good resolution to weak solutions for various Riemann problems, which are then numerically checked to be admissible as the viscosity-capillarity limits. The interesting phenomena of the shrinking of elliptic regions if they are present in the initial conditions were also observed.

Steady inviscid transonic flows over planar airfoils: A search for a simplified procedure

NASA Technical Reports Server (NTRS)

Magnus, R.; Yoshihara, H.

1973-01-01

A finite difference procedure based upon a system of unsteady equations in proper conservation form with either exact or small disturbance steady terms is used to calculate the steady flows over several classes of airfoils. The airfoil condition is fulfilled on a slab whose upstream extremity is a semi-circle overlaying the airfoil leading edge circle. The limitations of the small disturbance equations are demonstrated in an extreme example of a blunt-nosed, aft-cambered airfoil. The necessity of using the equations in proper conservation form to capture the shock properly is stressed. Ability of the steady relaxation procedures to capture the shock is briefly examined.

Application of Local Discretization Methods in the NASA Finite-Volume General Circulation Model

NASA Technical Reports Server (NTRS)

Yeh, Kao-San; Lin, Shian-Jiann; Rood, Richard B.

2002-01-01

We present the basic ideas of the dynamics system of the finite-volume General Circulation Model developed at NASA Goddard Space Flight Center for climate simulations and other applications in meteorology. The dynamics of this model is designed with emphases on conservative and monotonic transport, where the property of Lagrangian conservation is used to maintain the physical consistency of the computational fluid for long-term simulations. As the model benefits from the noise-free solutions of monotonic finite-volume transport schemes, the property of Lagrangian conservation also partly compensates the accuracy of transport for the diffusion effects due to the treatment of monotonicity. By faithfully maintaining the fundamental laws of physics during the computation, this model is able to achieve sufficient accuracy for the global consistency of climate processes. Because the computing algorithms are based on local memory, this model has the advantage of efficiency in parallel computation with distributed memory. Further research is yet desirable to reduce the diffusion effects of monotonic transport for better accuracy, and to mitigate the limitation due to fast-moving gravity waves for better efficiency.

Computation of Laminar and Turbulent Flow in 90-Degree Square-Duct and Pipe Bends Using the Navier-Stokes Equations

DTIC Science & Technology

1982-04-01

R.M. and Warming, R.F.: An Implicit Finite - Difference Algorithm for Hyperbolic Systems in Conservation Law Form. Journal of Computational Physics...Quincy Street C-40) Arlington, VA 22217 D 82 05-.10 I0, S4CURITY CLASSIFICATION OF THIS ’E(Wha, Doae Entotwed) Slength scale. Six different flow cases...forces upstream have produced a non-zero velocity gradient normal to the plane of curvature. Fluid with above (/below) average nioiiiei.tuili migrates

Wave propagation in anisotropic elastic materials and curvilinear coordinates using a summation-by-parts finite difference method

DOE PAGES

Petersson, N. Anders; Sjogreen, Bjorn

2015-07-20

We develop a fourth order accurate finite difference method for solving the three-dimensional elastic wave equation in general heterogeneous anisotropic materials on curvilinear grids. The proposed method is an extension of the method for isotropic materials, previously described in the paper by Sjögreen and Petersson (2012) [11]. The method we proposed discretizes the anisotropic elastic wave equation in second order formulation, using a node centered finite difference method that satisfies the principle of summation by parts. The summation by parts technique results in a provably stable numerical method that is energy conserving. Also, we generalize and evaluate the super-grid far-fieldmore » technique for truncating unbounded domains. Unlike the commonly used perfectly matched layers (PML), the super-grid technique is stable for general anisotropic material, because it is based on a coordinate stretching combined with an artificial dissipation. Moreover, the discretization satisfies an energy estimate, proving that the numerical approximation is stable. We demonstrate by numerical experiments that sufficiently wide super-grid layers result in very small artificial reflections. Applications of the proposed method are demonstrated by three-dimensional simulations of anisotropic wave propagation in crystals.« less

A new algorithm for DNS of turbulent polymer solutions using the FENE-P model

NASA Astrophysics Data System (ADS)

Vaithianathan, T.; Collins, Lance; Robert, Ashish; Brasseur, James

2004-11-01

Direct numerical simulations (DNS) of polymer solutions based on the finite extensible nonlinear elastic model with the Peterlin closure (FENE-P) solve for a conformation tensor with properties that must be maintained by the numerical algorithm. In particular, the eigenvalues of the tensor are all positive (to maintain positive definiteness) and the sum is bounded by the maximum extension length. Loss of either of these properties will give rise to unphysical instabilities. In earlier work, Vaithianathan & Collins (2003) devised an algorithm based on an eigendecomposition that allows you to update the eigenvalues of the conformation tensor directly, making it easier to maintain the necessary conditions for a stable calculation. However, simple fixes (such as ceilings and floors) yield results that violate overall conservation. The present finite-difference algorithm is inherently designed to satisfy all of the bounds on the eigenvalues, and thus restores overall conservation. New results suggest that the earlier algorithm may have exaggerated the energy exchange at high wavenumbers. In particular, feedback of the polymer elastic energy to the isotropic turbulence is now greatly reduced.

Storm Water Infiltration and Focused Groundwater Recharge in a Rain Garden: Finite Volume Model and Numerical Simulations for Different Configurations and Climates

NASA Astrophysics Data System (ADS)

Aravena, J.; Dussaillant, A. R.

2006-12-01

Source control is the fundamental principle behind sustainable management of stormwater. Rain gardens are an infiltration practice that provides volume and water quality control, recharge, and multiple landscape, ecological and economic potential benefits. The fulfillment of these objectives requires understanding their behavior during events as well as long term, and tools for their design. We have developed a model based on Richards equation coupled to a surface water balance, solved with a 2D finite volume Fortran code which allows alternating upper boundary conditions, including ponding, which is not present in available 2D models. Also, it can simulate non homogeneous water input, heterogeneous soil (layered or more complex geometries), and surface irregularities -e.g. terracing-, so as to estimate infiltration and recharge. The algorithm is conservative; being an advantage compared to available finite difference and finite element methods. We will present performance comparisons to known models, to experimental data from a bioretention cell, which receives roof water to its surface depression planted with native species in an organic-rich root zone soil layer (underlain by a high conductivity lower layer that, while providing inter-event storage, percolates water readily), as well as long term simulations for different rain garden configurations. Recharge predictions for different climates show significant increases from natural recharge, and that the optimal area ratio (raingarden vs. contributing impervious area) reduces from 20% (humid) to 5% (dry).

Generalised summation-by-parts operators and variable coefficients

NASA Astrophysics Data System (ADS)

Ranocha, Hendrik

2018-06-01

High-order methods for conservation laws can be highly efficient if their stability is ensured. A suitable means mimicking estimates of the continuous level is provided by summation-by-parts (SBP) operators and the weak enforcement of boundary conditions. Recently, there has been an increasing interest in generalised SBP operators both in the finite difference and the discontinuous Galerkin spectral element framework. However, if generalised SBP operators are used, the treatment of the boundaries becomes more difficult since some properties of the continuous level are no longer mimicked discretely - interpolating the product of two functions will in general result in a value different from the product of the interpolations. Thus, desired properties such as conservation and stability are more difficult to obtain. Here, new formulations are proposed, allowing the creation of discretisations using general SBP operators that are both conservative and stable. Thus, several shortcomings that might be attributed to generalised SBP operators are overcome (cf. Nordström and Ruggiu (2017) [38] and Manzanero et al. (2017) [39]).

A High-Order Finite Spectral Volume Method for Conservation Laws on Unstructured Grids

NASA Technical Reports Server (NTRS)

Wang, Z. J.; Liu, Yen; Kwak, Dochan (Technical Monitor)

2001-01-01

A time accurate, high-order, conservative, yet efficient method named Finite Spectral Volume (FSV) is developed for conservation laws on unstructured grids. The concept of a 'spectral volume' is introduced to achieve high-order accuracy in an efficient manner similar to spectral element and multi-domain spectral methods. In addition, each spectral volume is further sub-divided into control volumes (CVs), and cell-averaged data from these control volumes is used to reconstruct a high-order approximation in the spectral volume. Riemann solvers are used to compute the fluxes at spectral volume boundaries. Then cell-averaged state variables in the control volumes are updated independently. Furthermore, TVD (Total Variation Diminishing) and TVB (Total Variation Bounded) limiters are introduced in the FSV method to remove/reduce spurious oscillations near discontinuities. A very desirable feature of the FSV method is that the reconstruction is carried out only once, and analytically, and is the same for all cells of the same type, and that the reconstruction stencil is always non-singular, in contrast to the memory and CPU-intensive reconstruction in a high-order finite volume (FV) method. Discussions are made concerning why the FSV method is significantly more efficient than high-order finite volume and the Discontinuous Galerkin (DG) methods. Fundamental properties of the FSV method are studied and high-order accuracy is demonstrated for several model problems with and without discontinuities.

Finite elements and fluid dynamics. [instability effects on solution of nonlinear equations

NASA Technical Reports Server (NTRS)

Fix, G.

1975-01-01

Difficulties concerning a use of the finite element method in the solution of the nonlinear equations of fluid dynamics are partly related to various 'hidden' instabilities which often arise in fluid calculations. The instabilities are typically due to boundary effects or nonlinearities. It is shown that in certain cases these instabilities can be avoided if certain conservation laws are satisfied, and that the latter are often intimately related to finite elements.

Finite Difference Methods for the Solution of Unsteady Potential Flows.

DTIC Science & Technology

1982-06-01

prediction of loads on helicopter rotors in forward flight. Although aeroelastic effects are important, in this case the main source of unsteadiness is in the...and conservation, differencing schemes, and algorithm development. A number of applications, including unsteady three-dimensional rotor calculations...concerning tunnel turbulence, wall and scaling effects , and sepa- ration. We now know that many of these problems are magnified by the inherent susceptibility

An adaptive mesh-moving and refinement procedure for one-dimensional conservation laws

NASA Technical Reports Server (NTRS)

Biswas, Rupak; Flaherty, Joseph E.; Arney, David C.

1993-01-01

We examine the performance of an adaptive mesh-moving and /or local mesh refinement procedure for the finite difference solution of one-dimensional hyperbolic systems of conservation laws. Adaptive motion of a base mesh is designed to isolate spatially distinct phenomena, and recursive local refinement of the time step and cells of the stationary or moving base mesh is performed in regions where a refinement indicator exceeds a prescribed tolerance. These adaptive procedures are incorporated into a computer code that includes a MacCormack finite difference scheme wih Davis' artificial viscosity model and a discretization error estimate based on Richardson's extrapolation. Experiments are conducted on three problems in order to qualify the advantages of adaptive techniques relative to uniform mesh computations and the relative benefits of mesh moving and refinement. Key results indicate that local mesh refinement, with and without mesh moving, can provide reliable solutions at much lower computational cost than possible on uniform meshes; that mesh motion can be used to improve the results of uniform mesh solutions for a modest computational effort; that the cost of managing the tree data structure associated with refinement is small; and that a combination of mesh motion and refinement reliably produces solutions for the least cost per unit accuracy.

Some Aspects of Essentially Nonoscillatory (ENO) Formulations for the Euler Equations, Part 3

NASA Technical Reports Server (NTRS)

Chakravarthy, Sukumar R.

1990-01-01

An essentially nonoscillatory (ENO) formulation is described for hyperbolic systems of conservation laws. ENO approaches are based on smart interpolation to avoid spurious numerical oscillations. ENO schemes are a superset of Total Variation Diminishing (TVD) schemes. In the recent past, TVD formulations were used to construct shock capturing finite difference methods. At extremum points of the solution, TVD schemes automatically reduce to being first-order accurate discretizations locally, while away from extrema they can be constructed to be of higher order accuracy. The new framework helps construct essentially non-oscillatory finite difference methods without recourse to local reductions of accuracy to first order. Thus arbitrarily high orders of accuracy can be obtained. The basic general ideas of the new approach can be specialized in several ways and one specific implementation is described based on: (1) the integral form of the conservation laws; (2) reconstruction based on the primitive functions; (3) extension to multiple dimensions in a tensor product fashion; and (4) Runge-Kutta time integration. The resulting method is fourth-order accurate in time and space and is applicable to uniform Cartesian grids. The construction of such schemes for scalar equations and systems in one and two space dimensions is described along with several examples which illustrate interesting aspects of the new approach.

A direct Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3D

NASA Astrophysics Data System (ADS)

Boscheri, Walter; Dumbser, Michael

2014-10-01

In this paper we present a new family of high order accurate Arbitrary-Lagrangian-Eulerian (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear systems of conservative and non-conservative hyperbolic partial differential equations with stiff source terms on moving tetrahedral meshes in three space dimensions. A WENO reconstruction technique is used to achieve high order of accuracy in space, while an element-local space-time Discontinuous Galerkin finite element predictor on moving curved meshes is used to obtain a high order accurate one-step time discretization. Within the space-time predictor the physical element is mapped onto a reference element using a high order isoparametric approach, where the space-time basis and test functions are given by the Lagrange interpolation polynomials passing through a predefined set of space-time nodes. Since our algorithm is cell-centered, the final mesh motion is computed by using a suitable node solver algorithm. A rezoning step as well as a flattener strategy are used in some of the test problems to avoid mesh tangling or excessive element deformations that may occur when the computation involves strong shocks or shear waves. The ALE algorithm presented in this article belongs to the so-called direct ALE methods because the final Lagrangian finite volume scheme is based directly on a space-time conservation formulation of the governing PDE system, with the rezoned geometry taken already into account during the computation of the fluxes. We apply our new high order unstructured ALE schemes to the 3D Euler equations of compressible gas dynamics, for which a set of classical numerical test problems has been solved and for which convergence rates up to sixth order of accuracy in space and time have been obtained. We furthermore consider the equations of classical ideal magnetohydrodynamics (MHD) as well as the non-conservative seven-equation Baer-Nunziato model of compressible multi-phase flows with stiff relaxation source terms.

A shifted Jacobi collocation algorithm for wave type equations with non-local conservation conditions

NASA Astrophysics Data System (ADS)

Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohammed A.

2014-09-01

In this paper, we propose an efficient spectral collocation algorithm to solve numerically wave type equations subject to initial, boundary and non-local conservation conditions. The shifted Jacobi pseudospectral approximation is investigated for the discretization of the spatial variable of such equations. It possesses spectral accuracy in the spatial variable. The shifted Jacobi-Gauss-Lobatto (SJ-GL) quadrature rule is established for treating the non-local conservation conditions, and then the problem with its initial and non-local boundary conditions are reduced to a system of second-order ordinary differential equations in temporal variable. This system is solved by two-stage forth-order A-stable implicit RK scheme. Five numerical examples with comparisons are given. The computational results demonstrate that the proposed algorithm is more accurate than finite difference method, method of lines and spline collocation approach

On the Quality of Velocity Interpolation Schemes for Marker-In-Cell Methods on 3-D Staggered Grids

NASA Astrophysics Data System (ADS)

Kaus, B.; Pusok, A. E.; Popov, A.

2015-12-01

The marker-in-cell method is generally considered to be a flexible and robust method to model advection of heterogenous non-diffusive properties (i.e. rock type or composition) in geodynamic problems or incompressible Stokes problems. In this method, Lagrangian points carrying compositional information are advected with the ambient velocity field on an immobile, Eulerian grid. However, velocity interpolation from grid points to marker locations is often performed without preserving the zero divergence of the velocity field at the interpolated locations (i.e. non-conservative). Such interpolation schemes can induce non-physical clustering of markers when strong velocity gradients are present (Jenny et al., 2001) and this may, eventually, result in empty grid cells, a serious numerical violation of the marker-in-cell method. Solutions to this problem include: using larger mesh resolutions and/or marker densities, or repeatedly controlling the marker distribution (i.e. inject/delete), but which does not have an established physical background. To remedy this at low computational costs, Jenny et al. (2001) and Meyer and Jenny (2004) proposed a simple, conservative velocity interpolation (CVI) scheme for 2-D staggered grid, while Wang et al. (2015) extended the formulation to 3-D finite element methods. Here, we follow up with these studies and report on the quality of velocity interpolation methods for 2-D and 3-D staggered grids. We adapt the formulations from both Jenny et al. (2001) and Wang et al. (2015) for use on 3-D staggered grids, where the velocity components have different node locations as compared to finite element, where they share the same node location. We test the different interpolation schemes (CVI and non-CVI) in combination with different advection schemes (Euler, RK2 and RK4) and with/out marker control on Stokes problems with strong velocity gradients, which are discretized using a finite difference method. We show that a conservative formulation reduces the dispersion or clustering of markers and that the density of markers remains steady over time without the need of additional marker control. Jenny et al. (2001, J Comp Phys, 166, 218-252 Meyer and Jenny (2004), Proc Appl Math Mech, 4, 466-467 Wang et al. (2015), G3, Vol.16 Funding was provided by the ERC Starting Grant #258830.

Extinction and survival in two-species annihilation

DOE PAGES

Amar, J. G.; Ben-Naim, E.; Davis, S. M.; ...

2018-02-09

In this paper, we study diffusion-controlled two-species annihilation with a finite number of particles. In this stochastic process, particles move diffusively, and when two particles of opposite type come into contact, the two annihilate. We focus on the behavior in three spatial dimensions and for initial conditions where particles are confined to a compact domain. Generally, one species outnumbers the other, and we find that the difference between the number of majority and minority species, which is a conserved quantity, controls the behavior. When the number difference exceeds a critical value, the minority becomes extinct and a finite number of majority particles survive, while below this critical difference, a finite number of particles of both species survive. The critical differencemore » $${\\mathrm{{\\Delta}}}_{c}$$ grows algebraically with the total initial number of particles N, and when $$N{\\gg}1$$, the critical difference scales as $${\\mathrm{{\\Delta}}}_{c}{\\sim}{N}^{1/3}$$. Furthermore, when the initial concentrations of the two species are equal, the average number of surviving majority and minority particles $${M}_{+}$$ and $${M}_{{-}}$$, exhibit two distinct scaling behaviors, $${M}_{+}{\\sim}{N}^{1/2}$$ and $${M}_{{-}}{\\sim}{N}^{1/6}$$. Finally, in contrast, when the initial populations are equal, these two quantities are comparable $${M}_{+}{\\sim}{M}_{{-}}{\\sim}{N}^{1/3}$$.« less

Extinction and survival in two-species annihilation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Amar, J. G.; Ben-Naim, E.; Davis, S. M.

In this paper, we study diffusion-controlled two-species annihilation with a finite number of particles. In this stochastic process, particles move diffusively, and when two particles of opposite type come into contact, the two annihilate. We focus on the behavior in three spatial dimensions and for initial conditions where particles are confined to a compact domain. Generally, one species outnumbers the other, and we find that the difference between the number of majority and minority species, which is a conserved quantity, controls the behavior. When the number difference exceeds a critical value, the minority becomes extinct and a finite number of majority particles survive, while below this critical difference, a finite number of particles of both species survive. The critical differencemore » $${\\mathrm{{\\Delta}}}_{c}$$ grows algebraically with the total initial number of particles N, and when $$N{\\gg}1$$, the critical difference scales as $${\\mathrm{{\\Delta}}}_{c}{\\sim}{N}^{1/3}$$. Furthermore, when the initial concentrations of the two species are equal, the average number of surviving majority and minority particles $${M}_{+}$$ and $${M}_{{-}}$$, exhibit two distinct scaling behaviors, $${M}_{+}{\\sim}{N}^{1/2}$$ and $${M}_{{-}}{\\sim}{N}^{1/6}$$. Finally, in contrast, when the initial populations are equal, these two quantities are comparable $${M}_{+}{\\sim}{M}_{{-}}{\\sim}{N}^{1/3}$$.« less

Compatible Spatial Discretizations for Partial Differential Equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arnold, Douglas, N, ed.

From May 11--15, 2004, the Institute for Mathematics and its Applications held a hot topics workshop on Compatible Spatial Discretizations for Partial Differential Equations. The numerical solution of partial differential equations (PDE) is a fundamental task in science and engineering. The goal of the workshop was to bring together a spectrum of scientists at the forefront of the research in the numerical solution of PDEs to discuss compatible spatial discretizations. We define compatible spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. A wide varietymore » of discretization methods applied across a wide range of scientific and engineering applications have been designed to or found to inherit or mimic intrinsic spatial structure and reproduce fundamental properties of the solution of the continuous PDE model at the finite dimensional level. A profusion of such methods and concepts relevant to understanding them have been developed and explored: mixed finite element methods, mimetic finite differences, support operator methods, control volume methods, discrete differential forms, Whitney forms, conservative differencing, discrete Hodge operators, discrete Helmholtz decomposition, finite integration techniques, staggered grid and dual grid methods, etc. This workshop seeks to foster communication among the diverse groups of researchers designing, applying, and studying such methods as well as researchers involved in practical solution of large scale problems that may benefit from advancements in such discretizations; to help elucidate the relations between the different methods and concepts; and to generally advance our understanding in the area of compatible spatial discretization methods for PDE. Particular points of emphasis included: + Identification of intrinsic properties of PDE models that are critical for the fidelity of numerical simulations. + Identification and design of compatible spatial discretizations of PDEs, their classification, analysis, and relations. + Relationships between different compatible spatial discretization methods and concepts which have been developed; + Impact of compatible spatial discretizations upon physical fidelity, verification and validation of simulations, especially in large-scale, multiphysics settings. + How solvers address the demands placed upon them by compatible spatial discretizations. This report provides information about the program and abstracts of all the presentations.« less

A three-dimensional, time-dependent model of Mobile Bay

NASA Technical Reports Server (NTRS)

Pitts, F. H.; Farmer, R. C.

1976-01-01

A three-dimensional, time-variant mathematical model for momentum and mass transport in estuaries was developed and its solution implemented on a digital computer. The mathematical model is based on state and conservation equations applied to turbulent flow of a two-component, incompressible fluid having a free surface. Thus, bouyancy effects caused by density differences between the fresh and salt water, inertia from thare river and tidal currents, and differences in hydrostatic head are taken into account. The conservation equations, which are partial differential equations, are solved numerically by an explicit, one-step finite difference scheme and the solutions displayed numerically and graphically. To test the validity of the model, a specific estuary for which scaled model and experimental field data are available, Mobile Bay, was simulated. Comparisons of velocity, salinity and water level data show that the model is valid and a viable means of simulating the hydrodynamics and mass transport in non-idealized estuaries.

Computational Aeroacoustics by the Space-time CE/SE Method

NASA Technical Reports Server (NTRS)

Loh, Ching Y.

2001-01-01

In recent years, a new numerical methodology for conservation laws-the Space-Time Conservation Element and Solution Element Method (CE/SE), was developed by Dr. Chang of NASA Glenn Research Center and collaborators. In nature, the new method may be categorized as a finite volume method, where the conservation element (CE) is equivalent to a finite control volume (or cell) and the solution element (SE) can be understood as the cell interface. However, due to its rigorous treatment of the fluxes and geometry, it is different from the existing schemes. The CE/SE scheme features: (1) space and time treated on the same footing, the integral equations of conservation laws are solve( for with second order accuracy, (2) high resolution, low dispersion and low dissipation, (3) novel, truly multi-dimensional, simple but effective non-reflecting boundary condition, (4) effortless implementation of computation, no numerical fix or parameter choice is needed, an( (5) robust enough to cover a wide spectrum of compressible flow: from weak linear acoustic waves to strong, discontinuous waves (shocks) appropriate for linear and nonlinear aeroacoustics. Currently, the CE/SE scheme has been developed to such a stage that a 3-13 unstructured CE/SE Navier-Stokes solver is already available. However, in the present paper, as a general introduction to the CE/SE method, only the 2-D unstructured Euler CE/SE solver is chosen as a prototype and is sketched in Section 2. Then applications of the CE/SE scheme to linear, nonlinear aeroacoustics and airframe noise are depicted in Sections 3, 4, and 5 respectively to demonstrate its robustness and capability.

Large Eddy simulation of compressible flows with a low-numerical dissipation patch-based adaptive mesh refinement method

NASA Astrophysics Data System (ADS)

Pantano, Carlos

2005-11-01

We describe a hybrid finite difference method for large-eddy simulation (LES) of compressible flows with a low-numerical dissipation scheme and structured adaptive mesh refinement (SAMR). Numerical experiments and validation calculations are presented including a turbulent jet and the strongly shock-driven mixing of a Richtmyer-Meshkov instability. The approach is a conservative flux-based SAMR formulation and as such, it utilizes refinement to computational advantage. The numerical method for the resolved scale terms encompasses the cases of scheme alternation and internal mesh interfaces resulting from SAMR. An explicit centered scheme that is consistent with a skew-symmetric finite difference formulation is used in turbulent flow regions while a weighted essentially non-oscillatory (WENO) scheme is employed to capture shocks. The subgrid stresses and transports are calculated by means of the streched-vortex model, Misra & Pullin (1997)

A 3-dimensional mass conserving element for compressible flows

NASA Technical Reports Server (NTRS)

Fix, G.; Suri, M.

1985-01-01

A variety of finite element schemes has been used in the numerical approximation of compressible flows particularly in underwater acoustics. In many instances instabilities have been generated due to the lack of mass conservation. Two- and three-dimensional elements are developed which avoid these problems.

New Developments in the Method of Space-Time Conservation Element and Solution Element-Applications to Two-Dimensional Time-Marching Problems

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; Wang, Xiao-Yen; Chow, Chuen-Yen

1994-01-01

A new numerical discretization method for solving conservation laws is being developed. This new approach differs substantially in both concept and methodology from the well-established methods, i.e., finite difference, finite volume, finite element, and spectral methods. It is motivated by several important physical/numerical considerations and designed to avoid several key limitations of the above traditional methods. As a result of the above considerations, a set of key principles for the design of numerical schemes was put forth in a previous report. These principles were used to construct several numerical schemes that model a 1-D time-dependent convection-diffusion equation. These schemes were then extended to solve the time-dependent Euler and Navier-Stokes equations of a perfect gas. It was shown that the above schemes compared favorably with the traditional schemes in simplicity, generality, and accuracy. In this report, the 2-D versions of the above schemes, except the Navier-Stokes solver, are constructed using the same set of design principles. Their constructions are simplified greatly by the use of a nontraditional space-time mesh. Its use results in the simplest stencil possible, i.e., a tetrahedron in a 3-D space-time with a vertex at the upper time level and other three at the lower time level. Because of the similarity in their design, each of the present 2-D solvers virtually shares with its 1-D counterpart the same fundamental characteristics. Moreover, it is shown that the present Euler solver is capable of generating highly accurate solutions for a famous 2-D shock reflection problem. Specifically, both the incident and the reflected shocks can be resolved by a single data point without the presence of numerical oscillations near the discontinuity.

Implementing a Matrix-free Analytical Jacobian to Handle Nonlinearities in Models of 3D Lithospheric Deformation

NASA Astrophysics Data System (ADS)

Kaus, B.; Popov, A.

2015-12-01

The analytical expression for the Jacobian is a key component to achieve fast and robust convergence of the nonlinear Newton-Raphson iterative solver. Accomplishing this task in practice often requires a significant algebraic effort. Therefore it is quite common to use a cheap alternative instead, for example by approximating the Jacobian with a finite difference estimation. Despite its simplicity it is a relatively fragile and unreliable technique that is sensitive to the scaling of the residual and unknowns, as well as to the perturbation parameter selection. Unfortunately no universal rule can be applied to provide both a robust scaling and a perturbation. The approach we use here is to derive the analytical Jacobian for the coupled set of momentum, mass, and energy conservation equations together with the elasto-visco-plastic rheology and a marker in cell/staggered finite difference method. The software project LaMEM (Lithosphere and Mantle Evolution Model) is primarily developed for the thermo-mechanically coupled modeling of the 3D lithospheric deformation. The code is based on a staggered grid finite difference discretization in space, and uses customized scalable solvers form PETSc library to efficiently run on the massively parallel machines (such as IBM Blue Gene/Q). Currently LaMEM relies on the Jacobian-Free Newton-Krylov (JFNK) nonlinear solver, which approximates the Jacobian-vector product using a simple finite difference formula. This approach never requires an assembled Jacobian matrix and uses only the residual computation routine. We use an approximate Jacobian (Picard) matrix to precondition the Krylov solver with the Galerkin geometric multigrid. Because of the inherent problems of the finite difference Jacobian estimation, this approach doesn't always result in stable convergence. In this work we present and discuss a matrix-free technique in which the Jacobian-vector product is replaced by analytically-derived expressions and compare results with those obtained with a finite difference approximation of the Jacobian. This project is funded by ERC Starting Grant 258830 and computer facilities were provided by Jülich supercomputer center (Germany).

Long-time asymptotic solution structure of Camassa-Holm equation subject to an initial condition with non-zero reflection coefficient of the scattering data

NASA Astrophysics Data System (ADS)

Chang, Chueh-Hsin; Yu, Ching-Hao; Sheu, Tony Wen-Hann

2016-10-01

In this article, we numerically revisit the long-time solution behavior of the Camassa-Holm equation ut - uxxt + 2ux + 3uux = 2uxuxx + uuxxx. The finite difference solution of this integrable equation is sought subject to the newly derived initial condition with Delta-function potential. Our underlying strategy of deriving a numerical phase accurate finite difference scheme in time domain is to reduce the numerical dispersion error through minimization of the derived discrepancy between the numerical and exact modified wavenumbers. Additionally, to achieve the goal of conserving Hamiltonians in the completely integrable equation of current interest, a symplecticity-preserving time-stepping scheme is developed. Based on the solutions computed from the temporally symplecticity-preserving and the spatially wavenumber-preserving schemes, the long-time asymptotic CH solution characters can be accurately depicted in distinct regions of the space-time domain featuring with their own quantitatively very different solution behaviors. We also aim to numerically confirm that in the two transition zones their long-time asymptotics can indeed be described in terms of the theoretically derived Painlevé transcendents. Another attempt of this study is to numerically exhibit a close connection between the presently predicted finite-difference solution and the solution of the Painlevé ordinary differential equation of type II in two different transition zones.

Simplified Discontinuous Galerkin Methods for Systems of Conservation Laws with Convex Extension

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

1999-01-01

Simplified forms of the space-time discontinuous Galerkin (DG) and discontinuous Galerkin least-squares (DGLS) finite element method are developed and analyzed. The new formulations exploit simplifying properties of entropy endowed conservation law systems while retaining the favorable energy properties associated with symmetric variable formulations.

A Discontinuous Galerkin Finite Element Method for Hamilton-Jacobi Equations

NASA Technical Reports Server (NTRS)

Hu, Changqing; Shu, Chi-Wang

1998-01-01

In this paper, we present a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the Runge-Kutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method.

Mixed-RKDG Finite Element Methods for the 2-D Hydrodynamic Model for Semiconductor Device Simulation

DOE PAGES

Chen, Zhangxin; Cockburn, Bernardo; Jerome, Joseph W.; ...

1995-01-01

In this paper we introduce a new method for numerically solving the equations of the hydrodynamic model for semiconductor devices in two space dimensions. The method combines a standard mixed finite element method, used to obtain directly an approximation to the electric field, with the so-called Runge-Kutta Discontinuous Galerkin (RKDG) method, originally devised for numerically solving multi-dimensional hyperbolic systems of conservation laws, which is applied here to the convective part of the equations. Numerical simulations showing the performance of the new method are displayed, and the results compared with those obtained by using Essentially Nonoscillatory (ENO) finite difference schemes. Frommore » the perspective of device modeling, these methods are robust, since they are capable of encompassing broad parameter ranges, including those for which shock formation is possible. The simulations presented here are for Gallium Arsenide at room temperature, but we have tested them much more generally with considerable success.« less

A 3-D enlarged cell technique (ECT) for elastic wave modelling of a curved free surface

NASA Astrophysics Data System (ADS)

Wei, Songlin; Zhou, Jianyang; Zhuang, Mingwei; Liu, Qing Huo

2016-09-01

The conventional finite-difference time-domain (FDTD) method for elastic waves suffers from the staircasing error when applied to model a curved free surface because of its structured grid. In this work, an improved, stable and accurate 3-D FDTD method for elastic wave modelling on a curved free surface is developed based on the finite volume method and enlarged cell technique (ECT). To achieve a sufficiently accurate implementation, a finite volume scheme is applied to the curved free surface to remove the staircasing error; in the mean time, to achieve the same stability as the FDTD method without reducing the time step increment, the ECT is introduced to preserve the solution stability by enlarging small irregular cells into adjacent cells under the condition of conservation of force. This method is verified by several 3-D numerical examples. Results show that the method is stable at the Courant stability limit for a regular FDTD grid, and has much higher accuracy than the conventional FDTD method.

The Space-Time Conservative Schemes for Large-Scale, Time-Accurate Flow Simulations with Tetrahedral Meshes

NASA Technical Reports Server (NTRS)

Venkatachari, Balaji Shankar; Streett, Craig L.; Chang, Chau-Lyan; Friedlander, David J.; Wang, Xiao-Yen; Chang, Sin-Chung

2016-01-01

Despite decades of development of unstructured mesh methods, high-fidelity time-accurate simulations are still predominantly carried out on structured, or unstructured hexahedral meshes by using high-order finite-difference, weighted essentially non-oscillatory (WENO), or hybrid schemes formed by their combinations. In this work, the space-time conservation element solution element (CESE) method is used to simulate several flow problems including supersonic jet/shock interaction and its impact on launch vehicle acoustics, and direct numerical simulations of turbulent flows using tetrahedral meshes. This paper provides a status report for the continuing development of the space-time conservation element solution element (CESE) numerical and software framework under the Revolutionary Computational Aerosciences (RCA) project. Solution accuracy and large-scale parallel performance of the numerical framework is assessed with the goal of providing a viable paradigm for future high-fidelity flow physics simulations.

On the application of subcell resolution to conservation laws with stiff source terms

NASA Technical Reports Server (NTRS)

Chang, Shih-Hung

1989-01-01

LeVeque and Yee recently investigated a one-dimensional scalar conservation law with stiff source terms modeling the reacting flow problems and discovered that for the very stiff case most of the current finite difference methods developed for non-reacting flows would produce wrong solutions when there is a propagating discontinuity. A numerical scheme, essentially nonoscillatory/subcell resolution - characteristic direction (ENO/SRCD), is proposed for solving conservation laws with stiff source terms. This scheme is a modification of Harten's ENO scheme with subcell resolution, ENO/SR. The locations of the discontinuities and the characteristic directions are essential in the design. Strang's time-splitting method is used and time evolutions are done by advancing along the characteristics. Numerical experiment using this scheme shows excellent results on the model problem of LeVeque and Yee. Comparisons of the results of ENO, ENO/SR, and ENO/SRCD are also presented.

Semi-Analytic Reconstruction of Flux in Finite Volume Formulations

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2006-01-01

Semi-analytic reconstruction uses the analytic solution to a second-order, steady, ordinary differential equation (ODE) to simultaneously evaluate the convective and diffusive flux at all interfaces of a finite volume formulation. The second-order ODE is itself a linearized approximation to the governing first- and second- order partial differential equation conservation laws. Thus, semi-analytic reconstruction defines a family of formulations for finite volume interface fluxes using analytic solutions to approximating equations. Limiters are not applied in a conventional sense; rather, diffusivity is adjusted in the vicinity of changes in sign of eigenvalues in order to achieve a sufficiently small cell Reynolds number in the analytic formulation across critical points. Several approaches for application of semi-analytic reconstruction for the solution of one-dimensional scalar equations are introduced. Results are compared with exact analytic solutions to Burger s Equation as well as a conventional, upwind discretization using Roe s method. One approach, the end-point wave speed (EPWS) approximation, is further developed for more complex applications. One-dimensional vector equations are tested on a quasi one-dimensional nozzle application. The EPWS algorithm has a more compact difference stencil than Roe s algorithm but reconstruction time is approximately a factor of four larger than for Roe. Though both are second-order accurate schemes, Roe s method approaches a grid converged solution with fewer grid points. Reconstruction of flux in the context of multi-dimensional, vector conservation laws including effects of thermochemical nonequilibrium in the Navier-Stokes equations is developed.

Abstraction Techniques for Parameterized Verification

DTIC Science & Technology

2006-11-01

approach for applying model checking to unbounded systems is to extract finite state models from them using conservative abstraction techniques. Prop...36 2.5.1 Multiple Reference Processes . . . . . . . . . . . . . . . . . . . 36 2.5.2 Adding Monitor Processes...model checking to complex pieces of code like device drivers depends on the use of abstraction methods. An abstraction method extracts a small finite

Accuracy of the weighted essentially non-oscillatory conservative finite difference schemes

NASA Astrophysics Data System (ADS)

Don, Wai-Sun; Borges, Rafael

2013-10-01

In the reconstruction step of (2r-1) order weighted essentially non-oscillatory conservative finite difference schemes (WENO) for solving hyperbolic conservation laws, nonlinear weights αk and ωk, such as the WENO-JS weights by Jiang et al. and the WENO-Z weights by Borges et al., are designed to recover the formal (2r-1) order (optimal order) of the upwinded central finite difference scheme when the solution is sufficiently smooth. The smoothness of the solution is determined by the lower order local smoothness indicators βk in each substencil. These nonlinear weight formulations share two important free parameters in common: the power p, which controls the amount of numerical dissipation, and the sensitivity ε, which is added to βk to avoid a division by zero in the denominator of αk. However, ε also plays a role affecting the order of accuracy of WENO schemes, especially in the presence of critical points. It was recently shown that, for any design order (2r-1), ε should be of Ω(Δx2) (Ω(Δxm) means that ε⩾CΔxm for some C independent of Δx, as Δx→0) for the WENO-JS scheme to achieve the optimal order, regardless of critical points. In this paper, we derive an alternative proof of the sufficient condition using special properties of βk. Moreover, it is unknown if the WENO-Z scheme should obey the same condition on ε. Here, using same special properties of βk, we prove that in fact the optimal order of the WENO-Z scheme can be guaranteed with a much weaker condition ε=Ω(Δxm), where m(r,p)⩾2 is the optimal sensitivity order, regardless of critical points. Both theoretical results are confirmed numerically on smooth functions with arbitrary order of critical points. This is a highly desirable feature, as illustrated with the Lax problem and the Mach 3 shock-density wave interaction of one dimensional Euler equations, for a smaller ε allows a better essentially non-oscillatory shock capturing as it does not over-dominate over the size of βk. We also show that numerical oscillations can be further attenuated by increasing the power parameter 2⩽p⩽r-1, at the cost of increased numerical dissipation. Compact formulas of βk for WENO schemes are also presented.

On the Quality of Velocity Interpolation Schemes for Marker-in-Cell Method and Staggered Grids

NASA Astrophysics Data System (ADS)

Pusok, Adina E.; Kaus, Boris J. P.; Popov, Anton A.

2017-03-01

The marker-in-cell method is generally considered a flexible and robust method to model the advection of heterogenous non-diffusive properties (i.e., rock type or composition) in geodynamic problems. In this method, Lagrangian points carrying compositional information are advected with the ambient velocity field on an Eulerian grid. However, velocity interpolation from grid points to marker locations is often performed without considering the divergence of the velocity field at the interpolated locations (i.e., non-conservative). Such interpolation schemes can induce non-physical clustering of markers when strong velocity gradients are present (Journal of Computational Physics 166:218-252, 2001) and this may, eventually, result in empty grid cells, a serious numerical violation of the marker-in-cell method. To remedy this at low computational costs, Jenny et al. (Journal of Computational Physics 166:218-252, 2001) and Meyer and Jenny (Proceedings in Applied Mathematics and Mechanics 4:466-467, 2004) proposed a simple, conservative velocity interpolation scheme for 2-D staggered grid, while Wang et al. (Geochemistry, Geophysics, Geosystems 16(6):2015-2023, 2015) extended the formulation to 3-D finite element methods. Here, we adapt this formulation for 3-D staggered grids (correction interpolation) and we report on the quality of various velocity interpolation methods for 2-D and 3-D staggered grids. We test the interpolation schemes in combination with different advection schemes on incompressible Stokes problems with strong velocity gradients, which are discretized using a finite difference method. Our results suggest that a conservative formulation reduces the dispersion and clustering of markers, minimizing the need of unphysical marker control in geodynamic models.

A conservative numerical scheme for modeling nonlinear acoustic propagation in thermoviscous homogeneous media

NASA Astrophysics Data System (ADS)

Diaz, Manuel A.; Solovchuk, Maxim A.; Sheu, Tony W. H.

2018-06-01

A nonlinear system of partial differential equations capable of describing the nonlinear propagation and attenuation of finite amplitude perturbations in thermoviscous media is presented. This system constitutes a full nonlinear wave model that has been formulated in the conservation form. Initially, this model is investigated analytically in the inviscid limit where it has been found that the resulting flux function fulfills the Lax-Wendroff theorem, and the scheme can match the solutions of the Westervelt and Burgers equations numerically. Here, high-order numerical descriptions of strongly nonlinear wave propagations become of great interest. For that matter we consider finite difference formulations of the weighted essentially non-oscillatory (WENO) schemes associated with explicit strong stability preserving Runge-Kutta (SSP-RK) time integration methods. Although this strategy is known to be computationally demanding, it is found to be effective when implemented to be solved in graphical processing units (GPUs). As we consider wave propagations in unbounded domains, perfectly matching layers (PML) have been also considered in this work. The proposed system model is validated and illustrated by using one- and two-dimensional benchmark test cases proposed in the literature for nonlinear acoustic propagation in homogeneous thermoviscous media.

Further analytical study of hybrid rocket combustion

NASA Technical Reports Server (NTRS)

Hung, W. S. Y.; Chen, C. S.; Haviland, J. K.

1972-01-01

Analytical studies of the transient and steady-state combustion processes in a hybrid rocket system are discussed. The particular system chosen consists of a gaseous oxidizer flowing within a tube of solid fuel, resulting in a heterogeneous combustion. Finite rate chemical kinetics with appropriate reaction mechanisms were incorporated in the model. A temperature dependent Arrhenius type fuel surface regression rate equation was chosen for the current study. The governing mathematical equations employed for the reacting gas phase and for the solid phase are the general, two-dimensional, time-dependent conservation equations in a cylindrical coordinate system. Keeping the simplifying assumptions to a minimum, these basic equations were programmed for numerical computation, using two implicit finite-difference schemes, the Lax-Wendroff scheme for the gas phase, and, the Crank-Nicolson scheme for the solid phase.

Weak Galerkin finite element methods for Darcy flow: Anisotropy and heterogeneity

NASA Astrophysics Data System (ADS)

Lin, Guang; Liu, Jiangguo; Mu, Lin; Ye, Xiu

2014-11-01

This paper presents a family of weak Galerkin finite element methods (WGFEMs) for Darcy flow computation. The WGFEMs are new numerical methods that rely on the novel concept of discrete weak gradients. The WGFEMs solve for pressure unknowns both in element interiors and on the mesh skeleton. The numerical velocity is then obtained from the discrete weak gradient of the numerical pressure. The new methods are quite different than many existing numerical methods in that they are locally conservative by design, the resulting discrete linear systems are symmetric and positive-definite, and there is no need for tuning problem-dependent penalty factors. We test the WGFEMs on benchmark problems to demonstrate the strong potential of these new methods in handling strong anisotropy and heterogeneity in Darcy flow.

Numerical analysis of heat transfer in the exhaust gas flow in a diesel power generator

NASA Astrophysics Data System (ADS)

Brito, C. H. G.; Maia, C. B.; Sodré, J. R.

2016-09-01

This work presents a numerical study of heat transfer in the exhaust duct of a diesel power generator. The analysis was performed using two different approaches: the Finite Difference Method (FDM) and the Finite Volume Method (FVM), this last one by means of a commercial computer software, ANSYS CFX®. In FDM, the energy conservation equation was solved taking into account the estimated velocity profile for fully developed turbulent flow inside a tube and literature correlations for heat transfer. In FVM, the mass conservation, momentum, energy and transport equations were solved for turbulent quantities by the K-ω SST model. In both methods, variable properties were considered for the exhaust gas composed by six species: CO2, H2O, H2, O2, CO and N2. The entry conditions for the numerical simulations were given by experimental data available. The results were evaluated for the engine operating under loads of 0, 10, 20, and 37.5 kW. Test mesh and convergence were performed to determine the numerical error and uncertainty of the simulations. The results showed a trend of increasing temperature gradient with load increase. The general behaviour of the velocity and temperature profiles obtained by the numerical models were similar, with some divergence arising due to the assumptions made for the resolution of the models.

The Effect of the Density Ratio on the Nonlinear Dynamics of the Unstable Fluid Interface

NASA Technical Reports Server (NTRS)

Abarzhi, S. I.

2003-01-01

Here we report multiple harmonic theoretical solutions for a complete system of conservation laws, which describe the large-scale coherent dynamics in RTI and RMI for fluids with a finite density ratio in the general three-dimensional case. The analysis yields new properties of the bubble front dynamics. In either RTI or RMI, the obtained dependencies of the bubble velocity and curvature on the density ratio differ qualitatively and quantitatively from those suggested by the models of Sharp (1984), Oron et al. (2001), and Goncharov (2002). We show explicitly that these models violate the conservation laws. For the first time, our theory reveals an important qualitative distinction between the dynamics of the RT and RM bubbles.

Compression wave studies in Blair dolomite

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grady, D.E.; Hollenbach, R.E.; Schuler, K.W.

Dynamic compression wave studies have been conducted on Blair dolomite in the stress range of 0-7.0 GPa. Impact techniques were used to generate stress impulse input functions, and diffuse surface laser interferometry provided the dynamic instrumentation. Experimental particle velocity profiles obtained by this method were coupled with the conservation laws of mass and momentum to determine the stress-strain and stress-modulus constitutive properties of the material. Comparison between dynamic and quasistatic uniaxial stress-strain curves uncovered significant differences. Energy dissipated in a complete load and unload cycle differed by almost an order of magnitude and the longitudinal moduli differed by as muchmore » as a factor of two. Blair dolomite was observed to yield under dynamic loading at 2.5 GPa. Below 2.5 GPa the loading waves had a finite risetime and exhibited steady propagation. A finite linear viscoelastic constitutive model satisfactorily predicted the observed wave propagation. We speculate that dynamic properties of preexisting cracks provides a physical mechanism for both the rate dependent steady wave behavior and the difference between dynamic and quasistatic response.« less

Energy Stable Flux Formulas For The Discontinuous Galerkin Discretization Of First Order Nonlinear Conservation Laws

NASA Technical Reports Server (NTRS)

Barth, Timothy; Charrier, Pierre; Mansour, Nagi N. (Technical Monitor)

2001-01-01

We consider the discontinuous Galerkin (DG) finite element discretization of first order systems of conservation laws derivable as moments of the kinetic Boltzmann equation. This includes well known conservation law systems such as the Euler For the class of first order nonlinear conservation laws equipped with an entropy extension, an energy analysis of the DG method for the Cauchy initial value problem is developed. Using this DG energy analysis, several new variants of existing numerical flux functions are derived and shown to be energy stable.

Filtering of non-linear instabilities. [from finite difference solution of fluid dynamics equations

NASA Technical Reports Server (NTRS)

Khosla, P. K.; Rubin, S. G.

1979-01-01

For Courant numbers larger than one and cell Reynolds numbers larger than two, oscillations and in some cases instabilities are typically found with implicit numerical solutions of the fluid dynamics equations. This behavior has sometimes been associated with the loss of diagonal dominance of the coefficient matrix. It is shown here that these problems can in fact be related to the choice of the spatial differences, with the resulting instability related to aliasing or nonlinear interaction. Appropriate 'filtering' can reduce the intensity of these oscillations and in some cases possibly eliminate the instability. These filtering procedures are equivalent to a weighted average of conservation and non-conservation differencing. The entire spectrum of filtered equations retains a three-point character as well as second-order spatial accuracy. Burgers equation has been considered as a model. Several filters are examined in detail, and smooth solutions have been obtained for extremely large cell Reynolds numbers.

Nonlinear Aeroacoustics Computations by the Space-Time CE/SE Method

NASA Technical Reports Server (NTRS)

Loh, Ching Y.

2003-01-01

The Space-Time Conservation Element and Solution Element Method, or CE/SE Method for short, is a recently developed numerical method for conservation laws. Despite its second order accuracy in space and time, it possesses low dispersion errors and low dissipation. The method is robust enough to cover a wide range of compressible flows: from weak linear acoustic waves to strong discontinuous waves (shocks). An outstanding feature of the CE/SE scheme is its truly multi-dimensional, simple but effective non-reflecting boundary condition (NRBC), which is particularly valuable for computational aeroacoustics (CAA). In nature, the method may be categorized as a finite volume method, where the conservation element (CE) is equivalent to a finite control volume (or cell) and the solution element (SE) can be understood as the cell interface. However, due to its careful treatment of the surface fluxes and geometry, it is different from the existing schemes. Currently, the CE/SE scheme has been developed to a matured stage that a 3-D unstructured CE/SE Navier-Stokes solver is already available. However, in the present review paper, as a general introduction to the CE/SE method, only the 2-D unstructured Euler CE/SE solver is chosen and sketched in section 2. Then applications of the 2-D and 3-D CE/SE schemes to linear, and in particular, nonlinear aeroacoustics are depicted in sections 3, 4, and 5 to demonstrate its robustness and capability.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wight, L.; Zaslawsky, M.

Two approaches for calculating soil structure interaction (SSI) are compared: finite element and lumped mass. Results indicate that the calculations with the lumped mass method are generally conservative compared to those obtained by the finite element method. They also suggest that a closer agreement between the two sets of calculations is possible, depending on the use of frequency-dependent soil springs and dashpots in the lumped mass calculations. There is a total lack of suitable guidelines for implementing the lumped mass method of calculating SSI, which leads to the conclusion that the finite element method is generally superior for calculative purposes.

A spectral mimetic least-squares method for the Stokes equations with no-slip boundary condition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gerritsma, Marc; Bochev, Pavel

Formulation of locally conservative least-squares finite element methods (LSFEMs) for the Stokes equations with the no-slip boundary condition has been a long standing problem. Existing LSFEMs that yield exactly divergence free velocities require non-standard boundary conditions (Bochev and Gunzburger, 2009 [3]), while methods that admit the no-slip condition satisfy the incompressibility equation only approximately (Bochev and Gunzburger, 2009 [4, Chapter 7]). Here we address this problem by proving a new non-standard stability bound for the velocity–vorticity–pressure Stokes system augmented with a no-slip boundary condition. This bound gives rise to a norm-equivalent least-squares functional in which the velocity can be approximatedmore » by div-conforming finite element spaces, thereby enabling a locally-conservative approximations of this variable. Here, we also provide a practical realization of the new LSFEM using high-order spectral mimetic finite element spaces (Kreeft et al., 2011) and report several numerical tests, which confirm its mimetic properties.« less

Investigation of smoothness-increasing accuracy-conserving filters for improving streamline integration through discontinuous fields.

PubMed

Steffen, Michael; Curtis, Sean; Kirby, Robert M; Ryan, Jennifer K

2008-01-01

Streamline integration of fields produced by computational fluid mechanics simulations is a commonly used tool for the investigation and analysis of fluid flow phenomena. Integration is often accomplished through the application of ordinary differential equation (ODE) integrators--integrators whose error characteristics are predicated on the smoothness of the field through which the streamline is being integrated--smoothness which is not available at the inter-element level of finite volume and finite element data. Adaptive error control techniques are often used to ameliorate the challenge posed by inter-element discontinuities. As the root of the difficulties is the discontinuous nature of the data, we present a complementary approach of applying smoothness-enhancing accuracy-conserving filters to the data prior to streamline integration. We investigate whether such an approach applied to uniform quadrilateral discontinuous Galerkin (high-order finite volume) data can be used to augment current adaptive error control approaches. We discuss and demonstrate through numerical example the computational trade-offs exhibited when one applies such a strategy.

A spectral mimetic least-squares method for the Stokes equations with no-slip boundary condition

DOE PAGES

Gerritsma, Marc; Bochev, Pavel

2016-03-22

Formulation of locally conservative least-squares finite element methods (LSFEMs) for the Stokes equations with the no-slip boundary condition has been a long standing problem. Existing LSFEMs that yield exactly divergence free velocities require non-standard boundary conditions (Bochev and Gunzburger, 2009 [3]), while methods that admit the no-slip condition satisfy the incompressibility equation only approximately (Bochev and Gunzburger, 2009 [4, Chapter 7]). Here we address this problem by proving a new non-standard stability bound for the velocity–vorticity–pressure Stokes system augmented with a no-slip boundary condition. This bound gives rise to a norm-equivalent least-squares functional in which the velocity can be approximatedmore » by div-conforming finite element spaces, thereby enabling a locally-conservative approximations of this variable. Here, we also provide a practical realization of the new LSFEM using high-order spectral mimetic finite element spaces (Kreeft et al., 2011) and report several numerical tests, which confirm its mimetic properties.« less

Conservative multizonal interface algorithm for the 3-D Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Molvik, G. A.

1991-01-01

A conservative zonal interface algorithm using features of both structured and unstructured mesh CFD technology is presented. The flow solver within each of the zones is based on structured mesh CFD technology. The interface algorithm was implemented into two three-dimensional Navier-Stokes finite volume codes and was found to yield good results.

Computational design of the basic dynamical processes of the UCLA general circulation model

NASA Technical Reports Server (NTRS)

Arakawa, A.; Lamb, V. R.

1977-01-01

The 12-layer UCLA general circulation model encompassing troposphere and stratosphere (and superjacent 'sponge layer') is described. Prognostic variables are: surface pressure, horizontal velocity, temperature, water vapor and ozone in each layer, planetary boundary layer (PBL) depth, temperature, moisture and momentum discontinuities at PBL top, ground temperature and water storage, and mass of snow on ground. Selection of space finite-difference schemes for homogeneous incompressible flow, with/without a free surface, nonlinear two-dimensional nondivergent flow, enstrophy conserving schemes, momentum advection schemes, vertical and horizontal difference schemes, and time differencing schemes are discussed.

Numerical solution of a coupled pair of elliptic equations from solid state electronics

NASA Technical Reports Server (NTRS)

Phillips, T. N.

1983-01-01

Iterative methods are considered for the solution of a coupled pair of second order elliptic partial differential equations which arise in the field of solid state electronics. A finite difference scheme is used which retains the conservative form of the differential equations. Numerical solutions are obtained in two ways, by multigrid and dynamic alternating direction implicit methods. Numerical results are presented which show the multigrid method to be an efficient way of solving this problem.

Numerical simulation of steady supersonic flow. [spatial marching

NASA Technical Reports Server (NTRS)

Schiff, L. B.; Steger, J. L.

1981-01-01

A noniterative, implicit, space-marching, finite-difference algorithm was developed for the steady thin-layer Navier-Stokes equations in conservation-law form. The numerical algorithm is applicable to steady supersonic viscous flow over bodies of arbitrary shape. In addition, the same code can be used to compute supersonic inviscid flow or three-dimensional boundary layers. Computed results from two-dimensional and three-dimensional versions of the numerical algorithm are in good agreement with those obtained from more costly time-marching techniques.

The reality of artificial viscosity

DOE PAGES

Margolin, L. G.

2018-02-24

Artificial viscosity is used in the computer simulation of high Reynolds number flows and is one of the oldest numerical artifices. In this work, I will describe the origin and the interpretation of artificial viscosity as a physical phenomenon. The basis of this interpretation is the finite scale theory, which describes the evolution of integral averages of the fluid solution over finite (length) scales. I will outline the derivation of finite scale Navier–Stokes equations and highlight the particular properties of the equations that depend on the finite scales. Those properties include enslavement, inviscid dissipation, and a law concerning the partitionmore » of total flux of conserved quantities into advective and diffusive components.« less

The reality of artificial viscosity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Margolin, L. G.

Artificial viscosity is used in the computer simulation of high Reynolds number flows and is one of the oldest numerical artifices. In this work, I will describe the origin and the interpretation of artificial viscosity as a physical phenomenon. The basis of this interpretation is the finite scale theory, which describes the evolution of integral averages of the fluid solution over finite (length) scales. I will outline the derivation of finite scale Navier–Stokes equations and highlight the particular properties of the equations that depend on the finite scales. Those properties include enslavement, inviscid dissipation, and a law concerning the partitionmore » of total flux of conserved quantities into advective and diffusive components.« less

A third-order computational method for numerical fluxes to guarantee nonnegative difference coefficients for advection-diffusion equations in a semi-conservative form

NASA Astrophysics Data System (ADS)

Sakai, K.; Watabe, D.; Minamidani, T.; Zhang, G. S.

2012-10-01

According to Godunov theorem for numerical calculations of advection equations, there exist no higher-order schemes with constant positive difference coefficients in a family of polynomial schemes with an accuracy exceeding the first-order. We propose a third-order computational scheme for numerical fluxes to guarantee the non-negative difference coefficients of resulting finite difference equations for advection-diffusion equations in a semi-conservative form, in which there exist two kinds of numerical fluxes at a cell surface and these two fluxes are not always coincident in non-uniform velocity fields. The present scheme is optimized so as to minimize truncation errors for the numerical fluxes while fulfilling the positivity condition of the difference coefficients which are variable depending on the local Courant number and diffusion number. The feature of the present optimized scheme consists in keeping the third-order accuracy anywhere without any numerical flux limiter. We extend the present method into multi-dimensional equations. Numerical experiments for advection-diffusion equations showed nonoscillatory solutions.

BMS supertranslation symmetry implies Faddeev-Kulish amplitudes

NASA Astrophysics Data System (ADS)

Choi, Sangmin; Akhoury, Ratindranath

2018-02-01

We show explicitly that, among the scattering amplitudes constructed from eigenstates of the BMS supertranslation charge, the ones that conserve this charge, are equal to those constructed from Faddeev-Kulish states. Thus, Faddeev-Kulish states naturally arise as a consequence of the asymptotic symmetries of perturbative gravity and all charge conserving amplitudes are infrared finite. In the process we show an important feature of the Faddeev-Kulish clouds dressing the external hard particles: these clouds can be moved from the incoming states to the outgoing ones, and vice-versa, without changing the infrared finiteness properties of S matrix elements. We also apply our discussion to the problem of the decoherence of momentum configurations of hard particles due to soft boson effects.

An Advanced One-Dimensional Finite Element Model for Incompressible Thermally Expandable Flow

DOE PAGES

Hu, Rui

2017-03-27

Here, this paper provides an overview of a new one-dimensional finite element flow model for incompressible but thermally expandable flow. The flow model was developed for use in system analysis tools for whole-plant safety analysis of sodium fast reactors. Although the pressure-based formulation was implemented, the use of integral equations in the conservative form ensured the conservation laws of the fluid. A stabilization scheme based on streamline-upwind/Petrov-Galerkin and pressure-stabilizing/Petrov-Galerkin formulations is also introduced. The flow model and its implementation have been verified by many test problems, including density wave propagation, steep gradient problems, discharging between tanks, and the conjugate heatmore » transfer in a heat exchanger.« less

An Advanced One-Dimensional Finite Element Model for Incompressible Thermally Expandable Flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, Rui

Here, this paper provides an overview of a new one-dimensional finite element flow model for incompressible but thermally expandable flow. The flow model was developed for use in system analysis tools for whole-plant safety analysis of sodium fast reactors. Although the pressure-based formulation was implemented, the use of integral equations in the conservative form ensured the conservation laws of the fluid. A stabilization scheme based on streamline-upwind/Petrov-Galerkin and pressure-stabilizing/Petrov-Galerkin formulations is also introduced. The flow model and its implementation have been verified by many test problems, including density wave propagation, steep gradient problems, discharging between tanks, and the conjugate heatmore » transfer in a heat exchanger.« less

Bound-preserving Legendre-WENO finite volume schemes using nonlinear mapping

NASA Astrophysics Data System (ADS)

Smith, Timothy; Pantano, Carlos

2017-11-01

We present a new method to enforce field bounds in high-order Legendre-WENO finite volume schemes. The strategy consists of reconstructing each field through an intermediate mapping, which by design satisfies realizability constraints. Determination of the coefficients of the polynomial reconstruction involves nonlinear equations that are solved using Newton's method. The selection between the original or mapped reconstruction is implemented dynamically to minimize computational cost. The method has also been generalized to fields that exhibit interdependencies, requiring multi-dimensional mappings. Further, the method does not depend on the existence of a numerical flux function. We will discuss details of the proposed scheme and show results for systems in conservation and non-conservation form. This work was funded by the NSF under Grant DMS 1318161.

An HP Adaptive Discontinuous Galerkin Method for Hyperbolic Conservation Laws. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Bey, Kim S.

1994-01-01

This dissertation addresses various issues for model classes of hyperbolic conservation laws. The basic approach developed in this work employs a new family of adaptive, hp-version, finite element methods based on a special discontinuous Galerkin formulation for hyperbolic problems. The discontinuous Galerkin formulation admits high-order local approximations on domains of quite general geometry, while providing a natural framework for finite element approximations and for theoretical developments. The use of hp-versions of the finite element method makes possible exponentially convergent schemes with very high accuracies in certain cases; the use of adaptive hp-schemes allows h-refinement in regions of low regularity and p-enrichment to deliver high accuracy, while keeping problem sizes manageable and dramatically smaller than many conventional approaches. The use of discontinuous Galerkin methods is uncommon in applications, but the methods rest on a reasonable mathematical basis for low-order cases and has local approximation features that can be exploited to produce very efficient schemes, especially in a parallel, multiprocessor environment. The place of this work is to first and primarily focus on a model class of linear hyperbolic conservation laws for which concrete mathematical results, methodologies, error estimates, convergence criteria, and parallel adaptive strategies can be developed, and to then briefly explore some extensions to more general cases. Next, we provide preliminaries to the study and a review of some aspects of the theory of hyperbolic conservation laws. We also provide a review of relevant literature on this subject and on the numerical analysis of these types of problems.

Unsteady solute-transport simulation in streamflow using a finite-difference model

USGS Publications Warehouse

Land, Larry F.

1978-01-01

This report documents a rather simple, general purpose, one-dimensional, one-parameter, mass-transport model for field use. The model assumes a well-mixed conservative solute that may be coming from an unsteady source and is moving in unsteady streamflow. The quantity of solute being transported is in the units of concentration. Results are reported as such. An implicit finite-difference technique is used to solve the mass transport equation. It consists of creating a tridiagonal matrix and using the Thomas algorithm to solve the matrix for the unknown concentrations at the new time step. The computer program pesented is designed to compute the concentration of a water-quality constituent at any point and at any preselected time in a one-dimensional stream. The model is driven by the inflowing concentration of solute at the upstream boundary and is influenced by the solute entering the stream from tributaries and lateral ground-water inflow and from a source or sink. (Woodard-USGS)

Transpiration and film cooling boundary layer computer program. Volume 2: Computer program and user's manual

NASA Technical Reports Server (NTRS)

Gloss, R. J.

1971-01-01

A finite difference turbulent boundary layer computer program which allows for mass transfer wall cooling and equilibrium chemistry effects is presented. The program is capable of calculating laminar or turbulent boundary layer solutions for an arbitrary ideal gas or an equilibrium hydrogen oxygen system. Either two dimensional or axisymmetric geometric configurations may be considered. The equations are solved, in nondimension-alized physical coordinates, using the implicit Crank-Nicolson technique. The finite difference forms of the conservation of mass, momentum, total enthalpy and elements equations are linearized and uncoupled, thereby generating easily solvable tridiagonal sets of algebraic equations. A detailed description of the computer program, as well as a program user's manual is provided. Detailed descriptions of all boundary layer subroutines are included, as well as a section defining all program symbols of principal importance. Instructions are then given for preparing card input to the program and for interpreting the printed output. Finally, two sample cases are included to illustrate the use of the program.

High-order flux correction/finite difference schemes for strand grids

NASA Astrophysics Data System (ADS)

Katz, Aaron; Work, Dalon

2015-02-01

A novel high-order method combining unstructured flux correction along body surfaces and high-order finite differences normal to surfaces is formulated for unsteady viscous flows on strand grids. The flux correction algorithm is applied in each unstructured layer of the strand grid, and the layers are then coupled together via a source term containing derivatives in the strand direction. Strand-direction derivatives are approximated to high-order via summation-by-parts operators for first derivatives and second derivatives with variable coefficients. We show how this procedure allows for the proper truncation error canceling properties required for the flux correction scheme. The resulting scheme possesses third-order design accuracy, but often exhibits fourth-order accuracy when higher-order derivatives are employed in the strand direction, especially for highly viscous flows. We prove discrete conservation for the new scheme and time stability in the absence of the flux correction terms. Results in two dimensions are presented that demonstrate improvements in accuracy with minimal computational and algorithmic overhead over traditional second-order algorithms.

Mimetic finite difference method

NASA Astrophysics Data System (ADS)

Lipnikov, Konstantin; Manzini, Gianmarco; Shashkov, Mikhail

2014-01-01

The mimetic finite difference (MFD) method mimics fundamental properties of mathematical and physical systems including conservation laws, symmetry and positivity of solutions, duality and self-adjointness of differential operators, and exact mathematical identities of the vector and tensor calculus. This article is the first comprehensive review of the 50-year long history of the mimetic methodology and describes in a systematic way the major mimetic ideas and their relevance to academic and real-life problems. The supporting applications include diffusion, electromagnetics, fluid flow, and Lagrangian hydrodynamics problems. The article provides enough details to build various discrete operators on unstructured polygonal and polyhedral meshes and summarizes the major convergence results for the mimetic approximations. Most of these theoretical results, which are presented here as lemmas, propositions and theorems, are either original or an extension of existing results to a more general formulation using polyhedral meshes. Finally, flexibility and extensibility of the mimetic methodology are shown by deriving higher-order approximations, enforcing discrete maximum principles for diffusion problems, and ensuring the numerical stability for saddle-point systems.

Weak Galerkin finite element methods for Darcy flow: Anisotropy and heterogeneity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Guang; Liu, Jiangguo; Mu, Lin

2014-11-01

This paper presents a family of weak Galerkin finite element methods (WGFEMs) for Darcy flow computation. The WGFEMs are new numerical methods that rely on the novel concept of discrete weak gradients. The WGFEMs solve for pressure unknowns both in element interiors and on the mesh skeleton. The numerical velocity is then obtained from the discrete weak gradient of the numerical pressure. The new methods are quite different than many existing numerical methods in that they are locally conservative by design, the resulting discrete linear systems are symmetric and positive-definite, and there is no need for tuning problem-dependent penalty factors.more » We test the WGFEMs on benchmark problems to demonstrate the strong potential of these new methods in handling strong anisotropy and heterogeneity in Darcy flow.« less

A Robust Absorbing Boundary Condition for Compressible Flows

NASA Technical Reports Server (NTRS)

Loh, Ching Y.; orgenson, Philip C. E.

2005-01-01

An absorbing non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented with theoretical proof. This paper is a continuation and improvement of a previous paper by the author. The absorbing NRBC technique is based on a first principle of non reflecting, which contains the essential physics that a plane wave solution of the Euler equations remains intact across the boundary. The technique is theoretically shown to work for a large class of finite volume approaches. When combined with the hyperbolic conservation laws, the NRBC is simple, robust and truly multi-dimensional; no additional implementation is needed except the prescribed physical boundary conditions. Several numerical examples in multi-dimensional spaces using two different finite volume schemes are illustrated to demonstrate its robustness in practical computations. Limitations and remedies of the technique are also discussed.

Quantitative analysis of pulse thermography data for degradation assessment of historical buildings

NASA Astrophysics Data System (ADS)

Di Maio, Rosa; Piegari, Ester; Mancini, Cecilia; Chiapparino, Antonella

2015-06-01

In the last decades, infrared thermography has been successfully applied to various materials and structures for the assessment of their state of conservation and planning suitable restoration works. To this aim, mathematical models are required to characterize thermal anomaly sources, such as detachments, water infiltration and material decomposition processes. In this paper, an algorithm based on the conservative finite difference method is used to analyse pulse thermography data acquired on an ancient building in the Pompeii archaeological site (Naples, Italy). The numerical study is applied to both broad and narrow elongated thermal anomalies. In particular, from the comparison between simulated and experimental thermal decays, the plaster thickness was characterized in terms of thermal properties and areas of possible future detachments, and moisture infiltration depths were identified.

Thermochemical nonequilibrium in atomic hydrogen at elevated temperatures

NASA Technical Reports Server (NTRS)

Scott, R. K.

1972-01-01

A numerical study of the nonequilibrium flow of atomic hydrogen in a cascade arc was performed to obtain insight into the physics of the hydrogen cascade arc. A rigorous mathematical model of the flow problem was formulated, incorporating the important nonequilibrium transport phenomena and atomic processes which occur in atomic hydrogen. Realistic boundary conditions, including consideration of the wall electrostatic sheath phenomenon, were included in the model. The governing equations of the asymptotic region of the cascade arc were obtained by writing conservation of mass and energy equations for the electron subgas, an energy conservation equation for heavy particles and an equation of state. Finite-difference operators for variable grid spacing were applied to the governing equations and the resulting system of strongly coupled, stiff equations were solved numerically by the Newton-Raphson method.

How to reconcile wood production and biodiversity conservation? The Pan-European boreal forest history gradient as an "experiment".

PubMed

Naumov, Vladimir; Manton, Michael; Elbakidze, Marine; Rendenieks, Zigmars; Priednieks, Janis; Uhlianets, Siarhei; Yamelynets, Taras; Zhivotov, Anton; Angelstam, Per

2018-07-15

There are currently competing demands on Europe's forests and the finite resources and services that they can offer. Forestry intensification that aims at mitigating climate change and biodiversity conservation is one example. Whether or not these two objectives compete can be evaluated by comparative studies of forest landscapes with different histories. We test the hypothesis that indicators of wood production and biodiversity conservation are inversely related in a gradient of long to short forestry intensification histories. Forest management data containing stand age, volume and tree species were used to model the opportunity for wood production and biodiversity conservation in five north European forest regions representing a gradient in landscape history from very long in the West and short in the East. Wood production indicators captured the supply of coniferous wood and total biomass, as well as current accessibility by transport infrastructure. Biodiversity conservation indicators were based on modelling habitat network functionality for focal bird species dependent on different combinations of stand age and tree species composition representing naturally dynamic forests. In each region we randomly sampled 25 individual 100-km 2 areas with contiguous forest cover. Regarding wood production, Sweden's Bergslagen region had the largest areas of coniferous wood, followed by Vitebsk in Belarus and Zemgale in Latvia. NW Russia's case study regions in Pskov and Komi had the lowest values, except for the biomass indicator. The addition of forest accessibility for transportation made the Belarusian and Swedish study region most suitable for wood and biomass production, followed by Latvia and two study regions in NW Russian. Regarding biodiversity conservation, the overall rank among regions was opposite. Mixed and deciduous habitats were functional in Russia, Belarus and Latvia. Old Scots pine and Norway spruce habitats were only functional in Komi. Thus, different regional forest histories provide different challenges in terms of satisfying both wood production and biodiversity conservation objectives in a forest management unit. These regional differences in northern Europe create opportunities for exchanging experiences among different regional contexts about how to achieve both objectives. We discuss this in the context of land-sharing versus land-sparing. Copyright © 2018 Elsevier Ltd. All rights reserved.

A fully-neoclassical finite-orbit-width version of the CQL3D Fokker–Planck code

DOE Office of Scientific and Technical Information (OSTI.GOV)

Petrov, Yu V.; Harvey, R. W.

The time-dependent bounce-averaged CQL3D flux-conservative finite-difference Fokker–Planck equation (FPE) solver has been upgraded to include finite-orbit-width (FOW) capabilities which are necessary for an accurate description of neoclassical transport, losses to the walls, and transfer of particles, momentum, and heat to the scrape-off layer. The FOW modifications are implemented in the formulation of the neutral beam source, collision operator, RF quasilinear diffusion operator, and in synthetic particle diagnostics. The collisional neoclassical radial transport appears naturally in the FOW version due to the orbit-averaging of local collision coefficients coupled with transformation coefficients from local (R, Z) coordinates along each guiding-center orbit tomore » the corresponding midplane computational coordinates, where the FPE is solved. In a similar way, the local quasilinear RF diffusion terms give rise to additional radial transport of orbits. We note that the neoclassical results are obtained for ‘full’ orbits, not dependent on a common small orbit-width approximation. Results of validation tests for the FOW version are also presented.« less

A fully-neoclassical finite-orbit-width version of the CQL3D Fokker–Planck code

DOE PAGES

Petrov, Yu V.; Harvey, R. W.

2016-09-08

The time-dependent bounce-averaged CQL3D flux-conservative finite-difference Fokker–Planck equation (FPE) solver has been upgraded to include finite-orbit-width (FOW) capabilities which are necessary for an accurate description of neoclassical transport, losses to the walls, and transfer of particles, momentum, and heat to the scrape-off layer. The FOW modifications are implemented in the formulation of the neutral beam source, collision operator, RF quasilinear diffusion operator, and in synthetic particle diagnostics. The collisional neoclassical radial transport appears naturally in the FOW version due to the orbit-averaging of local collision coefficients coupled with transformation coefficients from local (R, Z) coordinates along each guiding-center orbit tomore » the corresponding midplane computational coordinates, where the FPE is solved. In a similar way, the local quasilinear RF diffusion terms give rise to additional radial transport of orbits. We note that the neoclassical results are obtained for ‘full’ orbits, not dependent on a common small orbit-width approximation. Results of validation tests for the FOW version are also presented.« less

Entropy stable discontinuous interfaces coupling for the three-dimensional compressible Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

2015-06-01

Non-linear entropy stability and a summation-by-parts (SBP) framework are used to derive entropy stable interior interface coupling for the semi-discretized three-dimensional (3D) compressible Navier-Stokes equations. A complete semi-discrete entropy estimate for the interior domain is achieved combining a discontinuous entropy conservative operator of any order [1,2] with an entropy stable coupling condition for the inviscid terms, and a local discontinuous Galerkin (LDG) approach with an interior penalty (IP) procedure for the viscous terms. The viscous penalty contributions scale with the inverse of the Reynolds number (Re) so that for Re → ∞ their contributions vanish and only the entropy stable inviscid interface penalty term is recovered. This paper extends the interface couplings presented [1,2] and provides a simple and automatic way to compute the magnitude of the viscous IP term. The approach presented herein is compatible with any diagonal norm summation-by-parts (SBP) spatial operator, including finite element, finite volume, finite difference schemes and the class of high-order accurate methods which include the large family of discontinuous Galerkin discretizations and flux reconstruction schemes.

Numerical simulation of axisymmetric turbulent flow in combustors and diffusors. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Yung, Chain Nan

1988-01-01

A method for predicting turbulent flow in combustors and diffusers is developed. The Navier-Stokes equations, incorporating a turbulence kappa-epsilon model equation, were solved in a nonorthogonal curvilinear coordinate system. The solution applied the finite volume method to discretize the differential equations and utilized the SIMPLE algorithm iteratively to solve the differenced equations. A zonal grid method, wherein the flow field was divided into several subsections, was developed. This approach permitted different computational schemes to be used in the various zones. In addition, grid generation was made a more simple task. However, treatment of the zonal boundaries required special handling. Boundary overlap and interpolating techniques were used and an adjustment of the flow variables was required to assure conservation of mass, momentum and energy fluxes. The numerical accuracy was assessed using different finite differencing methods, i.e., hybrid, quadratic upwind and skew upwind, to represent the convection terms. Flows in different geometries of combustors and diffusers were simulated and results compared with experimental data and good agreement was obtained.

Finite-time synchronization of complex networks with non-identical nodes and impulsive disturbances

NASA Astrophysics Data System (ADS)

Zhang, Wanli; Li, Chuandong; He, Xing; Li, Hongfei

2018-01-01

This paper investigates the finite-time synchronization of complex networks (CNs) with non-identical nodes and impulsive disturbances. By utilizing stability theories, new 1-norm-based analytical techniques and suitable comparison, systems, several sufficient conditions are obtained to realize the synchronization goal in finite time. State feedback controllers with and without the sign function are designed. Results show that the controllers with sign function can reduce the conservativeness of control gains and the controllers without sign function can overcome the chattering phenomenon. Numerical simulations are offered to verify the effectiveness of the theoretical analysis.

Finite element procedures for coupled linear analysis of heat transfer, fluid and solid mechanics

NASA Technical Reports Server (NTRS)

Sutjahjo, Edhi; Chamis, Christos C.

1993-01-01

Coupled finite element formulations for fluid mechanics, heat transfer, and solid mechanics are derived from the conservation laws for energy, mass, and momentum. To model the physics of interactions among the participating disciplines, the linearized equations are coupled by combining domain and boundary coupling procedures. Iterative numerical solution strategy is presented to solve the equations, with the partitioning of temporal discretization implemented.

Mapping behavioral landscapes for animal movement: a finite mixture modeling approach

USGS Publications Warehouse

Tracey, Jeff A.; Zhu, Jun; Boydston, Erin E.; Lyren, Lisa M.; Fisher, Robert N.; Crooks, Kevin R.

2013-01-01

Because of its role in many ecological processes, movement of animals in response to landscape features is an important subject in ecology and conservation biology. In this paper, we develop models of animal movement in relation to objects or fields in a landscape. We take a finite mixture modeling approach in which the component densities are conceptually related to different choices for movement in response to a landscape feature, and the mixing proportions are related to the probability of selecting each response as a function of one or more covariates. We combine particle swarm optimization and an Expectation-Maximization (EM) algorithm to obtain maximum likelihood estimates of the model parameters. We use this approach to analyze data for movement of three bobcats in relation to urban areas in southern California, USA. A behavioral interpretation of the models revealed similarities and differences in bobcat movement response to urbanization. All three bobcats avoided urbanization by moving either parallel to urban boundaries or toward less urban areas as the proportion of urban land cover in the surrounding area increased. However, one bobcat, a male with a dispersal-like large-scale movement pattern, avoided urbanization at lower densities and responded strictly by moving parallel to the urban edge. The other two bobcats, which were both residents and occupied similar geographic areas, avoided urban areas using a combination of movements parallel to the urban edge and movement toward areas of less urbanization. However, the resident female appeared to exhibit greater repulsion at lower levels of urbanization than the resident male, consistent with empirical observations of bobcats in southern California. Using the parameterized finite mixture models, we mapped behavioral states to geographic space, creating a representation of a behavioral landscape. This approach can provide guidance for conservation planning based on analysis of animal movement data using statistical models, thereby linking connectivity evaluations to empirical data.

Intensity Conserving Spectral Fitting

NASA Technical Reports Server (NTRS)

Klimchuk, J. A.; Patsourakos, S.; Tripathi, D.

2015-01-01

The detailed shapes of spectral line profiles provide valuable information about the emitting plasma, especially when the plasma contains an unresolved mixture of velocities, temperatures, and densities. As a result of finite spectral resolution, the intensity measured by a spectrometer is the average intensity across a wavelength bin of non-zero size. It is assigned to the wavelength position at the center of the bin. However, the actual intensity at that discrete position will be different if the profile is curved, as it invariably is. Standard fitting routines (spline, Gaussian, etc.) do not account for this difference, and this can result in significant errors when making sensitive measurements. Detection of asymmetries in solar coronal emission lines is one example. Removal of line blends is another. We have developed an iterative procedure that corrects for this effect. It can be used with any fitting function, but we employ a cubic spline in a new analysis routine called Intensity Conserving Spline Interpolation (ICSI). As the name implies, it conserves the observed intensity within each wavelength bin, which ordinary fits do not. Given the rapid convergence, speed of computation, and ease of use, we suggest that ICSI be made a standard component of the processing pipeline for spectroscopic data.

A freestream-preserving fourth-order finite-volume method in mapped coordinates with adaptive-mesh refinement

DOE PAGES

Guzik, Stephen M.; Gao, Xinfeng; Owen, Landon D.; ...

2015-12-20

We present a fourth-order accurate finite-volume method for solving time-dependent hyperbolic systems of conservation laws on mapped grids that are adaptively refined in space and time. Some novel considerations for formulating the semi-discrete system of equations in computational space are combined with detailed mechanisms for accommodating the adapting grids. Furthermore, these considerations ensure that conservation is maintained and that the divergence of a constant vector field is always zero (freestream-preservation property). The solution in time is advanced with a fourth-order Runge-Kutta method. A series of tests verifies that the expected accuracy is achieved in smooth flows and the solution ofmore » a Mach reflection problem demonstrates the effectiveness of the algorithm in resolving strong discontinuities.« less

Upwind methods for the Baer–Nunziato equations and higher-order reconstruction using artificial viscosity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fraysse, F., E-mail: francois.fraysse@rs2n.eu; E. T. S. de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Madrid; Redondo, C.

This article is devoted to the numerical discretisation of the hyperbolic two-phase flow model of Baer and Nunziato. A special attention is paid on the discretisation of intercell flux functions in the framework of Finite Volume and Discontinuous Galerkin approaches, where care has to be taken to efficiently approximate the non-conservative products inherent to the model equations. Various upwind approximate Riemann solvers have been tested on a bench of discontinuous test cases. New discretisation schemes are proposed in a Discontinuous Galerkin framework following the criterion of Abgrall and the path-conservative formalism. A stabilisation technique based on artificial viscosity is appliedmore » to the high-order Discontinuous Galerkin method and compared against classical TVD-MUSCL Finite Volume flux reconstruction.« less

Asymptotic symmetries of Rindler space at the horizon and null infinity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chung, Hyeyoun

2010-08-15

We investigate the asymptotic symmetries of Rindler space at null infinity and at the event horizon using both systematic and ad hoc methods. We find that the approaches that yield infinite-dimensional asymptotic symmetry algebras in the case of anti-de Sitter and flat spaces only give a finite-dimensional algebra for Rindler space at null infinity. We calculate the charges corresponding to these symmetries and confirm that they are finite, conserved, and integrable, and that the algebra of charges gives a representation of the asymptotic symmetry algebra. We also use relaxed boundary conditions to find infinite-dimensional asymptotic symmetry algebras for Rindler spacemore » at null infinity and at the event horizon. We compute the charges corresponding to these symmetries and confirm that they are finite and integrable. We also determine sufficient conditions for the charges to be conserved on-shell, and for the charge algebra to give a representation of the asymptotic symmetry algebra. In all cases, we find that the central extension of the charge algebra is trivial.« less

The PLUTO code for astrophysical gasdynamics .

NASA Astrophysics Data System (ADS)

Mignone, A.

Present numerical codes appeal to a consolidated theory based on finite difference and Godunov-type schemes. In this context we have developed a versatile numerical code, PLUTO, suitable for the solution of high-mach number flow in 1, 2 and 3 spatial dimensions and different systems of coordinates. Different hydrodynamic modules and algorithms may be independently selected to properly describe Newtonian, relativistic, MHD, or relativistic MHD fluids. The modular structure exploits a general framework for integrating a system of conservation laws, built on modern Godunov-type shock-capturing schemes. The code is freely distributed under the GNU public license and it is available for download to the astrophysical community at the URL http://plutocode.to.astro.it.

Dynamic mortar finite element method for modeling of shear rupture on frictional rough surfaces

NASA Astrophysics Data System (ADS)

Tal, Yuval; Hager, Bradford H.

2017-09-01

This paper presents a mortar-based finite element formulation for modeling the dynamics of shear rupture on rough interfaces governed by slip-weakening and rate and state (RS) friction laws, focusing on the dynamics of earthquakes. The method utilizes the dual Lagrange multipliers and the primal-dual active set strategy concepts, together with a consistent discretization and linearization of the contact forces and constraints, and the friction laws to obtain a semi-smooth Newton method. The discretization of the RS friction law involves a procedure to condense out the state variables, thus eliminating the addition of another set of unknowns into the system. Several numerical examples of shear rupture on frictional rough interfaces demonstrate the efficiency of the method and examine the effects of the different time discretization schemes on the convergence, energy conservation, and the time evolution of shear traction and slip rate.

Quantum Quenches in a Spinor Condensate

NASA Astrophysics Data System (ADS)

Lamacraft, Austen

2007-04-01

We discuss the ordering of a spin-1 condensate when quenched from its paramagnetic phase to its ferromagnetic phase by reducing the magnetic field. We first elucidate the nature of the equilibrium quantum phase transition. Quenching rapidly through this transition reveals XY ordering either at a specific wave vector, or the “light-cone” correlations familiar from relativistic theories, depending on the end point of the quench. For a quench proceeding at a finite rate the ordering scale is governed by the Kibble-Zurek mechanism. The creation of vortices through growth of the magnetization fluctuations is also discussed. The long-time dynamics again depends on the end point, conserving the order parameter in a zero field, but not at a finite field, with differing exponents for the coarsening of magnetic order. The results are discussed in the light of a recent experiment by Sadler et al.

A discontinuous control volume finite element method for multi-phase flow in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Salinas, P.; Pavlidis, D.; Xie, Z.; Osman, H.; Pain, C. C.; Jackson, M. D.

2018-01-01

We present a new, high-order, control-volume-finite-element (CVFE) method for multiphase porous media flow with discontinuous 1st-order representation for pressure and discontinuous 2nd-order representation for velocity. The method has been implemented using unstructured tetrahedral meshes to discretize space. The method locally and globally conserves mass. However, unlike conventional CVFE formulations, the method presented here does not require the use of control volumes (CVs) that span the boundaries between domains with differing material properties. We demonstrate that the approach accurately preserves discontinuous saturation changes caused by permeability variations across such boundaries, allowing efficient simulation of flow in highly heterogeneous models. Moreover, accurate solutions are obtained at significantly lower computational cost than using conventional CVFE methods. We resolve a long-standing problem associated with the use of classical CVFE methods to model flow in highly heterogeneous porous media.

Stable finite element approximations of two-phase flow with soluble surfactant

NASA Astrophysics Data System (ADS)

Barrett, John W.; Garcke, Harald; Nürnberg, Robert

2015-09-01

A parametric finite element approximation of incompressible two-phase flow with soluble surfactants is presented. The Navier-Stokes equations are coupled to bulk and surfaces PDEs for the surfactant concentrations. At the interface adsorption, desorption and stress balances involving curvature effects and Marangoni forces have to be considered. A parametric finite element approximation for the advection of the interface, which maintains good mesh properties, is coupled to the evolving surface finite element method, which is used to discretize the surface PDE for the interface surfactant concentration. The resulting system is solved together with standard finite element approximations of the Navier-Stokes equations and of the bulk parabolic PDE for the surfactant concentration. Semidiscrete and fully discrete approximations are analyzed with respect to stability, conservation and existence/uniqueness issues. The approach is validated for simple test cases and for complex scenarios, including colliding drops in a shear flow, which are computed in two and three space dimensions.

On cell entropy inequality for discontinuous Galerkin methods

NASA Technical Reports Server (NTRS)

Jiang, Guangshan; Shu, Chi-Wang

1993-01-01

We prove a cell entropy inequality for a class of high order discontinuous Galerkin finite element methods approximating conservation laws, which implies convergence for the one dimensional scalar convex case.

A mixed finite difference/Galerkin method for three-dimensional Rayleigh-Benard convection

NASA Technical Reports Server (NTRS)

Buell, Jeffrey C.

1988-01-01

A fast and accurate numerical method, for nonlinear conservation equation systems whose solutions are periodic in two of the three spatial dimensions, is presently implemented for the case of Rayleigh-Benard convection between two rigid parallel plates in the parameter region where steady, three-dimensional convection is known to be stable. High-order streamfunctions secure the reduction of the system of five partial differential equations to a system of only three. Numerical experiments are presented which verify both the expected convergence rates and the absolute accuracy of the method.

Numerical Modeling of Three-Dimensional Confined Flows

NASA Technical Reports Server (NTRS)

Greywall, M. S.

1981-01-01

A three dimensional confined flow model is presented. The flow field is computed by calculating velocity and enthalpy along a set of streamlines. The finite difference equations are obtained by applying conservation principles to streamtubes constructed around the chosen streamlines. With appropriate substitutions for the body force terms, the approach computes three dimensional magnetohydrodynamic channel flows. A listing of a computer code, based on this approach is presented in FORTRAN IV language. The code computes three dimensional compressible viscous flow through a rectangular duct, with the duct cross section specified along the axis.

Development of the general interpolants method for the CYBER 200 series of supercomputers

NASA Technical Reports Server (NTRS)

Stalnaker, J. F.; Robinson, M. A.; Spradley, L. W.; Kurzius, S. C.; Thoenes, J.

1988-01-01

The General Interpolants Method (GIM) is a 3-D, time-dependent, hybrid procedure for generating numerical analogs of the conservation laws. This study is directed toward the development and application of the GIM computer code for fluid dynamic research applications as implemented for the Cyber 200 series of supercomputers. An elliptic and quasi-parabolic version of the GIM code are discussed. Turbulence models, algebraic and differential equations, were added to the basic viscous code. An equilibrium reacting chemistry model and an implicit finite difference scheme are also included.

High-order central ENO finite-volume scheme for hyperbolic conservation laws on three-dimensional cubed-sphere grids

NASA Astrophysics Data System (ADS)

Ivan, L.; De Sterck, H.; Susanto, A.; Groth, C. P. T.

2015-02-01

A fourth-order accurate finite-volume scheme for hyperbolic conservation laws on three-dimensional (3D) cubed-sphere grids is described. The approach is based on a central essentially non-oscillatory (CENO) finite-volume method that was recently introduced for two-dimensional compressible flows and is extended to 3D geometries with structured hexahedral grids. Cubed-sphere grids feature hexahedral cells with nonplanar cell surfaces, which are handled with high-order accuracy using trilinear geometry representations in the proposed approach. Varying stencil sizes and slope discontinuities in grid lines occur at the boundaries and corners of the six sectors of the cubed-sphere grid where the grid topology is unstructured, and these difficulties are handled naturally with high-order accuracy by the multidimensional least-squares based 3D CENO reconstruction with overdetermined stencils. A rotation-based mechanism is introduced to automatically select appropriate smaller stencils at degenerate block boundaries, where fewer ghost cells are available and the grid topology changes, requiring stencils to be modified. Combining these building blocks results in a finite-volume discretization for conservation laws on 3D cubed-sphere grids that is uniformly high-order accurate in all three grid directions. While solution-adaptivity is natural in the multi-block setting of our code, high-order accurate adaptive refinement on cubed-sphere grids is not pursued in this paper. The 3D CENO scheme is an accurate and robust solution method for hyperbolic conservation laws on general hexahedral grids that is attractive because it is inherently multidimensional by employing a K-exact overdetermined reconstruction scheme, and it avoids the complexity of considering multiple non-central stencil configurations that characterizes traditional ENO schemes. Extensive numerical tests demonstrate fourth-order convergence for stationary and time-dependent Euler and magnetohydrodynamic flows on cubed-sphere grids, and robustness against spurious oscillations at 3D shocks. Performance tests illustrate efficiency gains that can be potentially achieved using fourth-order schemes as compared to second-order methods for the same error level. Applications on extended cubed-sphere grids incorporating a seventh root block that discretizes the interior of the inner sphere demonstrate the versatility of the spatial discretization method.

An interpolation-free ALE scheme for unsteady inviscid flows computations with large boundary displacements over three-dimensional adaptive grids

NASA Astrophysics Data System (ADS)

Re, B.; Dobrzynski, C.; Guardone, A.

2017-07-01

A novel strategy to solve the finite volume discretization of the unsteady Euler equations within the Arbitrary Lagrangian-Eulerian framework over tetrahedral adaptive grids is proposed. The volume changes due to local mesh adaptation are treated as continuous deformations of the finite volumes and they are taken into account by adding fictitious numerical fluxes to the governing equation. This peculiar interpretation enables to avoid any explicit interpolation of the solution between different grids and to compute grid velocities so that the Geometric Conservation Law is automatically fulfilled also for connectivity changes. The solution on the new grid is obtained through standard ALE techniques, thus preserving the underlying scheme properties, such as conservativeness, stability and monotonicity. The adaptation procedure includes node insertion, node deletion, edge swapping and points relocation and it is exploited both to enhance grid quality after the boundary movement and to modify the grid spacing to increase solution accuracy. The presented approach is assessed by three-dimensional simulations of steady and unsteady flow fields. The capability of dealing with large boundary displacements is demonstrated by computing the flow around the translating infinite- and finite-span NACA 0012 wing moving through the domain at the flight speed. The proposed adaptive scheme is applied also to the simulation of a pitching infinite-span wing, where the bi-dimensional character of the flow is well reproduced despite the three-dimensional unstructured grid. Finally, the scheme is exploited in a piston-induced shock-tube problem to take into account simultaneously the large deformation of the domain and the shock wave. In all tests, mesh adaptation plays a crucial role.

Pressure- and buoyancy-driven thermal convection in a rectangular enclosure

NASA Technical Reports Server (NTRS)

Spradley, L. W.; Churchill, S. W.

1975-01-01

Results are presented for unsteady laminar thermal convection in compressible fluids at various reduced levels of gravity in a rectangular enclosure which is heated on one side and cooled on the opposite side. The results were obtained by solving numerically the equations of conservation for a viscous, compressible, heat-conducting, ideal gas in the presence of a gravitational body force. The formulation differs from the Boussinesq simplification in that the effects of variable density are completely retained. A conservative, explicit, time-dependent, finite-difference technique was used and good agreement was found for the limited cases where direct comparison with previous investigations was possible. The solutions show that the thermally induced motion is acoustic in nature at low levels of gravity and that the unsteady-state rate of heat transfer is thereby greatly enhanced relative to pure conduction. The nonlinear variable density profile skews the streamlines towards the cooler walls but is shown to have little effect on the steady-state isotherms.

Recent applications of the transonic wing analysis computer code, TWING

NASA Technical Reports Server (NTRS)

Subramanian, N. R.; Holst, T. L.; Thomas, S. D.

1982-01-01

An evaluation of the transonic-wing-analysis computer code TWING is given. TWING utilizes a fully implicit approximate factorization iteration scheme to solve the full potential equation in conservative form. A numerical elliptic-solver grid-generation scheme is used to generate the required finite-difference mesh. Several wing configurations were analyzed, and the limits of applicability of this code was evaluated. Comparisons of computed results were made with available experimental data. Results indicate that the code is robust, accurate (when significant viscous effects are not present), and efficient. TWING generally produces solutions an order of magnitude faster than other conservative full potential codes using successive-line overrelaxation. The present method is applicable to a wide range of isolated wing configurations including high-aspect-ratio transport wings and low-aspect-ratio, high-sweep, fighter configurations.

Geometric integration in Born-Oppenheimer molecular dynamics.

PubMed

Odell, Anders; Delin, Anna; Johansson, Börje; Cawkwell, Marc J; Niklasson, Anders M N

2011-12-14

Geometric integration schemes for extended Lagrangian self-consistent Born-Oppenheimer molecular dynamics, including a weak dissipation to remove numerical noise, are developed and analyzed. The extended Lagrangian framework enables the geometric integration of both the nuclear and electronic degrees of freedom. This provides highly efficient simulations that are stable and energy conserving even under incomplete and approximate self-consistent field (SCF) convergence. We investigate three different geometric integration schemes: (1) regular time reversible Verlet, (2) second order optimal symplectic, and (3) third order optimal symplectic. We look at energy conservation, accuracy, and stability as a function of dissipation, integration time step, and SCF convergence. We find that the inclusion of dissipation in the symplectic integration methods gives an efficient damping of numerical noise or perturbations that otherwise may accumulate from finite arithmetics in a perfect reversible dynamics. © 2011 American Institute of Physics

On a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws. II - Five-point schemes

NASA Technical Reports Server (NTRS)

Harten, A.; Tal-Ezer, H.

1981-01-01

This paper presents a family of two-level five-point implicit schemes for the solution of one-dimensional systems of hyperbolic conservation laws, which generalized the Crank-Nicholson scheme to fourth order accuracy (4-4) in both time and space. These 4-4 schemes are nondissipative and unconditionally stable. Special attention is given to the system of linear equations associated with these 4-4 implicit schemes. The regularity of this system is analyzed and efficiency of solution-algorithms is examined. A two-datum representation of these 4-4 implicit schemes brings about a compactification of the stencil to three mesh points at each time-level. This compact two-datum representation is particularly useful in deriving boundary treatments. Numerical results are presented to illustrate some properties of the proposed scheme.

Two-Layer Viscous Shallow-Water Equations and Conservation Laws

NASA Astrophysics Data System (ADS)

Kanayama, Hiroshi; Dan, Hiroshi

In our previous papers, the two-layer viscous shallow-water equations were derived from the three-dimensional Navier-Stokes equations under the hydrostatic assumption. Also, it was noted that the combination of upper and lower equations in the two-layer model produces the classical one-layer equations if the density of each layer is the same. Then, the two-layer equations were approximated by a finite element method which followed our numerical scheme established for the one-layer model in 1978. Also, it was numerically demonstrated that the interfacial instability generated when the densities are the same can be eliminated by providing a sufficient density difference. In this paper, we newly show that conservation laws are still valid in the two-layer model. Also, we show results of a new physical experiment for the interfacial instability.

Asymptotic charges cannot be measured in finite time

DOE PAGES

Bousso, Raphael; Chandrasekaran, Venkatesa; Halpern, Illan F.; ...

2018-02-28

To study quantum gravity in asymptotically flat spacetimes, one would like to understand the algebra of observables at null infinity. Here we show that the Bondi mass cannot be observed in finite retarded time, and so is not contained in the algebra on any finite portion of I +. This follows immediately from recently discovered asymptotic entropy bounds. We verify this explicitly, and we find that attempts to measure a conserved charge at arbitrarily large radius in fixed retarded time are thwarted by quantum fluctuations. We comment on the implications of our results to flat space holography and the BMSmore » charges at I +.« less

The Chiral Separation Effect in quenched finite-density QCD

NASA Astrophysics Data System (ADS)

Puhr, Matthias; Buividovich, Pavel

2018-03-01

We present results of a study of the Chiral Separation Effect (CSE) in quenched finite-density QCD. Using a recently developed numerical method we calculate the conserved axial current for exactly chiral overlap fermions at finite density for the first time. We compute the anomalous transport coeffcient for the CSE in the confining and deconfining phase and investigate possible deviations from the universal value. In both phases we find that non-perturbative corrections to the CSE are absent and we reproduce the universal value for the transport coeffcient within small statistical errors. Our results suggest that the CSE can be used to determine the renormalisation factor of the axial current.

Asymptotic charges cannot be measured in finite time

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bousso, Raphael; Chandrasekaran, Venkatesa; Halpern, Illan F.

To study quantum gravity in asymptotically flat spacetimes, one would like to understand the algebra of observables at null infinity. Here we show that the Bondi mass cannot be observed in finite retarded time, and so is not contained in the algebra on any finite portion of I +. This follows immediately from recently discovered asymptotic entropy bounds. We verify this explicitly, and we find that attempts to measure a conserved charge at arbitrarily large radius in fixed retarded time are thwarted by quantum fluctuations. We comment on the implications of our results to flat space holography and the BMSmore » charges at I +.« less

Flux-Based Finite Volume representations for general thermal problems

NASA Technical Reports Server (NTRS)

Mohan, Ram V.; Tamma, Kumar K.

1993-01-01

Flux-Based Finite Volume (FV) element representations for general thermal problems are given in conjunction with a generalized trapezoidal gamma-T family of algorithms, formulated following the spirit of what we term as the Lax-Wendroff based FV formulations. The new flux-based representations introduced offer an improved physical interpretation of the problem along with computationally convenient and attractive features. The space and time discretization emanate from a conservation form of the governing equation for thermal problems, and in conjunction with the flux-based element representations give rise to a physically improved and locally conservative numerical formulations. The present representations seek to involve improved locally conservative properties, improved physical representations and computational features; these are based on a 2D, bilinear FV element and can be extended for other cases. Time discretization based on a gamma-T family of algorithms in the spirit of a Lax-Wendroff based FV formulations are employed. Numerical examples involving linear/nonlinear steady and transient situations are shown to demonstrate the applicability of the present representations for thermal analysis situations.

Relativistic extension of a charge-conservative finite element solver for time-dependent Maxwell-Vlasov equations

NASA Astrophysics Data System (ADS)

Na, D.-Y.; Moon, H.; Omelchenko, Y. A.; Teixeira, F. L.

2018-01-01

Accurate modeling of relativistic particle motion is essential for physical predictions in many problems involving vacuum electronic devices, particle accelerators, and relativistic plasmas. A local, explicit, and charge-conserving finite-element time-domain (FETD) particle-in-cell (PIC) algorithm for time-dependent (non-relativistic) Maxwell-Vlasov equations on irregular (unstructured) meshes was recently developed by Moon et al. [Comput. Phys. Commun. 194, 43 (2015); IEEE Trans. Plasma Sci. 44, 1353 (2016)]. Here, we extend this FETD-PIC algorithm to the relativistic regime by implementing and comparing three relativistic particle-pushers: (relativistic) Boris, Vay, and Higuera-Cary. We illustrate the application of the proposed relativistic FETD-PIC algorithm for the analysis of particle cyclotron motion at relativistic speeds, harmonic particle oscillation in the Lorentz-boosted frame, and relativistic Bernstein modes in magnetized charge-neutral (pair) plasmas.

Total Variation Diminishing (TVD) schemes of uniform accuracy

NASA Technical Reports Server (NTRS)

Hartwich, PETER-M.; Hsu, Chung-Hao; Liu, C. H.

1988-01-01

Explicit second-order accurate finite-difference schemes for the approximation of hyperbolic conservation laws are presented. These schemes are nonlinear even for the constant coefficient case. They are based on first-order upwind schemes. Their accuracy is enhanced by locally replacing the first-order one-sided differences with either second-order one-sided differences or central differences or a blend thereof. The appropriate local difference stencils are selected such that they give TVD schemes of uniform second-order accuracy in the scalar, or linear systems, case. Like conventional TVD schemes, the new schemes avoid a Gibbs phenomenon at discontinuities of the solution, but they do not switch back to first-order accuracy, in the sense of truncation error, at extrema of the solution. The performance of the new schemes is demonstrated in several numerical tests.

The Numerical Simulation of the Shock Wave of Coal Gas Explosions in Gas Pipe*

NASA Astrophysics Data System (ADS)

Chen, Zhenxing; Hou, Kepeng; Chen, Longwei

2018-03-01

For the problem of large deformation and vortex, the method of Euler and Lagrange has both advantage and disadvantage. In this paper we adopt special fuzzy interface method(volume of fluid). Gas satisfies the conditions of conservation equations of mass, momentum, and energy. Based on explosion and three-dimension fluid dynamics theory, using unsteady, compressible, inviscid hydrodynamic equations and state equations, this paper considers pressure gradient’s effects to velocity, mass and energy in Lagrange steps by the finite difference method. To minimize transport errors of material, energy and volume in Finite Difference mesh, it also considers material transport in Euler steps. Programmed with Fortran PowerStation 4.0 and visualized with the software designed independently, we design the numerical simulation of gas explosion with specific pipeline structure, check the key points of the pressure change in the flow field, reproduce the gas explosion in pipeline of shock wave propagation, from the initial development, flame and accelerate the process of shock wave. This offers beneficial reference and experience to coal gas explosion accidents or safety precautions.

Flux-corrected transport algorithms for continuous Galerkin methods based on high order Bernstein finite elements

NASA Astrophysics Data System (ADS)

Lohmann, Christoph; Kuzmin, Dmitri; Shadid, John N.; Mabuza, Sibusiso

2017-09-01

This work extends the flux-corrected transport (FCT) methodology to arbitrary order continuous finite element discretizations of scalar conservation laws on simplex meshes. Using Bernstein polynomials as local basis functions, we constrain the total variation of the numerical solution by imposing local discrete maximum principles on the Bézier net. The design of accuracy-preserving FCT schemes for high order Bernstein-Bézier finite elements requires the development of new algorithms and/or generalization of limiting techniques tailored for linear and multilinear Lagrange elements. In this paper, we propose (i) a new discrete upwinding strategy leading to local extremum bounded low order approximations with compact stencils, (ii) high order variational stabilization based on the difference between two gradient approximations, and (iii) new localized limiting techniques for antidiffusive element contributions. The optional use of a smoothness indicator, based on a second derivative test, makes it possible to potentially avoid unnecessary limiting at smooth extrema and achieve optimal convergence rates for problems with smooth solutions. The accuracy of the proposed schemes is assessed in numerical studies for the linear transport equation in 1D and 2D.

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.

"Ersatz" and "hybrid" NMR spectral estimates using the filter diagonalization method.

PubMed

Ridge, Clark D; Shaka, A J

2009-03-12

The filter diagonalization method (FDM) is an efficient and elegant way to make a spectral estimate purely in terms of Lorentzian peaks. As NMR spectral peaks of liquids conform quite well to this model, the FDM spectral estimate can be accurate with far fewer time domain points than conventional discrete Fourier transform (DFT) processing. However, noise is not efficiently characterized by a finite number of Lorentzian peaks, or by any other analytical form, for that matter. As a result, noise can affect the FDM spectrum in different ways than it does the DFT spectrum, and the effect depends on the dimensionality of the spectrum. Regularization to suppress (or control) the influence of noise to give an "ersatz", or EFDM, spectrum is shown to sometimes miss weak features, prompting a more conservative implementation of filter diagonalization. The spectra obtained, called "hybrid" or HFDM spectra, are acquired by using regularized FDM to obtain an "infinite time" spectral estimate and then adding to it the difference between the DFT of the data and the finite time FDM estimate, over the same time interval. HFDM has a number of advantages compared to the EFDM spectra, where all features must be Lorentzian. They also show better resolution than DFT spectra. The HFDM spectrum is a reliable and robust way to try to extract more information from noisy, truncated data records and is less sensitive to the choice of regularization parameter. In multidimensional NMR of liquids, HFDM is a conservative way to handle the problems of noise, truncation, and spectral peaks that depart significantly from the model of a multidimensional Lorentzian peak.

Application of viscous-inviscid interaction methods to transonic turbulent flows

NASA Technical Reports Server (NTRS)

Lee, D.; Pletcher, R. H.

1986-01-01

Two different viscous-inviscid interaction schemes were developed for the analysis of steady, turbulent, transonic, separated flows over axisymmetric bodies. The viscous and inviscid solutions are coupled through the displacement concept using a transpiration velocity approach. In the semi-inverse interaction scheme, the viscous and inviscid equations are solved in an explicitly separate manner and the displacement thickness distribution is iteratively updated by a simple coupling algorithm. In the simultaneous interaction method, local solutions of viscous and inviscid equations are treated simultaneously, and the displacement thickness is treated as an unknown and is obtained as a part of the solution through a global iteration procedure. The inviscid flow region is described by a direct finite-difference solution of a velocity potential equation in conservative form. The potential equation is solved on a numerically generated mesh by an approximate factorization (AF2) scheme in the semi-inverse interaction method and by a successive line overrelaxation (SLOR) scheme in the simultaneous interaction method. The boundary-layer equations are used for the viscous flow region. The continuity and momentum equations are solved inversely in a coupled manner using a fully implicit finite-difference scheme.

Solving the Fluid Pressure Poisson Equation Using Multigrid-Evaluation and Improvements.

PubMed

Dick, Christian; Rogowsky, Marcus; Westermann, Rudiger

2016-11-01

In many numerical simulations of fluids governed by the incompressible Navier-Stokes equations, the pressure Poisson equation needs to be solved to enforce mass conservation. Multigrid solvers show excellent convergence in simple scenarios, yet they can converge slowly in domains where physically separated regions are combined at coarser scales. Moreover, existing multigrid solvers are tailored to specific discretizations of the pressure Poisson equation, and they cannot easily be adapted to other discretizations. In this paper we analyze the convergence properties of existing multigrid solvers for the pressure Poisson equation in different simulation domains, and we show how to further improve the multigrid convergence rate by using a graph-based extension to determine the coarse grid hierarchy. The proposed multigrid solver is generic in that it can be applied to different kinds of discretizations of the pressure Poisson equation, by using solely the specification of the simulation domain and pre-assembled computational stencils. We analyze the proposed solver in combination with finite difference and finite volume discretizations of the pressure Poisson equation. Our evaluations show that, despite the common assumption, multigrid schemes can exploit their potential even in the most complicated simulation scenarios, yet this behavior is obtained at the price of higher memory consumption.

Preparing CAM-SE for Multi-Tracer Applications: CAM-SE-Cslam

NASA Astrophysics Data System (ADS)

Lauritzen, P. H.; Taylor, M.; Goldhaber, S.

2014-12-01

The NCAR-DOE spectral element (SE) dynamical core comes from the HOMME (High-Order Modeling Environment; Dennis et al., 2012) and it is available in CAM. The CAM-SE dynamical core is designed with intrinsic mimetic properties guaranteeing total energy conservation (to time-truncation errors) and mass-conservation, and has demonstrated excellent scalability on massively parallel compute platforms (Taylor, 2011). For applications involving many tracers such as chemistry and biochemistry modeling, CAM-SE has been found to be significantly more computationally costly than the current "workhorse" model CAM-FV (Finite-Volume; Lin 2004). Hence a multi-tracer efficient scheme, called the CSLAM (Conservative Semi-Lagrangian Multi-tracer; Lauritzen et al., 2011) scheme, has been implemented in the HOMME (Erath et al., 2012). The CSLAM scheme has recently been cast in flux-form in HOMME so that it can be coupled to the SE dynamical core through conventional flux-coupling methods where the SE dynamical core provides background air mass fluxes to CSLAM. Since the CSLAM scheme makes use of a finite-volume gnomonic cubed-sphere grid and hence does not operate on the SE quadrature grid, the capability of running tracer advection, the physical parameterization suite and dynamics on separate grids has been implemented in CAM-SE. The default CAM-SE-CSLAM setup is to run physics on the quasi-equal area CSLAM grid. The capability of running physics on a different grid than the SE dynamical core may provide a more consistent coupling since the physics grid option operates with quasi-equal-area cell average values rather than non-equi-distant grid-point (SE quadrature point) values. Preliminary results on the performance of CAM-SE-CSLAM will be presented.

The Discontinuous Galerkin Finite Element Method for Solving the MEG and the Combined MEG/EEG Forward Problem

PubMed Central

Piastra, Maria Carla; Nüßing, Andreas; Vorwerk, Johannes; Bornfleth, Harald; Oostenveld, Robert; Engwer, Christian; Wolters, Carsten H.

2018-01-01

In Electro- (EEG) and Magnetoencephalography (MEG), one important requirement of source reconstruction is the forward model. The continuous Galerkin finite element method (CG-FEM) has become one of the dominant approaches for solving the forward problem over the last decades. Recently, a discontinuous Galerkin FEM (DG-FEM) EEG forward approach has been proposed as an alternative to CG-FEM (Engwer et al., 2017). It was shown that DG-FEM preserves the property of conservation of charge and that it can, in certain situations such as the so-called skull leakages, be superior to the standard CG-FEM approach. In this paper, we developed, implemented, and evaluated two DG-FEM approaches for the MEG forward problem, namely a conservative and a non-conservative one. The subtraction approach was used as source model. The validation and evaluation work was done in statistical investigations in multi-layer homogeneous sphere models, where an analytic solution exists, and in a six-compartment realistically shaped head volume conductor model. In agreement with the theory, the conservative DG-FEM approach was found to be superior to the non-conservative DG-FEM implementation. This approach also showed convergence with increasing resolution of the hexahedral meshes. While in the EEG case, in presence of skull leakages, DG-FEM outperformed CG-FEM, in MEG, DG-FEM achieved similar numerical errors as the CG-FEM approach, i.e., skull leakages do not play a role for the MEG modality. In particular, for the finest mesh resolution of 1 mm sources with a distance of 1.59 mm from the brain-CSF surface, DG-FEM yielded mean topographical errors (relative difference measure, RDM%) of 1.5% and mean magnitude errors (MAG%) of 0.1% for the magnetic field. However, if the goal is a combined source analysis of EEG and MEG data, then it is highly desirable to employ the same forward model for both EEG and MEG data. Based on these results, we conclude that the newly presented conservative DG-FEM can at least complement and in some scenarios even outperform the established CG-FEM approaches in EEG or combined MEG/EEG source analysis scenarios, which motivates a further evaluation of DG-FEM for applications in bioelectromagnetism. PMID:29456487

Black hole thermodynamics from a variational principle: asymptotically conical backgrounds

DOE PAGES

An, Ok Song; Cvetič, Mirjam; Papadimitriou, Ioannis

2016-03-14

The variational problem of gravity theories is directly related to black hole thermodynamics. For asymptotically locally AdS backgrounds it is known that holographic renormalization results in a variational principle in terms of equivalence classes of boundary data under the local asymptotic symmetries of the theory, which automatically leads to finite conserved charges satisfying the first law of thermodynamics. We show that this connection holds well beyond asymptotically AdS black holes. In particular, we formulate the variational problem for N = 2 STU supergravity in four dimensions with boundary conditions corresponding to those obeyed by the so called ‘subtracted geometries’. Wemore » show that such boundary conditions can be imposed covariantly in terms of a set of asymptotic second class constraints, and we derive the appropriate boundary terms that render the variational problem well posed in two different duality frames of the STU model. This allows us to define finite conserved charges associated with any asymptotic Killing vector and to demonstrate that these charges satisfy the Smarr formula and the first law of thermodynamics. Moreover, by uplifting the theory to five dimensions and then reducing on a 2-sphere, we provide a precise map between the thermodynamic observables of the subtracted geometries and those of the BTZ black hole. Finally, surface terms play a crucial role in this identification.« less

Black hole thermodynamics from a variational principle: asymptotically conical backgrounds

DOE Office of Scientific and Technical Information (OSTI.GOV)

An, Ok Song; Cvetič, Mirjam; Papadimitriou, Ioannis

The variational problem of gravity theories is directly related to black hole thermodynamics. For asymptotically locally AdS backgrounds it is known that holographic renormalization results in a variational principle in terms of equivalence classes of boundary data under the local asymptotic symmetries of the theory, which automatically leads to finite conserved charges satisfying the first law of thermodynamics. We show that this connection holds well beyond asymptotically AdS black holes. In particular, we formulate the variational problem for N = 2 STU supergravity in four dimensions with boundary conditions corresponding to those obeyed by the so called ‘subtracted geometries’. Wemore » show that such boundary conditions can be imposed covariantly in terms of a set of asymptotic second class constraints, and we derive the appropriate boundary terms that render the variational problem well posed in two different duality frames of the STU model. This allows us to define finite conserved charges associated with any asymptotic Killing vector and to demonstrate that these charges satisfy the Smarr formula and the first law of thermodynamics. Moreover, by uplifting the theory to five dimensions and then reducing on a 2-sphere, we provide a precise map between the thermodynamic observables of the subtracted geometries and those of the BTZ black hole. Finally, surface terms play a crucial role in this identification.« less

Prediction of shear critical behavior of high-strength reinforced concrete columns using finite element methods

NASA Astrophysics Data System (ADS)

Alrasyid, Harun; Safi, Fahrudin; Iranata, Data; Chen-Ou, Yu

2017-11-01

This research shows the prediction of shear behavior of High-Strength Reinforced Concrete Columns using Finite-Element Method. The experimental data of nine half scale high-strength reinforced concrete were selected. These columns using specified concrete compressive strength of 70 MPa, specified yield strength of longitudinal and transverse reinforcement of 685 and 785 MPa, respectively. The VecTor2 finite element software was used to simulate the shear critical behavior of these columns. The combination axial compression load and monotonic loading were applied at this prediction. It is demonstrated that VecTor2 finite element software provides accurate prediction of load-deflection up to peak at applied load, but provide similar behavior at post peak load. The shear strength prediction provide by VecTor 2 are slightly conservative compare to test result.

A Lagrangian discontinuous Galerkin hydrodynamic method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Xiaodong; Morgan, Nathaniel Ray; Burton, Donald E.

Here, we present a new Lagrangian discontinuous Galerkin (DG) hydrodynamic method for solving the two-dimensional gas dynamic equations on unstructured hybrid meshes. The physical conservation laws for the momentum and total energy are discretized using a DG method based on linear Taylor expansions. Three different approaches are investigated for calculating the density variation over the element. The first approach evolves a Taylor expansion of the specific volume field. The second approach follows certain finite element methods and uses the strong mass conservation to calculate the density field at a location inside the element or on the element surface. The thirdmore » approach evolves a Taylor expansion of the density field. The nodal velocity, and the corresponding forces, are explicitly calculated by solving a multidirectional approximate Riemann problem. An effective limiting strategy is presented that ensures monotonicity of the primitive variables. This new Lagrangian DG hydrodynamic method conserves mass, momentum, and total energy. Results from a suite of test problems are presented to demonstrate the robustness and expected second-order accuracy of this new method.« less

Comparing volume of fluid and level set methods for evaporating liquid-gas flows

NASA Astrophysics Data System (ADS)

Palmore, John; Desjardins, Olivier

2016-11-01

This presentation demonstrates three numerical strategies for simulating liquid-gas flows undergoing evaporation. The practical aim of this work is to choose a framework capable of simulating the combustion of liquid fuels in an internal combustion engine. Each framework is analyzed with respect to its accuracy and computational cost. All simulations are performed using a conservative, finite volume code for simulating reacting, multiphase flows under the low-Mach assumption. The strategies used in this study correspond to different methods for tracking the liquid-gas interface and handling the transport of the discontinuous momentum and vapor mass fractions fields. The first two strategies are based on conservative, geometric volume of fluid schemes using directionally split and un-split advection, respectively. The third strategy is the accurate conservative level set method. For all strategies, special attention is given to ensuring the consistency between the fluxes of mass, momentum, and vapor fractions. The study performs three-dimensional simulations of an isolated droplet of a single component fuel evaporating into air. Evaporation rates and vapor mass fractions are compared to analytical results.

Two-level schemes for the advection equation

NASA Astrophysics Data System (ADS)

Vabishchevich, Petr N.

2018-06-01

The advection equation is the basis for mathematical models of continuum mechanics. In the approximate solution of nonstationary problems it is necessary to inherit main properties of the conservatism and monotonicity of the solution. In this paper, the advection equation is written in the symmetric form, where the advection operator is the half-sum of advection operators in conservative (divergent) and non-conservative (characteristic) forms. The advection operator is skew-symmetric. Standard finite element approximations in space are used. The standard explicit two-level scheme for the advection equation is absolutely unstable. New conditionally stable regularized schemes are constructed, on the basis of the general theory of stability (well-posedness) of operator-difference schemes, the stability conditions of the explicit Lax-Wendroff scheme are established. Unconditionally stable and conservative schemes are implicit schemes of the second (Crank-Nicolson scheme) and fourth order. The conditionally stable implicit Lax-Wendroff scheme is constructed. The accuracy of the investigated explicit and implicit two-level schemes for an approximate solution of the advection equation is illustrated by the numerical results of a model two-dimensional problem.

A Lagrangian discontinuous Galerkin hydrodynamic method

DOE PAGES

Liu, Xiaodong; Morgan, Nathaniel Ray; Burton, Donald E.

2017-12-11

Here, we present a new Lagrangian discontinuous Galerkin (DG) hydrodynamic method for solving the two-dimensional gas dynamic equations on unstructured hybrid meshes. The physical conservation laws for the momentum and total energy are discretized using a DG method based on linear Taylor expansions. Three different approaches are investigated for calculating the density variation over the element. The first approach evolves a Taylor expansion of the specific volume field. The second approach follows certain finite element methods and uses the strong mass conservation to calculate the density field at a location inside the element or on the element surface. The thirdmore » approach evolves a Taylor expansion of the density field. The nodal velocity, and the corresponding forces, are explicitly calculated by solving a multidirectional approximate Riemann problem. An effective limiting strategy is presented that ensures monotonicity of the primitive variables. This new Lagrangian DG hydrodynamic method conserves mass, momentum, and total energy. Results from a suite of test problems are presented to demonstrate the robustness and expected second-order accuracy of this new method.« less

Asymptotic Charges at Null Infinity in Any Dimension

NASA Astrophysics Data System (ADS)

Campoleoni, Andrea; Francia, Dario; Heissenberg, Carlo

2018-03-01

We analyse the conservation laws associated with large gauge transformations of massless fields in Minkowski space. Our aim is to highlight the interplay between boundary conditions and finiteness of the asymptotically conserved charges in any space-time dimension, both even and odd, greater than or equal to three. After discussing non-linear Yang-Mills theory and revisiting linearised gravity, our investigation extends to cover the infrared behaviour of bosonic massless quanta of any spin.

Rigged String Configurations, Bethe Ansatz Qubits, and Conservation of Parity

NASA Astrophysics Data System (ADS)

Lulek, T.

Bethe Ansatz solutions for the Heisenberg Hamiltonian of a one - dimensional magnetic ring of N nodes, each with the spin 1/2, within the XXX model, have been presented as some composite systems, in a spirit of quantum information theory. The constituents are single - node spin states, which organize into strings of various length, and "seas of holes". The former are responsible for dynamics, whereas the latter determine the range of riggings for strings. Another aim was to demonstrate a unification of Bethe Ansatz eigenstates by means of Galois symmetries of finite field extensions. The key observation is that the original eigenproblem is expressible in integers, and thus, for a finite fixed N, the splitting field of the characteristic polynom of the Heisenberg Hamiltonian is also finite. The Galois group of the latter field permutes, by definition, roots of this polynom, which implies permutation of eigenstates. General considerations are demonstrated on the example of heptagon (N = 7), which admits an implementation of a collection of arithmetic qubits, and also demonstrates a special case of degeneration of the spectrum of the Hamiltonian, resulting from conservation of parity, within the realm of rigged string configurations.

Three-dimensional finite element analysis for high velocity impact. [of projectiles from space debris

NASA Technical Reports Server (NTRS)

Chan, S. T. K.; Lee, C. H.; Brashears, M. R.

1975-01-01

A finite element algorithm for solving unsteady, three-dimensional high velocity impact problems is presented. A computer program was developed based on the Eulerian hydroelasto-viscoplastic formulation and the utilization of the theorem of weak solutions. The equations solved consist of conservation of mass, momentum, and energy, equation of state, and appropriate constitutive equations. The solution technique is a time-dependent finite element analysis utilizing three-dimensional isoparametric elements, in conjunction with a generalized two-step time integration scheme. The developed code was demonstrated by solving one-dimensional as well as three-dimensional impact problems for both the inviscid hydrodynamic model and the hydroelasto-viscoplastic model.

HYDRODYNAMIC SIMULATION OF THE UPPER POTOMAC ESTUARY.

USGS Publications Warehouse

Schaffranck, Raymond W.

1986-01-01

Hydrodynamics of the upper extent of the Potomac Estuary between Indian Head and Morgantown, Md. , are simulated using a two-dimensional model. The model computes water-surface elevations and depth-averaged velocities by numerically integrating finite-difference forms of the equations of mass and momentum conservation using the alternating direction implicit method. The fundamental, non-linear, unsteady-flow equations, upon which the model is formulated, include additional terms to account for Coriolis acceleration and meteorological influences. Preliminary model/prototype data comparisons show agreement to within 9% for tidal flow volumes and phase differences within the measured-data-recording interval. Use of the model to investigate the hydrodynamics and certain aspects of transport within this Potomac Estuary reach is demonstrated. Refs.

A multi-dimensional nonlinearly implicit, electromagnetic Vlasov-Darwin particle-in-cell (PIC) algorithm

NASA Astrophysics Data System (ADS)

Chen, Guangye; Chacón, Luis; CoCoMans Team

2014-10-01

For decades, the Vlasov-Darwin model has been recognized to be attractive for PIC simulations (to avoid radiative noise issues) in non-radiative electromagnetic regimes. However, the Darwin model results in elliptic field equations that renders explicit time integration unconditionally unstable. Improving on linearly implicit schemes, fully implicit PIC algorithms for both electrostatic and electromagnetic regimes, with exact discrete energy and charge conservation properties, have been recently developed in 1D. This study builds on these recent algorithms to develop an implicit, orbit-averaged, time-space-centered finite difference scheme for the particle-field equations in multiple dimensions. The algorithm conserves energy, charge, and canonical-momentum exactly, even with grid packing. A simple fluid preconditioner allows efficient use of large timesteps, O (√{mi/me}c/veT) larger than the explicit CFL. We demonstrate the accuracy and efficiency properties of the of the algorithm with various numerical experiments in 2D3V.

Irreducible Representations of Oscillatory and Swirling Flows in Active Soft Matter

NASA Astrophysics Data System (ADS)

Ghose, Somdeb; Adhikari, R.

2014-03-01

Recent experiments imaging fluid flow around swimming microorganisms have revealed complex time-dependent velocity fields that differ qualitatively from the stresslet flow commonly employed in theoretical descriptions of active matter. Here we obtain the most general flow around a finite sized active particle by expanding the surface stress in irreducible Cartesian tensors. This expansion, whose first term is the stresslet, must include, respectively, third-rank polar and axial tensors to minimally capture crucial features of the active oscillatory flow around translating Chlamydomonas and the active swirling flow around rotating Volvox. The representation provides explicit expressions for the irreducible symmetric, antisymmetric, and isotropic parts of the continuum active stress. Antisymmetric active stresses do not conserve orbital angular momentum and our work thus shows that spin angular momentum is necessary to restore angular momentum conservation in continuum hydrodynamic descriptions of active soft matter.

Calculation of flow about two-dimensional bodies by means of the velocity-vorticity formulation on a staggered grid

NASA Technical Reports Server (NTRS)

Stremel, Paul M.

1991-01-01

A method for calculating the incompressible viscous flow about two-dimensional bodies, utilizing the velocity-vorticity form of the Navier-Stokes equations using a staggered-grid formulation is presented. The solution is obtained by employing an alternative-direction implicit method for the solution of the block tridiagonal matrix resulting from the finite-difference representation of the governing equations. The boundary vorticity and the conservation of mass are calculated implicitly as a part of the solution. The mass conservation is calculated to machine zero for the duration of the computation. Calculations for the flow about a circular cylinder, a 2-pct thick flat plate at 90-deg incidence, an elliptic cylinder at 45-deg incidence, and a NACA 0012, with and without a deflected flap, at - 90-deg incidence are performed and compared with the results of other numerical investigations.

The development of flux-split algorithms for flows with non-equilibrium thermodynamics and chemical reactions

NASA Technical Reports Server (NTRS)

Grossman, B.; Cinella, P.

1988-01-01

A finite-volume method for the numerical computation of flows with nonequilibrium thermodynamics and chemistry is presented. A thermodynamic model is described which simplifies the coupling between the chemistry and thermodynamics and also results in the retention of the homogeneity property of the Euler equations (including all the species continuity and vibrational energy conservation equations). Flux-splitting procedures are developed for the fully coupled equations involving fluid dynamics, chemical production and thermodynamic relaxation processes. New forms of flux-vector split and flux-difference split algorithms are embodied in a fully coupled, implicit, large-block structure, including all the species conservation and energy production equations. Several numerical examples are presented, including high-temperature shock tube and nozzle flows. The methodology is compared to other existing techniques, including spectral and central-differenced procedures, and favorable comparisons are shown regarding accuracy, shock-capturing and convergence rates.

Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

1997-01-01

In these lecture notes we describe the construction, analysis, and application of ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes for hyperbolic conservation laws and related Hamilton- Jacobi equations. ENO and WENO schemes are high order accurate finite difference schemes designed for problems with piecewise smooth solutions containing discontinuities. The key idea lies at the approximation level, where a nonlinear adaptive procedure is used to automatically choose the locally smoothest stencil, hence avoiding crossing discontinuities in the interpolation procedure as much as possible. ENO and WENO schemes have been quite successful in applications, especially for problems containing both shocks and complicated smooth solution structures, such as compressible turbulence simulations and aeroacoustics. These lecture notes are basically self-contained. It is our hope that with these notes and with the help of the quoted references, the reader can understand the algorithms and code them up for applications.

Fourth-Order Conservative Vlasov-Maxwell Solver for Cartesian and Cylindrical Phase Space Coordinates

NASA Astrophysics Data System (ADS)

Vogman, Genia

Plasmas are made up of charged particles whose short-range and long-range interactions give rise to complex behavior that can be difficult to fully characterize experimentally. One of the most complete theoretical descriptions of a plasma is that of kinetic theory, which treats each particle species as a probability distribution function in a six-dimensional position-velocity phase space. Drawing on statistical mechanics, these distribution functions mathematically represent a system of interacting particles without tracking individual ions and electrons. The evolution of the distribution function(s) is governed by the Boltzmann equation coupled to Maxwell's equations, which together describe the dynamics of the plasma and the associated electromagnetic fields. When collisions can be neglected, the Boltzmann equation is reduced to the Vlasov equation. High-fidelity simulation of the rich physics in even a subset of the full six-dimensional phase space calls for low-noise high-accuracy numerical methods. To that end, this dissertation investigates a fourth-order finite-volume discretization of the Vlasov-Maxwell equation system, and addresses some of the fundamental challenges associated with applying these types of computationally intensive enhanced-accuracy numerical methods to phase space simulations. The governing equations of kinetic theory are described in detail, and their conservation-law weak form is derived for Cartesian and cylindrical phase space coordinates. This formulation is well known when it comes to Cartesian geometries, as it is used in finite-volume and finite-element discretizations to guarantee local conservation for numerical solutions. By contrast, the conservation-law weak form of the Vlasov equation in cylindrical phase space coordinates is largely unexplored, and to the author's knowledge has never previously been solved numerically. Thereby the methods described in this dissertation for simulating plasmas in cylindrical phase space coordinates present a new development in the field of computational plasma physics. A fourth-order finite-volume method for solving the Vlasov-Maxwell equation system is presented first for Cartesian and then for cylindrical phase space coordinates. Special attention is given to the treatment of the discrete primary variables and to the quadrature rule for evaluating the surface and line integrals that appear in the governing equations. The finite-volume treatment of conducting wall and axis boundaries is particularly nuanced when it comes to phase space coordinates, and is described in detail. In addition to the mechanics of each part of the finite-volume discretization in the two different coordinate systems, the complete algorithm is also presented. The Cartesian coordinate discretization is applied to several well-known test problems. Since even linear analysis of kinetic theory governing equations is complicated on account of velocity being an independent coordinate, few analytic or semi-analytic predictions exist. Benchmarks are particularly scarce for configurations that have magnetic fields and involve more than two phase space dimensions. Ensuring that simulations are true to the physics thus presents a difficulty in the development of robust numerical methods. The research described in this dissertation addresses this challenge through the development of more complete physics-based benchmarks based on the Dory-Guest-Harris instability. The instability is a special case of perpendicularly-propagating kinetic electrostatic waves in a warm uniformly magnetized plasma. A complete derivation of the closed-form linear theory dispersion relation for the instability is presented. The electric field growth rates and oscillation frequencies specified by the dispersion relation provide concrete measures against which simulation results can be quantitatively compared. Furthermore, a specialized form of perturbation is shown to strongly excite the fastest growing mode. The fourth-order finite-volume algorithm is benchmarked against the instability, and is demonstrated to have good convergence properties and close agreement with theoretical growth rate and oscillation frequency predictions. The Dory-Guest-Harris instability benchmark extends the scope of standard test problems by providing a substantive means of validating continuum kinetic simulations of warm magnetized plasmas in higher-dimensional 3D ( x,vx,vy) phase space. The linear theory analysis, initial conditions, algorithm description, and comparisons between theoretical predictions and simulation results are presented. The cylindrical coordinate finite-volume discretization is applied to model axisymmetric systems. Since mitigating the prohibitive computational cost of simulating six dimensions is another challenge in phase space simulations, the development of a robust means of exploiting symmetry is a major advance when it comes to numerically solving the Vlasov-Maxwell equation system. The discretization is applied to a uniform distribution function to assess the nature of the singularity at the axis, and is demonstrated to converge at fourth-order accuracy. The numerical method is then applied to simulate electrostatic ion confinement in an axisymmetric Z-pinch configuration. To the author's knowledge this presents the first instance of a conservative finite-volume discretization of the cylindrical coordinate Vlasov equation. The computational framework for the Vlasov-Maxwell solver is described, and an outlook for future research is presented.

The Relation of Finite Element and Finite Difference Methods

NASA Technical Reports Server (NTRS)

Vinokur, M.

1976-01-01

Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.

On mass and momentum conservation in the variable-parameter Muskingum method

NASA Astrophysics Data System (ADS)

Reggiani, Paolo; Todini, Ezio; Meißner, Dennis

2016-12-01

In this paper we investigate mass and momentum conservation in one-dimensional routing models. To this end we formulate the conservation equations for a finite-dimensional reach and compute individual terms using three standard Saint-Venant (SV) solvers: SOBEK, HEC-RAS and MIKE11. We also employ two different variable-parameter Muskingum (VPM) formulations: the classical Muskingum-Cunge (MC) and the revised, mass-conservative Muskingum-Cunge-Todini (MCT) approach, whereby geometrical cross sections are treated analytically in both cases. We initially compare the three SV solvers for a straight mild-sloping prismatic channel with geometric cross sections and a synthetic hydrograph as boundary conditions against the analytical MC and MCT solutions. The comparison is substantiated by the fact that in this flow regime the conditions for the parabolic equation model solved by MC and MCT are met. Through this intercomparison we show that all approaches have comparable mass and momentum conservation properties, except the MC. Then we extend the MCT to use natural cross sections for a real irregular river channel forced by an observed triple-peak event and compare the results with SOBEK. The model intercomparison demonstrates that the VPM in the form of MCT can be a computationally efficient, fully mass and momentum conservative approach and therefore constitutes a valid alternative to Saint-Venant based flood wave routing for a wide variety of rivers and channels in the world when downstream boundary conditions or hydraulic structures are non-influential.

Pinching solutions of slender cylindrical jets

NASA Technical Reports Server (NTRS)

Papageorgiou, Demetrios T.; Orellana, Oscar

1993-01-01

Simplified equations for slender jets are derived for a circular jet of one fluid flowing into an ambient second fluid, the flow being confined in a circular tank. Inviscid flows are studied which include both surface tension effects and Kelvin-Helmholtz instability. For slender jets a coupled nonlinear system of equations is found for the jet shape and the axial velocity jump across it. The equations can break down after a finite time and similarity solutions are constructed, and studied analytically and numerically. The break-ups found pertain to the jet pinching after a finite time, without violation of the slender jet ansatz. The system is conservative and admissible singular solutions are those which conserve the total energy, mass, and momentum. Such solutions are constructed analytically and numerically, and in the case of vortex sheets with no surface tension certain solutions are given in closed form.

Science and society test VI: Energy economics

NASA Astrophysics Data System (ADS)

Hafemeister, David W.

1982-01-01

Simple numerical estimates are developed in order to quantify a variety of energy economics issues. The Verhulst equation, which considers the effect of finite resources on petroleum production, is modified to take into account supply and demand economics. Numerical and analytical solutions to these differential equations are presented in terms of supply and demand elasticity functions, various finite resources, and the rate of increase in fuel costs. The indirect cost per barrel of imported oil from OPEC is shown to be about the same as the direct cost. These effects, as well as those of discounted benefits and deregulation, are used in a calculation of payback periods for various energy conserving devices. A phenomenological model for market penetration is developed along with the factors for future energy growth rates. A brief analysis of the economic returns of the ''house doctor'' program to reprofit houses for energy conservation is presented.

A Runge-Kutta discontinuous finite element method for high speed flows

NASA Technical Reports Server (NTRS)

Bey, Kim S.; Oden, J. T.

1991-01-01

A Runge-Kutta discontinuous finite element method is developed for hyperbolic systems of conservation laws in two space variables. The discontinuous Galerkin spatial approximation to the conservation laws results in a system of ordinary differential equations which are marched in time using Runge-Kutta methods. Numerical results for the two-dimensional Burger's equation show that the method is (p+1)-order accurate in time and space, where p is the degree of the polynomial approximation of the solution within an element and is capable of capturing shocks over a single element without oscillations. Results for this problem also show that the accuracy of the solution in smooth regions is unaffected by the local projection and that the accuracy in smooth regions increases as p increases. Numerical results for the Euler equations show that the method captures shocks without oscillations and with higher resolution than a first-order scheme.

Influence of the Numerical Scheme on the Solution Quality of the SWE for Tsunami Numerical Codes: The Tohoku-Oki, 2011Example.

NASA Astrophysics Data System (ADS)

Reis, C.; Clain, S.; Figueiredo, J.; Baptista, M. A.; Miranda, J. M. A.

2015-12-01

Numerical tools turn to be very important for scenario evaluations of hazardous phenomena such as tsunami. Nevertheless, the predictions highly depends on the numerical tool quality and the design of efficient numerical schemes still receives important attention to provide robust and accurate solutions. In this study we propose a comparative study between the efficiency of two volume finite numerical codes with second-order discretization implemented with different method to solve the non-conservative shallow water equations, the MUSCL (Monotonic Upstream-Centered Scheme for Conservation Laws) and the MOOD methods (Multi-dimensional Optimal Order Detection) which optimize the accuracy of the approximation in function of the solution local smoothness. The MUSCL is based on a priori criteria where the limiting procedure is performed before updated the solution to the next time-step leading to non-necessary accuracy reduction. On the contrary, the new MOOD technique uses a posteriori detectors to prevent the solution from oscillating in the vicinity of the discontinuities. Indeed, a candidate solution is computed and corrections are performed only for the cells where non-physical oscillations are detected. Using a simple one-dimensional analytical benchmark, 'Single wave on a sloping beach', we show that the classical 1D shallow-water system can be accurately solved with the finite volume method equipped with the MOOD technique and provide better approximation with sharper shock and less numerical diffusion. For the code validation, we also use the Tohoku-Oki 2011 tsunami and reproduce two DART records, demonstrating that the quality of the solution may deeply interfere with the scenario one can assess. This work is funded by the Portugal-France research agreement, through the research project GEONUM FCT-ANR/MAT-NAN/0122/2012.Numerical tools turn to be very important for scenario evaluations of hazardous phenomena such as tsunami. Nevertheless, the predictions highly depends on the numerical tool quality and the design of efficient numerical schemes still receives important attention to provide robust and accurate solutions. In this study we propose a comparative study between the efficiency of two volume finite numerical codes with second-order discretization implemented with different method to solve the non-conservative shallow water equations, the MUSCL (Monotonic Upstream-Centered Scheme for Conservation Laws) and the MOOD methods (Multi-dimensional Optimal Order Detection) which optimize the accuracy of the approximation in function of the solution local smoothness. The MUSCL is based on a priori criteria where the limiting procedure is performed before updated the solution to the next time-step leading to non-necessary accuracy reduction. On the contrary, the new MOOD technique uses a posteriori detectors to prevent the solution from oscillating in the vicinity of the discontinuities. Indeed, a candidate solution is computed and corrections are performed only for the cells where non-physical oscillations are detected. Using a simple one-dimensional analytical benchmark, 'Single wave on a sloping beach', we show that the classical 1D shallow-water system can be accurately solved with the finite volume method equipped with the MOOD technique and provide better approximation with sharper shock and less numerical diffusion. For the code validation, we also use the Tohoku-Oki 2011 tsunami and reproduce two DART records, demonstrating that the quality of the solution may deeply interfere with the scenario one can assess. This work is funded by the Portugal-France research agreement, through the research project GEONUM FCT-ANR/MAT-NAN/0122/2012.

Predicting Long-term Temperature Increase for Time-Dependent SAR Levels with a Single Short-term Temperature Response

PubMed Central

Carluccio, Giuseppe; Bruno, Mary; Collins, Christopher M.

2015-01-01

Purpose Present a novel method for rapid prediction of temperature in vivo for a series of pulse sequences with differing levels and distributions of specific energy absorption rate (SAR). Methods After the temperature response to a brief period of heating is characterized, a rapid estimate of temperature during a series of periods at different heating levels is made using a linear heat equation and Impulse-Response (IR) concepts. Here the initial characterization and long-term prediction for a complete spine exam are made with the Pennes’ bioheat equation where, at first, core body temperature is allowed to increase and local perfusion is not. Then corrections through time allowing variation in local perfusion are introduced. Results The fast IR-based method predicted maximum temperature increase within 1% of that with a full finite difference simulation, but required less than 3.5% of the computation time. Even higher accelerations are possible depending on the time step size chosen, with loss in temporal resolution. Correction for temperature-dependent perfusion requires negligible additional time, and can be adjusted to be more or less conservative than the corresponding finite difference simulation. Conclusion With appropriate methods, it is possible to rapidly predict temperature increase throughout the body for actual MR examinations. (200/200 words) PMID:26096947

Predicting long-term temperature increase for time-dependent SAR levels with a single short-term temperature response.

PubMed

Carluccio, Giuseppe; Bruno, Mary; Collins, Christopher M

2016-05-01

Present a novel method for rapid prediction of temperature in vivo for a series of pulse sequences with differing levels and distributions of specific energy absorption rate (SAR). After the temperature response to a brief period of heating is characterized, a rapid estimate of temperature during a series of periods at different heating levels is made using a linear heat equation and impulse-response (IR) concepts. Here the initial characterization and long-term prediction for a complete spine exam are made with the Pennes' bioheat equation where, at first, core body temperature is allowed to increase and local perfusion is not. Then corrections through time allowing variation in local perfusion are introduced. The fast IR-based method predicted maximum temperature increase within 1% of that with a full finite difference simulation, but required less than 3.5% of the computation time. Even higher accelerations are possible depending on the time step size chosen, with loss in temporal resolution. Correction for temperature-dependent perfusion requires negligible additional time and can be adjusted to be more or less conservative than the corresponding finite difference simulation. With appropriate methods, it is possible to rapidly predict temperature increase throughout the body for actual MR examinations. © 2015 Wiley Periodicals, Inc.

A model of transverse fuel injection applied to the computation of supersonic combustor flow

NASA Technical Reports Server (NTRS)

Rogers, R. C.

1979-01-01

A two-dimensional, nonreacting flow model of the aerodynamic interaction of a transverse hydrogen jet within a supersonic mainstream has been developed. The model assumes profile shapes of mass flux, pressure, flow angle, and hydrogen concentration and produces downstream profiles of the other flow parameters under the constraints of the integrated conservation equations. These profiles are used as starting conditions for an existing finite difference parabolic computer code for the turbulent supersonic combustion of hydrogen. Integrated mixing and flow profile results obtained from the computer code compare favorably with existing data for the supersonic combustion of hydrogen.

Well-balanced Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming meshes for the Euler equations of gas dynamics with gravity

NASA Astrophysics Data System (ADS)

Gaburro, Elena; Castro, Manuel J.; Dumbser, Michael

2018-06-01

In this work, we present a novel second-order accurate well-balanced arbitrary Lagrangian-Eulerian (ALE) finite volume scheme on moving nonconforming meshes for the Euler equations of compressible gas dynamics with gravity in cylindrical coordinates. The main feature of the proposed algorithm is the capability of preserving many of the physical properties of the system exactly also on the discrete level: besides being conservative for mass, momentum and total energy, also any known steady equilibrium between pressure gradient, centrifugal force, and gravity force can be exactly maintained up to machine precision. Perturbations around such equilibrium solutions are resolved with high accuracy and with minimal dissipation on moving contact discontinuities even for very long computational times. This is achieved by the novel combination of well-balanced path-conservative finite volume schemes, which are expressly designed to deal with source terms written via non-conservative products, with ALE schemes on moving grids, which exhibit only very little numerical dissipation on moving contact waves. In particular, we have formulated a new HLL-type and a novel Osher-type flux that are both able to guarantee the well balancing in a gas cloud rotating around a central object. Moreover, to maintain a high level of quality of the moving mesh, we have adopted a nonconforming treatment of the sliding interfaces that appear due to the differential rotation. A large set of numerical tests has been carried out in order to check the accuracy of the method close and far away from the equilibrium, both, in one- and two-space dimensions.

Modelling the oscillations of the thermocline in a lake by means of a fully consistent and conservative 3D finite-element model with a vertically adaptive mesh

NASA Astrophysics Data System (ADS)

Delandmeter, Philippe; Lambrechts, Jonathan; Vallaeys, Valentin; Naithani, Jaya; Remacle, Jean-François; Legat, Vincent; Deleersnijder, Eric

2017-04-01

Vertical discretisation is crucial in the modelling of lake thermocline oscillations. For finite element methods, a simple way to increase the resolution close to the oscillating thermocline is to use vertical adaptive coordinates. With an Arbitrary Lagrangian-Eulerian (ALE) formulation, the mesh can be adapted to increase the resolution in regions with strong shear or stratification. In such an application, consistency and conservativity must be strictly enforced. SLIM 3D, a discontinuous-Galerkin finite element model for shallow-water flows (www.climate.be/slim, e.g. Kärnä et al., 2013, Delandmeter et al., 2015), was designed to be strictly consistent and conservative in its discrete formulation. In this context, special care must be paid to the coupling of the external and internal modes of the model and the moving mesh algorithm. In this framework, the mesh can be adapted arbitrarily in the vertical direction. Two moving mesh algorithms were implemented: the first one computes an a-priori optimal mesh; the second one diffuses vertically the mesh (Burchard et al., 2004, Hofmeister et al., 2010). The criteria used to define the optimal mesh and the diffusion function are related to a suitable measure of shear and stratification. We will present in detail the design of the model and how the consistency and conservativity is obtained. Then we will apply it to both idealised benchmarks and the wind-forced thermocline oscillations in Lake Tanganyika (Naithani et al. 2002). References Tuomas Kärnä, Vincent Legat and Eric Deleersnijder. A baroclinic discontinuous Galerkin finite element model for coastal flows, Ocean Modelling, 61:1-20, 2013. Philippe Delandmeter, Stephen E Lewis, Jonathan Lambrechts, Eric Deleersnijder, Vincent Legat and Eric Wolanski. The transport and fate of riverine fine sediment exported to a semi-open system. Estuarine, Coastal and Shelf Science, 167:336-346, 2015. Hans Burchard and Jean-Marie Beckers. Non-uniform adaptive vertical grids in one-dimensional numerical ocean models. Ocean Modelling, 6:51-81, 2004. Richard Hofmeister, Hans Burchard and Jean-Marie Beckers. Non-uniform adaptive vertical grids for 3d numerical ocean models. Ocean Modelling, 33:70-86, 2010. Jaya Naithani, Eric Deleersnijder and Pierre-Denis Plisnier. Origin of intraseasonal variability in Lake Tanganyika. Geophysical Research Letters, 29(23), doi:10.1029/2002GL015843, 2002.

Multidimensional, fully implicit, exactly conserving electromagnetic particle-in-cell simulations

NASA Astrophysics Data System (ADS)

Chacon, Luis

2015-09-01

We discuss a new, conservative, fully implicit 2D-3V particle-in-cell algorithm for non-radiative, electromagnetic kinetic plasma simulations, based on the Vlasov-Darwin model. Unlike earlier linearly implicit PIC schemes and standard explicit PIC schemes, fully implicit PIC algorithms are unconditionally stable and allow exact discrete energy and charge conservation. This has been demonstrated in 1D electrostatic and electromagnetic contexts. In this study, we build on these recent algorithms to develop an implicit, orbit-averaged, time-space-centered finite difference scheme for the Darwin field and particle orbit equations for multiple species in multiple dimensions. The Vlasov-Darwin model is very attractive for PIC simulations because it avoids radiative noise issues in non-radiative electromagnetic regimes. The algorithm conserves global energy, local charge, and particle canonical-momentum exactly, even with grid packing. The nonlinear iteration is effectively accelerated with a fluid preconditioner, which allows efficient use of large timesteps, O(√{mi/me}c/veT) larger than the explicit CFL. In this presentation, we will introduce the main algorithmic components of the approach, and demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 1D and 2D. Support from the LANL LDRD program and the DOE-SC ASCR office.

Effects of Nonequilibrium Chemistry and Darcy-Forchheimer Pyrolysis Flow for Charring Ablator

NASA Technical Reports Server (NTRS)

Chen, Yih-Kanq; Milos, Frank S.

2013-01-01

The fully implicit ablation and thermal response code simulates pyrolysis and ablation of thermal protection materials and systems. The governing equations, which include energy conservation, a three-component decomposition model, and a surface energy balance, are solved with a moving grid.This work describes new modeling capabilities that are added to a special version of code. These capabilities include a time-dependent pyrolysis gas flow momentum equation with Darcy-Forchheimer terms and pyrolysis gas species conservation equations with finite rate homogeneous chemical reactions. The total energy conservation equation is also enhanced for consistency with these new additions. Two groups of parametric studies of the phenolic impregnated carbon ablator are performed. In the first group, an Orion flight environment for a proposed lunar-return trajectory is considered. In the second group, various test conditions for arcjet models are examined. The central focus of these parametric studies is to understand the effect of pyrolysis gas momentum transfer on material in-depth thermal responses with finite-rate, equilibrium, or frozen homogeneous gas chemistry. Results indicate that the presence of chemical nonequilibrium pyrolysis gas flow does not significantly alter the in-depth thermal response performance predicted using the chemical equilibrium gas model.

Progress with the COGENT Edge Kinetic Code: Implementing the Fokker-Plank Collision Operator

DOE PAGES

Dorf, M. A.; Cohen, R. H.; Dorr, M.; ...

2014-06-20

Here, COGENT is a continuum gyrokinetic code for edge plasma simulations being developed by the Edge Simulation Laboratory collaboration. The code is distinguished by application of a fourth-order finite-volume (conservative) discretization, and mapped multiblock grid technology to handle the geometric complexity of the tokamak edge. The distribution function F is discretized in v∥ – μ (parallel velocity – magnetic moment) velocity coordinates, and the code presently solves an axisymmetric full-f gyro-kinetic equation coupled to the long-wavelength limit of the gyro-Poisson equation. COGENT capabilities are extended by implementing the fully nonlinear Fokker-Plank operator to model Coulomb collisions in magnetized edge plasmas.more » The corresponding Rosenbluth potentials are computed by making use of a finite-difference scheme and multipole-expansion boundary conditions. Details of the numerical algorithms and results of the initial verification studies are discussed. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)« less

Setting conservation priorities.

PubMed

Wilson, Kerrie A; Carwardine, Josie; Possingham, Hugh P

2009-04-01

A generic framework for setting conservation priorities based on the principles of classic decision theory is provided. This framework encapsulates the key elements of any problem, including the objective, the constraints, and knowledge of the system. Within the context of this framework the broad array of approaches for setting conservation priorities are reviewed. While some approaches prioritize assets or locations for conservation investment, it is concluded here that prioritization is incomplete without consideration of the conservation actions required to conserve the assets at particular locations. The challenges associated with prioritizing investments through time in the face of threats (and also spatially and temporally heterogeneous costs) can be aided by proper problem definition. Using the authors' general framework for setting conservation priorities, multiple criteria can be rationally integrated and where, how, and when to invest conservation resources can be scheduled. Trade-offs are unavoidable in priority setting when there are multiple considerations, and budgets are almost always finite. The authors discuss how trade-offs, risks, uncertainty, feedbacks, and learning can be explicitly evaluated within their generic framework for setting conservation priorities. Finally, they suggest ways that current priority-setting approaches may be improved.

Verification of Orthogrid Finite Element Modeling Techniques

NASA Technical Reports Server (NTRS)

Steeve, B. E.

1996-01-01

The stress analysis of orthogrid structures, specifically with I-beam sections, is regularly performed using finite elements. Various modeling techniques are often used to simplify the modeling process but still adequately capture the actual hardware behavior. The accuracy of such 'Oshort cutso' is sometimes in question. This report compares three modeling techniques to actual test results from a loaded orthogrid panel. The finite element models include a beam, shell, and mixed beam and shell element model. Results show that the shell element model performs the best, but that the simpler beam and beam and shell element models provide reasonable to conservative results for a stress analysis. When deflection and stiffness is critical, it is important to capture the effect of the orthogrid nodes in the model.

Electro-kinetically driven peristaltic transport of viscoelastic physiological fluids through a finite length capillary: Mathematical modeling.

PubMed

Tripathi, Dharmendra; Yadav, Ashu; Bég, O Anwar

2017-01-01

Analytical solutions are developed for the electro-kinetic flow of a viscoelastic biological liquid in a finite length cylindrical capillary geometry under peristaltic waves. The Jefferys' non-Newtonian constitutive model is employed to characterize rheological properties of the fluid. The unsteady conservation equations for mass and momentum with electro-kinetic and Darcian porous medium drag force terms are reduced to a system of steady linearized conservation equations in an axisymmetric coordinate system. The long wavelength, creeping (low Reynolds number) and Debye-Hückel linearization approximations are utilized. The resulting boundary value problem is shown to be controlled by a number of parameters including the electro-osmotic parameter, Helmholtz-Smoluchowski velocity (maximum electro-osmotic velocity), and Jefferys' first parameter (ratio of relaxation and retardation time), wave amplitude. The influence of these parameters and also time on axial velocity, pressure difference, maximum volumetric flow rate and streamline distributions (for elucidating trapping phenomena) is visualized graphically and interpreted in detail. Pressure difference magnitudes are enhanced consistently with both increasing electro-osmotic parameter and Helmholtz-Smoluchowski velocity, whereas they are only elevated with increasing Jefferys' first parameter for positive volumetric flow rates. Maximum time averaged flow rate is enhanced with increasing electro-osmotic parameter, Helmholtz-Smoluchowski velocity and Jefferys' first parameter. Axial flow is accelerated in the core (plug) region of the conduit with greater values of electro-osmotic parameter and Helmholtz-Smoluchowski velocity whereas it is significantly decelerated with increasing Jefferys' first parameter. The simulations find applications in electro-osmotic (EO) transport processes in capillary physiology and also bio-inspired EO pump devices in chemical and aerospace engineering. Copyright © 2016 Elsevier Inc. All rights reserved.

A high-order vertex-based central ENO finite-volume scheme for three-dimensional compressible flows

DOE PAGES

Charest, Marc R.J.; Canfield, Thomas R.; Morgan, Nathaniel R.; ...

2015-03-11

High-order discretization methods offer the potential to reduce the computational cost associated with modeling compressible flows. However, it is difficult to obtain accurate high-order discretizations of conservation laws that do not produce spurious oscillations near discontinuities, especially on multi-dimensional unstructured meshes. A novel, high-order, central essentially non-oscillatory (CENO) finite-volume method that does not have these difficulties is proposed for tetrahedral meshes. The proposed unstructured method is vertex-based, which differs from existing cell-based CENO formulations, and uses a hybrid reconstruction procedure that switches between two different solution representations. It applies a high-order k-exact reconstruction in smooth regions and a limited linearmore » reconstruction when discontinuities are encountered. Both reconstructions use a single, central stencil for all variables, making the application of CENO to arbitrary unstructured meshes relatively straightforward. The new approach was applied to the conservation equations governing compressible flows and assessed in terms of accuracy and computational cost. For all problems considered, which included various function reconstructions and idealized flows, CENO demonstrated excellent reliability and robustness. Up to fifth-order accuracy was achieved in smooth regions and essentially non-oscillatory solutions were obtained near discontinuities. The high-order schemes were also more computationally efficient for high-accuracy solutions, i.e., they took less wall time than the lower-order schemes to achieve a desired level of error. In one particular case, it took a factor of 24 less wall-time to obtain a given level of error with the fourth-order CENO scheme than to obtain the same error with the second-order scheme.« less

Numerical computation of transonic flows by finite-element and finite-difference methods

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Wellford, L. C.; Merkle, C. L.; Murman, E. M.

1978-01-01

Studies on applications of the finite element approach to transonic flow calculations are reported. Different discretization techniques of the differential equations and boundary conditions are compared. Finite element analogs of Murman's mixed type finite difference operators for small disturbance formulations were constructed and the time dependent approach (using finite differences in time and finite elements in space) was examined.

A priori error estimates for an hp-version of the discontinuous Galerkin method for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Bey, Kim S.; Oden, J. Tinsley

1993-01-01

A priori error estimates are derived for hp-versions of the finite element method for discontinuous Galerkin approximations of a model class of linear, scalar, first-order hyperbolic conservation laws. These estimates are derived in a mesh dependent norm in which the coefficients depend upon both the local mesh size h(sub K) and a number p(sub k) which can be identified with the spectral order of the local approximations over each element.

Research in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Murman, Earll M.

1987-01-01

The numerical integration of quasi-one-dimensional unsteady flow problems which involve finite rate chemistry are discussed, and are expressed in terms of conservative form Euler and species conservation equations. Hypersonic viscous calculations for delta wing geometries is also examined. The conical Navier-Stokes equations model was selected in order to investigate the effects of viscous-inviscid interations. The more complete three-dimensional model is beyond the available computing resources. The flux vector splitting method with van Leer's MUSCL differencing is being used. Preliminary results were computed for several conditions.

Full-thickness tears of the supraspinatus tendon: A three-dimensional finite element analysis.

PubMed

Quental, C; Folgado, J; Monteiro, J; Sarmento, M

2016-12-08

Knowledge regarding the likelihood of propagation of supraspinatus tears is important to allow an early identification of patients for whom a conservative treatment is more likely to fail, and consequently, to improve their clinical outcome. The aim of this study was to investigate the potential for propagation of posterior, central, and anterior full-thickness tears of different sizes using the finite element method. A three-dimensional finite element model of the supraspinatus tendon was generated from the Visible Human Project data. The mechanical behaviour of the tendon was fitted from experimental data using a transversely isotropic hyperelastic constitutive model. The full-thickness tears were simulated at the supraspinatus tendon insertion by decreasing the interface area. Tear sizes from 10% to 90%, in 10% increments, of the anteroposterior length of the supraspinatus footprint were considered in the posterior, central, and anterior regions of the tendon. For each tear, three finite element analyses were performed for a supraspinatus force of 100N, 200N, and 400N. Considering a correlation between tendon strain and the risk of tear propagation, the simulated tears were compared qualitatively and quantitatively by evaluating the volume of tendon for which a maximum strain criterion was not satisfied. The finite element analyses showed a significant impact of tear size and location not only on the magnitude, but also on the patterns of the maximum principal strains. The mechanical outcome of the anterior full-thickness tears was consistently, and significantly, more severe than that of the central or posterior full-thickness tears, which suggests that the anterior tears are at greater risk of propagating than the central or posterior tears. Copyright © 2016 Elsevier Ltd. All rights reserved.

Dual-scale Galerkin methods for Darcy flow

NASA Astrophysics Data System (ADS)

Wang, Guoyin; Scovazzi, Guglielmo; Nouveau, Léo; Kees, Christopher E.; Rossi, Simone; Colomés, Oriol; Main, Alex

2018-02-01

The discontinuous Galerkin (DG) method has found widespread application in elliptic problems with rough coefficients, of which the Darcy flow equations are a prototypical example. One of the long-standing issues of DG approximations is the overall computational cost, and many different strategies have been proposed, such as the variational multiscale DG method, the hybridizable DG method, the multiscale DG method, the embedded DG method, and the Enriched Galerkin method. In this work, we propose a mixed dual-scale Galerkin method, in which the degrees-of-freedom of a less computationally expensive coarse-scale approximation are linked to the degrees-of-freedom of a base DG approximation. We show that the proposed approach has always similar or improved accuracy with respect to the base DG method, with a considerable reduction in computational cost. For the specific definition of the coarse-scale space, we consider Raviart-Thomas finite elements for the mass flux and piecewise-linear continuous finite elements for the pressure. We provide a complete analysis of stability and convergence of the proposed method, in addition to a study on its conservation and consistency properties. We also present a battery of numerical tests to verify the results of the analysis, and evaluate a number of possible variations, such as using piecewise-linear continuous finite elements for the coarse-scale mass fluxes.

Thermoelastic response of metal matrix composites with large-diameter fibers subjected to thermal gradients

NASA Technical Reports Server (NTRS)

Aboudi, Jacob; Pindera, Marek-Jerzy; Arnold, Steven M.

1993-01-01

A new micromechanical theory is presented for the response of heterogeneous metal matrix composites subjected to thermal gradients. In contrast to existing micromechanical theories that utilize classical homogenization schemes in the course of calculating microscopic and macroscopic field quantities, in the present approach the actual microstructural details are explicitly coupled with the macrostructure of the composite. Examples are offered that illustrate limitations of the classical homogenization approach in predicting the response of thin-walled metal matrix composites with large-diameter fibers when subjected to thermal gradients. These examples include composites with a finite number of fibers in the thickness direction that may be uniformly or nonuniformly spaced, thus admitting so-called functionally gradient composites. The results illustrate that the classical approach of decoupling micromechanical and macromechanical analyses in the presence of a finite number of large-diameter fibers, finite dimensions of the composite, and temperature gradient may produce excessively conservative estimates for macroscopic field quantities, while both underestimating and overestimating the local fluctuations of the microscopic quantities in different regions of the composite. Also demonstrated is the usefulness of the present approach in generating favorable stress distributions in the presence of thermal gradients by appropriately tailoring the internal microstructure details of the composite.

Long-term dynamic modeling of tethered spacecraft using nodal position finite element method and symplectic integration

NASA Astrophysics Data System (ADS)

Li, G. Q.; Zhu, Z. H.

2015-12-01

Dynamic modeling of tethered spacecraft with the consideration of elasticity of tether is prone to the numerical instability and error accumulation over long-term numerical integration. This paper addresses the challenges by proposing a globally stable numerical approach with the nodal position finite element method (NPFEM) and the implicit, symplectic, 2-stage and 4th order Gaussian-Legendre Runge-Kutta time integration. The NPFEM eliminates the numerical error accumulation by using the position instead of displacement of tether as the state variable, while the symplectic integration enforces the energy and momentum conservation of the discretized finite element model to ensure the global stability of numerical solution. The effectiveness and robustness of the proposed approach is assessed by an elastic pendulum problem, whose dynamic response resembles that of tethered spacecraft, in comparison with the commonly used time integrators such as the classical 4th order Runge-Kutta schemes and other families of non-symplectic Runge-Kutta schemes. Numerical results show that the proposed approach is accurate and the energy of the corresponding numerical model is conservative over the long-term numerical integration. Finally, the proposed approach is applied to the dynamic modeling of deorbiting process of tethered spacecraft over a long period.

High-order conservative finite difference GLM-MHD schemes for cell-centered MHD

NASA Astrophysics Data System (ADS)

Mignone, Andrea; Tzeferacos, Petros; Bodo, Gianluigi

2010-08-01

We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different reconstruction techniques based on recently improved versions of the weighted essentially non-oscillatory (WENO) schemes, monotonicity preserving (MP) schemes as well as slope-limited polynomial reconstruction. The proposed numerical methods are highly accurate in smooth regions of the flow, avoid loss of accuracy in proximity of smooth extrema and provide sharp non-oscillatory transitions at discontinuities. We suggest a numerical formulation based on a cell-centered approach where all of the primary flow variables are discretized at the zone center. The divergence-free condition is enforced by augmenting the MHD equations with a generalized Lagrange multiplier yielding a mixed hyperbolic/parabolic correction, as in Dedner et al. [J. Comput. Phys. 175 (2002) 645-673]. The resulting family of schemes is robust, cost-effective and straightforward to implement. Compared to previous existing approaches, it completely avoids the CPU intensive workload associated with an elliptic divergence cleaning step and the additional complexities required by staggered mesh algorithms. Extensive numerical testing demonstrate the robustness and reliability of the proposed framework for computations involving both smooth and discontinuous features.

Simulations of viscous and compressible gas-gas flows using high-order finite difference schemes

NASA Astrophysics Data System (ADS)

Capuano, M.; Bogey, C.; Spelt, P. D. M.

2018-05-01

A computational method for the simulation of viscous and compressible gas-gas flows is presented. It consists in solving the Navier-Stokes equations associated with a convection equation governing the motion of the interface between two gases using high-order finite-difference schemes. A discontinuity-capturing methodology based on sensors and a spatial filter enables capturing shock waves and deformable interfaces. One-dimensional test cases are performed as validation and to justify choices in the numerical method. The results compare well with analytical solutions. Shock waves and interfaces are accurately propagated, and remain sharp. Subsequently, two-dimensional flows are considered including viscosity and thermal conductivity. In Richtmyer-Meshkov instability, generated on an air-SF6 interface, the influence of the mesh refinement on the instability shape is studied, and the temporal variations of the instability amplitude is compared with experimental data. Finally, for a plane shock wave propagating in air and impacting a cylindrical bubble filled with helium or R22, numerical Schlieren pictures obtained using different grid refinements are found to compare well with experimental shadow-photographs. The mass conservation is verified from the temporal variations of the mass of the bubble. The mean velocities of pressure waves and bubble interface are similar to those obtained experimentally.

An Implicit Characteristic Based Method for Electromagnetics

NASA Technical Reports Server (NTRS)

Beggs, John H.; Briley, W. Roger

2001-01-01

An implicit characteristic-based approach for numerical solution of Maxwell's time-dependent curl equations in flux conservative form is introduced. This method combines a characteristic based finite difference spatial approximation with an implicit lower-upper approximate factorization (LU/AF) time integration scheme. This approach is advantageous for three-dimensional applications because the characteristic differencing enables a two-factor approximate factorization that retains its unconditional stability in three space dimensions, and it does not require solution of tridiagonal systems. Results are given both for a Fourier analysis of stability, damping and dispersion properties, and for one-dimensional model problems involving propagation and scattering for free space and dielectric materials using both uniform and nonuniform grids. The explicit Finite Difference Time Domain Method (FDTD) algorithm is used as a convenient reference algorithm for comparison. The one-dimensional results indicate that for low frequency problems on a highly resolved uniform or nonuniform grid, this LU/AF algorithm can produce accurate solutions at Courant numbers significantly greater than one, with a corresponding improvement in efficiency for simulating a given period of time. This approach appears promising for development of dispersion optimized LU/AF schemes for three dimensional applications.

On the statistical mechanics of the 2D stochastic Euler equation

NASA Astrophysics Data System (ADS)

Bouchet, Freddy; Laurie, Jason; Zaboronski, Oleg

2011-12-01

The dynamics of vortices and large scale structures is qualitatively very different in two dimensional flows compared to its three dimensional counterparts, due to the presence of multiple integrals of motion. These are believed to be responsible for a variety of phenomena observed in Euler flow such as the formation of large scale coherent structures, the existence of meta-stable states and random abrupt changes in the topology of the flow. In this paper we study stochastic dynamics of the finite dimensional approximation of the 2D Euler flow based on Lie algebra su(N) which preserves all integrals of motion. In particular, we exploit rich algebraic structure responsible for the existence of Euler's conservation laws to calculate the invariant measures and explore their properties and also study the approach to equilibrium. Unexpectedly, we find deep connections between equilibrium measures of finite dimensional su(N) truncations of the stochastic Euler equations and random matrix models. Our work can be regarded as a preparation for addressing the questions of large scale structures, meta-stability and the dynamics of random transitions between different flow topologies in stochastic 2D Euler flows.

An efficient flexible-order model for 3D nonlinear water waves

NASA Astrophysics Data System (ADS)

Engsig-Karup, A. P.; Bingham, H. B.; Lindberg, O.

2009-04-01

The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal scaling of the solution effort multigrid is employed to precondition a GMRES iterative solution of the discretized Laplace problem. A robust multigrid method based on Gauss-Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom. A new discretization scheme using one layer of grid points outside the fluid domain is presented and shown to provide convergent solutions over the full physical and discrete parameter space of interest. Linear analysis of the fundamental properties of the scheme with respect to accuracy, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental measurements and other calculations from the literature.

Development of cost-effective surfactant flooding technology. Final report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pope, G.A.; Sepehrnoori, K.

1996-11-01

Task 1 of this research was the development of a high-resolution, fully implicit, finite-difference, multiphase, multicomponent, compositional simulator for chemical flooding. The major physical phenomena modeled in this simulator are dispersion, heterogeneous permeability and porosity, adsorption, interfacial tension, relative permeability and capillary desaturation, compositional phase viscosity, compositional phase density and gravity effects, capillary pressure, and aqueous-oleic-microemulsion phase behavior. Polymer and its non-Newtonian rheology properties include shear-thinning viscosity, permeability reduction, inaccessible pore volume, and adsorption. Options of constant or variable space grids and time steps, constant-pressure or constant-rate well conditions, horizontal and vertical wells, and multiple slug injections are also availablemore » in the simulator. The solution scheme used in this simulator is fully implicit. The pressure equation and the mass-conservation equations are solved simultaneously for the aqueous-phase pressure and the total concentrations of each component. A third-order-in-space, second-order-in-time finite-difference method and a new total-variation-diminishing (TVD) third-order flux limiter are used that greatly reduce numerical dispersion effects. Task 2 was the optimization of surfactant flooding. The code UTCHEM was used to simulate surfactant polymer flooding.« less

An adaptive moving finite volume scheme for modeling flood inundation over dry and complex topography

NASA Astrophysics Data System (ADS)

Zhou, Feng; Chen, Guoxian; Huang, Yuefei; Yang, Jerry Zhijian; Feng, Hui

2013-04-01

A new geometrical conservative interpolation on unstructured meshes is developed for preserving still water equilibrium and positivity of water depth at each iteration of mesh movement, leading to an adaptive moving finite volume (AMFV) scheme for modeling flood inundation over dry and complex topography. Unlike traditional schemes involving position-fixed meshes, the iteration process of the AFMV scheme moves a fewer number of the meshes adaptively in response to flow variables calculated in prior solutions and then simulates their posterior values on the new meshes. At each time step of the simulation, the AMFV scheme consists of three parts: an adaptive mesh movement to shift the vertices position, a geometrical conservative interpolation to remap the flow variables by summing the total mass over old meshes to avoid the generation of spurious waves, and a partial differential equations(PDEs) discretization to update the flow variables for a new time step. Five different test cases are presented to verify the computational advantages of the proposed scheme over nonadaptive methods. The results reveal three attractive features: (i) the AMFV scheme could preserve still water equilibrium and positivity of water depth within both mesh movement and PDE discretization steps; (ii) it improved the shock-capturing capability for handling topographic source terms and wet-dry interfaces by moving triangular meshes to approximate the spatial distribution of time-variant flood processes; (iii) it was able to solve the shallow water equations with a relatively higher accuracy and spatial-resolution with a lower computational cost.

Two-fluid and finite Larmor radius effects on helicity evolution in a plasma pinch

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sauppe, J. P., E-mail: jpsauppe@gmail.com; Department of Physics, University of Wisconsin-Madison, 1150 University Avenue, Madison, Wisconsin 53706; Sovinec, C. R., E-mail: csovinec@wisc.edu

2016-03-15

The evolution of magnetic energy, helicity, and hybrid helicity during nonlinear relaxation of a driven-damped plasma pinch is compared in visco-resistive magnetohydrodynamics and two-fluid models with and without the ion gyroviscous stress tensor. Magnetic energy and helicity are supplied via a boundary electric field which initially balances the resistive dissipation, and the plasma undergoes multiple relaxation events during the nonlinear evolution. The magnetic helicity is well conserved relative to the magnetic energy over each event, which is short compared with the global resistive diffusion time. The magnetic energy decreases by roughly 1.5% of its initial value over a relaxation event,more » while the magnetic helicity changes by at most 0.2% of the initial value. The hybrid helicity is dominated by magnetic helicity in low-β pinch conditions and is also well conserved. Differences of less than 1% between magnetic helicity and hybrid helicity are observed with two-fluid modeling and result from cross helicity evolution. The cross helicity is found to change appreciably due to the first-order finite Larmor radius effects which have not been included in contemporary relaxation theories. The plasma current evolves towards the flat parallel current state predicted by Taylor relaxation theory but does not achieve it. Plasma flow develops significant structure for two-fluid models, and the flow perpendicular to the magnetic field is much more substantial than the flow along it.« less

High order entropy conservative central schemes for wide ranges of compressible gas dynamics and MHD flows

NASA Astrophysics Data System (ADS)

Sjögreen, Björn; Yee, H. C.

2018-07-01

The Sjogreen and Yee [31] high order entropy conservative numerical method for compressible gas dynamics is extended to include discontinuities and also extended to equations of ideal magnetohydrodynamics (MHD). The basic idea is based on Tadmor's [40] original work for inviscid perfect gas flows. For the MHD four formulations of the MHD are considered: (a) the conservative MHD, (b) the Godunov [14] non-conservative form, (c) the Janhunen [19] - MHD with magnetic field source terms, and (d) a MHD with source terms by Brackbill and Barnes [5]. Three forms of the high order entropy numerical fluxes for the MHD in the finite difference framework are constructed. They are based on the extension of the low order form of Chandrashekar and Klingenberg [9], and two forms with modifications of the Winters and Gassner [49] numerical fluxes. For flows containing discontinuities and multiscale turbulence fluctuations the high order entropy conservative numerical fluxes as the new base scheme under the Yee and Sjogreen [31] and Kotov et al. [21,22] high order nonlinear filter approach is developed. The added nonlinear filter step on the high order centered entropy conservative spatial base scheme is only utilized at isolated computational regions, while maintaining high accuracy almost everywhere for long time integration of unsteady flows and DNS and LES of turbulence computations. Representative test cases for both smooth flows and problems containing discontinuities for the gas dynamics and the ideal MHD are included. The results illustrate the improved stability by using the high order entropy conservative numerical flux as the base scheme instead of the pure high order central scheme.

On a new class of completely integrable nonlinear wave equations. II. Multi-Hamiltonian structure

NASA Astrophysics Data System (ADS)

Nutku, Y.

1987-11-01

The multi-Hamiltonian structure of a class of nonlinear wave equations governing the propagation of finite amplitude waves is discussed. Infinitely many conservation laws had earlier been obtained for these equations. Starting from a (primary) Hamiltonian formulation of these equations the necessary and sufficient conditions for the existence of bi-Hamiltonian structure are obtained and it is shown that the second Hamiltonian operator can be constructed solely through a knowledge of the first Hamiltonian function. The recursion operator which first appears at the level of bi-Hamiltonian structure gives rise to an infinite sequence of conserved Hamiltonians. It is found that in general there exist two different infinite sequences of conserved quantities for these equations. The recursion relation defining higher Hamiltonian structures enables one to obtain the necessary and sufficient conditions for the existence of the (k+1)st Hamiltonian operator which depends on the kth Hamiltonian function. The infinite sequence of conserved Hamiltonians are common to all the higher Hamiltonian structures. The equations of gas dynamics are discussed as an illustration of this formalism and it is shown that in general they admit tri-Hamiltonian structure with two distinct infinite sets of conserved quantities. The isothermal case of γ=1 is an exceptional one that requires separate treatment. This corresponds to a specialization of the equations governing the expansion of plasma into vacuum which will be shown to be equivalent to Poisson's equation in nonlinear acoustics.

An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D-3V Vlasov-Darwin particle-in-cell algorithm

NASA Astrophysics Data System (ADS)

Chen, G.; Chacón, L.

2014-10-01

A recent proof-of-principle study proposes a nonlinear electrostatic implicit particle-in-cell (PIC) algorithm in one dimension (Chen et al., 2011). The algorithm employs a kinetically enslaved Jacobian-free Newton-Krylov (JFNK) method, and conserves energy and charge to numerical round-off. In this study, we generalize the method to electromagnetic simulations in 1D using the Darwin approximation to Maxwell's equations, which avoids radiative noise issues by ordering out the light wave. An implicit, orbit-averaged, time-space-centered finite difference scheme is employed in both the 1D Darwin field equations (in potential form) and the 1D-3V particle orbit equations to produce a discrete system that remains exactly charge- and energy-conserving. Furthermore, enabled by the implicit Darwin equations, exact conservation of the canonical momentum per particle in any ignorable direction is enforced via a suitable scattering rule for the magnetic field. We have developed a simple preconditioner that targets electrostatic waves and skin currents, and allows us to employ time steps O(√{mi /me } c /veT) larger than the explicit CFL. Several 1D numerical experiments demonstrate the accuracy, performance, and conservation properties of the algorithm. In particular, the scheme is shown to be second-order accurate, and CPU speedups of more than three orders of magnitude vs. an explicit Vlasov-Maxwell solver are demonstrated in the "cold" plasma regime (where kλD ≪ 1).

Recovery Schemes for Primitive Variables in General-relativistic Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Siegel, Daniel M.; Mösta, Philipp; Desai, Dhruv; Wu, Samantha

2018-05-01

General-relativistic magnetohydrodynamic (GRMHD) simulations are an important tool to study a variety of astrophysical systems such as neutron star mergers, core-collapse supernovae, and accretion onto compact objects. A conservative GRMHD scheme numerically evolves a set of conservation equations for “conserved” quantities and requires the computation of certain primitive variables at every time step. This recovery procedure constitutes a core part of any conservative GRMHD scheme and it is closely tied to the equation of state (EOS) of the fluid. In the quest to include nuclear physics, weak interactions, and neutrino physics, state-of-the-art GRMHD simulations employ finite-temperature, composition-dependent EOSs. While different schemes have individually been proposed, the recovery problem still remains a major source of error, failure, and inefficiency in GRMHD simulations with advanced microphysics. The strengths and weaknesses of the different schemes when compared to each other remain unclear. Here we present the first systematic comparison of various recovery schemes used in different dynamical spacetime GRMHD codes for both analytic and tabulated microphysical EOSs. We assess the schemes in terms of (i) speed, (ii) accuracy, and (iii) robustness. We find large variations among the different schemes and that there is not a single ideal scheme. While the computationally most efficient schemes are less robust, the most robust schemes are computationally less efficient. More robust schemes may require an order of magnitude more calls to the EOS, which are computationally expensive. We propose an optimal strategy of an efficient three-dimensional Newton–Raphson scheme and a slower but more robust one-dimensional scheme as a fall-back.

A new flux conserving Newton's method scheme for the two-dimensional, steady Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Scott, James R.; Chang, Sin-Chung

1993-01-01

A new numerical method is developed for the solution of the two-dimensional, steady Navier-Stokes equations. The method that is presented differs in significant ways from the established numerical methods for solving the Navier-Stokes equations. The major differences are described. First, the focus of the present method is on satisfying flux conservation in an integral formulation, rather than on simulating conservation laws in their differential form. Second, the present approach provides a unified treatment of the dependent variables and their unknown derivatives. All are treated as unknowns together to be solved for through simulating local and global flux conservation. Third, fluxes are balanced at cell interfaces without the use of interpolation or flux limiters. Fourth, flux conservation is achieved through the use of discrete regions known as conservation elements and solution elements. These elements are not the same as the standard control volumes used in the finite volume method. Fifth, the discrete approximation obtained on each solution element is a functional solution of both the integral and differential form of the Navier-Stokes equations. Finally, the method that is presented is a highly localized approach in which the coupling to nearby cells is only in one direction for each spatial coordinate, and involves only the immediately adjacent cells. A general third-order formulation for the steady, compressible Navier-Stokes equations is presented, and then a Newton's method scheme is developed for the solution of incompressible, low Reynolds number channel flow. It is shown that the Jacobian matrix is nearly block diagonal if the nonlinear system of discrete equations is arranged approximately and a proper pivoting strategy is used. Numerical results are presented for Reynolds numbers of 100, 1000, and 2000. Finally, it is shown that the present scheme can resolve the developing channel flow boundary layer using as few as six to ten cells per channel width, depending on the Reynolds number.

A modified dodge algorithm for the parabolized Navier-Stokes equations and compressible duct flows

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1981-01-01

A revised version of a split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three-dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard successive overrelaxation iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition.

Analysis of viscous transonic flow over airfoil sections

NASA Technical Reports Server (NTRS)

Huff, Dennis L.; Wu, Jiunn-Chi; Sankar, L. N.

1987-01-01

A full Navier-Stokes solver has been used to model transonic flow over three airfoil sections. The method uses a two-dimensional, implicit, conservative finite difference scheme for solving the compressible Navier-Stokes equations. Results are presented as prescribed for the Viscous Transonic Airfoil Workshop to be held at the AIAA 25th Aerospace Sciences Meeting. The NACA 0012, RAE 2822 and Jones airfoils have been investigated for both attached and separated transonic flows. Predictions for pressure distributions, loads, skin friction coefficients, boundary layer displacement thickness and velocity profiles are included and compared with experimental data when possible. Overall, the results are in good agreement with experimental data.

Influence of land-surface evapotranspiration on the earth's climate

NASA Technical Reports Server (NTRS)

Shukla, J.; Mintz, Y.

1982-01-01

Land-surface evapotranspiration is shown to strongly influence global fields of rainfall, temperature and motion by calculations using a numerical model of the atmosphere, confirming the general belief in the importance of evapotranspiration-producing surface vegetation for the earth's climate. The current version of the Goddard Laboratory atmospheric general circulation model is used in the present experiment, in which conservation equations for mass, momentum, moisture and energy are expressed in finite-difference form for a spherical grid to calculate (1) surface pressure field evolution, and (2) the wind, temperature, and water vapor fields at nine levels between the surface and a 20 km height.

Adaptively-refined overlapping grids for the numerical solution of systems of hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Brislawn, Kristi D.; Brown, David L.; Chesshire, Geoffrey S.; Saltzman, Jeffrey S.

1995-01-01

Adaptive mesh refinement (AMR) in conjunction with higher-order upwind finite-difference methods have been used effectively on a variety of problems in two and three dimensions. In this paper we introduce an approach for resolving problems that involve complex geometries in which resolution of boundary geometry is important. The complex geometry is represented by using the method of overlapping grids, while local resolution is obtained by refining each component grid with the AMR algorithm, appropriately generalized for this situation. The CMPGRD algorithm introduced by Chesshire and Henshaw is used to automatically generate the overlapping grid structure for the underlying mesh.

Modified Hartree-Fock-Bogoliubov theory at finite temperature

NASA Astrophysics Data System (ADS)

Dinh Dang, Nguyen; Arima, Akito

2003-07-01

The modified Hartree-Fock-Bogoliubov (MHFB) theory at finite temperature is derived, which conserves the unitarity relation of the particle-density matrix. This is achieved by constructing a modified-quasiparticle-density matrix, where the fluctuation of the quasiparticle number is microscopically built in. This matrix can be directly obtained from the usual quasiparticle-density matrix by applying the secondary Bogoliubov transformation, which includes the quasiparticle-occupation number. It is shown that, in the limit of constant pairing parameter, the MHFB theory yields the previously obtained modified BCS (MBCS) equations. It is also proved that the modified quasiparticle-random-phase approximation, which is based on the MBCS quasiparticle excitations, conserves the Ikeda sum rule. The numerical calculations of the pairing gap, heat capacity, level density, and level-density parameter within the MBCS theory are carried out for 120Sn. The results show that the superfluid-normal phase transition is completely washed out. The applicability of the MBCS up to a temperature as high as T˜5 MeV is analyzed in detail.

Discontinuous Galerkin Methods for NonLinear Differential Systems

NASA Technical Reports Server (NTRS)

Barth, Timothy; Mansour, Nagi (Technical Monitor)

2001-01-01

This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the PDE (partial differential equation) system. Central to the development of the simplified DG methods is the Eigenvalue Scaling Theorem which characterizes right symmetrizers of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobian matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler equations of gas dynamics and extended conservation law systems derivable as moments of the Boltzmann equation. Using results from kinetic Boltzmann moment closure theory, we then derive and prove energy stability for several approximate DG fluxes which have practical and theoretical merit.

A Vertically Lagrangian Finite-Volume Dynamical Core for Global Models

NASA Technical Reports Server (NTRS)

Lin, Shian-Jiann

2003-01-01

A finite-volume dynamical core with a terrain-following Lagrangian control-volume discretization is described. The vertically Lagrangian discretization reduces the dimensionality of the physical problem from three to two with the resulting dynamical system closely resembling that of the shallow water dynamical system. The 2D horizontal-to-Lagrangian-surface transport and dynamical processes are then discretized using the genuinely conservative flux-form semi-Lagrangian algorithm. Time marching is split- explicit, with large-time-step for scalar transport, and small fractional time step for the Lagrangian dynamics, which permits the accurate propagation of fast waves. A mass, momentum, and total energy conserving algorithm is developed for mapping the state variables periodically from the floating Lagrangian control-volume to an Eulerian terrain-following coordinate for dealing with physical parameterizations and to prevent severe distortion of the Lagrangian surfaces. Deterministic baroclinic wave growth tests and long-term integrations using the Held-Suarez forcing are presented. Impact of the monotonicity constraint is discussed.

A finite volume Fokker-Planck collision operator in constants-of-motion coordinates

NASA Astrophysics Data System (ADS)

Xiong, Z.; Xu, X. Q.; Cohen, B. I.; Cohen, R.; Dorr, M. R.; Hittinger, J. A.; Kerbel, G.; Nevins, W. M.; Rognlien, T.

2006-04-01

TEMPEST is a 5D gyrokinetic continuum code for edge plasmas. Constants of motion, namely, the total energy E and the magnetic moment μ, are chosen as coordinate s because of their advantage in minimizing numerical diffusion in advection operato rs. Most existing collision operators are written in other coordinates; using them by interpolating is shown to be less satisfactory in maintaining overall numerical accuracy and conservation. Here we develop a Fokker-Planck collision operator directly in (E,μ) space usin g a finite volume approach. The (E, μ) grid is Cartesian, and the turning point boundary represents a straight line cutting through the grid that separates the ph ysical and non-physical zones. The resulting cut-cells are treated by a cell-mergin g technique to ensure a complete particle conservation. A two dimensional fourth or der reconstruction scheme is devised to achieve good numerical accuracy with modest number of grid points. The new collision operator will be benchmarked by numerical examples.

Finite area method for nonlinear supersonic conical flows

NASA Technical Reports Server (NTRS)

Sritharan, S. S.; Seebass, A. R.

1983-01-01

A fully conservative numerical method for the computation of steady inviscid supersonic flow about general conical bodies at incidence is described. The procedure utilizes the potential approximation and implements a body conforming mesh generator. The conical potential is assumed to have its best linear variation inside each mesh cell; a secondary interlocking cell system is used to establish the flux balance required to conserve mass. In the supersonic regions the scheme is symmetrized by adding artificial viscosity in conservation form. The algorithm is nearly an order of a magnitude faster than present Euler methods and predicts known results accurately and qualitative features such as nodal point lift off correctly. Results are compared with those of other investigators.

Phosphorus Fate and Transport across Fields and Catchments: Addressing the Paradoxical Dilemma

NASA Astrophysics Data System (ADS)

Sharpley, Andrew; Jarvie, Helen; Johnson, Laura; Smith, Doug

2017-04-01

Awareness and scrutiny of agriculture's role in contributing phosphorus (P) to surface water impairment has increased due to recent high profile harmful algal bloom outbreaks. In addition, an inability to meet target P-load reductions in large catchments in the USA, such as Chesapeake Bay, Lake Erie, and Mississippi River, has brought into question the effectiveness of current and future conservation strategies designed to mitigate such loads. This has led many to question the efficacy of these measures and to call for stricter land and P-management strategies and the recognition of several paradoxes related to the management of agricultural P. "The Finite Resource and Environmental Abundance Paradox" While P is a finite resource, with an expected life of 300 years using modern mining technologies, less than 20% of mined fertilizer P reaches the food products consumed, only 10% of the P in human wastes is recycled back onto agricultural land, yet P deficits occur across 30% of global cropland. "The Blue - Green Paradox" An increasingly affluent population is becoming more demanding of cheap, reliable food sources and wanting inexpensive clean, safe water for many essential and recreational uses. We now face many challenges in balancing competing demands for protecting and restoring water quality and aquatic ecology, with sustainable and efficient agricultural production. After the low hanging fruit of remedial measures are adopted, remaining conservation practices become increasingly less cost-beneficial and raises the old conundrum of "who benefits and who pays?" "The Conservation Legacy P Paradox" Many conservation practices have been implemented to retain (e.g., no-tillage, cover crops, contour plowing, ridge tillage) and trap P (e.g., buffer strips, riparian zones, wetlands) on the landscape rather than enter waterways. Yet, the capacity of those practices to retain is finite and there are more and more examples of conservation practices transitioning from P sinks to P sources. In this presentation, we examine the drivers of legacy P at the watershed scale, specifically in relation to the physical cascades and biogeochemical spirals of P along the continuum from soils to rivers and lakes, and via surface and subsurface flow pathways. Close examination of long-term P flux, weather patterns, and land management identified several natural and managed drivers that have inadvertently accelerated the accumulation of P at the soil surface and flux of P via subsurface drainage. This indicates a paradoxical conundrum where well-intended conservation measures may have cumulative impacts, which have converged with changing weather patterns and catchment hydrology to increase P fluxes. In seeking solutions, we must better quantify P sinks and sources as they are transported through catchments, to develop realistic expectations for adoption of conservation strategies and timescales for aquatic ecosystem recovery.

Effects of Non-Equilibrium Chemistry and Darcy-Forchheimer Flow of Pyrolysis Gas for a Charring Ablator

NASA Technical Reports Server (NTRS)

Chen, Yih-Kanq; Milos, Frank S.

2011-01-01

The Fully Implicit Ablation and Thermal Response code, FIAT, simulates pyrolysis and ablation of thermal protection materials and systems. The governing equations, which include energy conservation, a three-component decomposition model, and a surface energy balance, are solved with a moving grid. This work describes new modeling capabilities that are added to a special version of FIAT. These capabilities include a time-dependent pyrolysis gas flow momentum equation with Darcy-Forchheimer terms and pyrolysis gas species conservation equations with finite-rate homogeneous chemical reactions. The total energy conservation equation is also enhanced for consistency with these new additions. Parametric studies are performed using this enhanced version of FIAT. Two groups of analyses of Phenolic Impregnated Carbon Ablator (PICA) are presented. In the first group, an Orion flight environment for a proposed Lunar-return trajectory is considered. In the second group, various test conditions for arcjet models are examined. The central focus of these parametric studies is to understand the effect of pyrolysis gas momentum transfer on PICA material in-depth thermal responses with finite-rate, equilibrium, or frozen homogeneous gas chemistry. Results are presented, discussed, and compared with those predicted by the baseline PICA/FIAT ablation and thermal response model developed by the Orion Thermal Protection System Advanced Development Project.

A Numerical Model for Trickle Bed Reactors

NASA Astrophysics Data System (ADS)

Propp, Richard M.; Colella, Phillip; Crutchfield, William Y.; Day, Marcus S.

2000-12-01

Trickle bed reactors are governed by equations of flow in porous media such as Darcy's law and the conservation of mass. Our numerical method for solving these equations is based on a total-velocity splitting, sequential formulation which leads to an implicit pressure equation and a semi-implicit mass conservation equation. We use high-resolution finite-difference methods to discretize these equations. Our solution scheme extends previous work in modeling porous media flows in two ways. First, we incorporate physical effects due to capillary pressure, a nonlinear inlet boundary condition, spatial porosity variations, and inertial effects on phase mobilities. In particular, capillary forces introduce a parabolic component into the recast evolution equation, and the inertial effects give rise to hyperbolic nonconvexity. Second, we introduce a modification of the slope-limiting algorithm to prevent our numerical method from producing spurious shocks. We present a numerical algorithm for accommodating these difficulties, show the algorithm is second-order accurate, and demonstrate its performance on a number of simplified problems relevant to trickle bed reactor modeling.

A Direct Numerical Simulation of a Temporally Evolving Liquid-Gas Turbulent Mixing Layer

NASA Astrophysics Data System (ADS)

Vu, Lam Xuan; Chiodi, Robert; Desjardins, Olivier

2017-11-01

Air-blast atomization occurs when streams of co-flowing high speed gas and low speed liquid shear to form drops. Air-blast atomization has numerous industrial applications from combustion engines in jets to sprays used for medical coatings. The high Reynolds number and dynamic pressure ratio of a realistic air-blast atomization case requires large eddy simulation and the use of multiphase sub-grid scale (SGS) models. A direct numerical simulations (DNS) of a temporally evolving mixing layer is presented to be used as a base case from which future multiphase SGS models can be developed. To construct the liquid-gas mixing layer, half of a channel flow from Kim et al. (JFM, 1987) is placed on top of a static liquid layer that then evolves over time. The DNS is performed using a conservative finite volume incompressible multiphase flow solver where phase tracking is handled with a discretely conservative volume of fluid method. This study presents statistics on velocity and volume fraction at different Reynolds and Weber numbers.

Two fundamentally different classes of microbial genes.

PubMed

Wolf, Yuri I; Makarova, Kira S; Lobkovsky, Alexander E; Koonin, Eugene V

2016-11-07

The evolution of bacterial and archaeal genomes is highly dynamic and involves extensive horizontal gene transfer and gene loss 1-4 . Furthermore, many microbial species appear to have open pangenomes, where each newly sequenced genome contains more than 10% ORFans, that is, genes without detectable homologues in other species 5,6 . Here, we report a quantitative analysis of microbial genome evolution by fitting the parameters of a simple, steady-state evolutionary model to the comparative genomic data on the gene content and gene order similarity between archaeal genomes. The results reveal two sharply distinct classes of microbial genes, one of which is characterized by effectively instantaneous gene replacement, and the other consists of genes with finite, distributed replacement rates. These findings imply a conservative estimate of the size of the prokaryotic genomic universe, which appears to consist of at least a billion distinct genes. Furthermore, the same distribution of constraints is shown to govern the evolution of gene complement and gene order, without the need to invoke long-range conservation or the selfish operon concept 7 .

Thermophoresis on boundary layer heat and mass transfer flow of Walters-B fluid past a radiate plate with heat sink/source

NASA Astrophysics Data System (ADS)

Vasu, B.; Gorla, Rama Subba Reddy; Murthy, P. V. S. N.

2017-05-01

The Walters-B liquid model is employed to simulate medical creams and other rheological liquids encountered in biotechnology and chemical engineering. This rheological model introduces supplementary terms into the momentum conservation equation. The combined effects of thermal radiation and heat sink/source on transient free convective, laminar flow and mass transfer in a viscoelastic fluid past a vertical plate are presented by taking thermophoresis effect into account. The transformed conservation equations are solved using a stable, robust finite difference method. A parametric study illustrating the influence of viscoelasticity parameter ( Γ), thermophoretic parameter ( τ), thermal radiation parameter ( F), heat sink/source ( ϕ), Prandtl number ( Pr), Schmidt number ( Sc), thermal Grashof number ( Gr), solutal Grashof number ( Gm), temperature and concentration profiles as well as local skin-friction, Nusselt and Sherwood number is conducted. The results of this parametric study are shown graphically and inform of table. The study has applications in polymer materials processing.

Thermalization without eigenstate thermalization hypothesis after a quantum quench.

PubMed

Mori, Takashi; Shiraishi, Naoto

2017-08-01

Nonequilibrium dynamics of a nonintegrable system without the eigenstate thermalization hypothesis is studied. It is shown that, in the thermodynamic limit, this model thermalizes after an arbitrary quantum quench at finite temperature, although it does not satisfy the eigenstate thermalization hypothesis. In contrast, when the system size is finite and the temperature is low enough, the system may not thermalize. In this case, the steady state is well described by the generalized Gibbs ensemble constructed by using highly nonlocal conserved quantities. We also show that this model exhibits prethermalization, in which the prethermalized state is characterized by nonthermal energy eigenstates.

A diagonal implicit scheme for computing flows with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Eberhardt, Scott; Imlay, Scott

1990-01-01

A new algorithm for solving steady, finite-rate chemistry, flow problems is presented. The new scheme eliminates the expense of inverting large block matrices that arise when species conservation equations are introduced. The source Jacobian matrix is replaced by a diagonal matrix which is tailored to account for the fastest reactions in the chemical system. A point-implicit procedure is discussed and then the algorithm is included into the LU-SGS scheme. Solutions are presented for hypervelocity reentry and Hydrogen-Oxygen combustion. For the LU-SGS scheme a CFL number in excess of 10,000 has been achieved.

Generalization of mixed multiscale finite element methods with applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, C S

Many science and engineering problems exhibit scale disparity and high contrast. The small scale features cannot be omitted in the physical models because they can affect the macroscopic behavior of the problems. However, resolving all the scales in these problems can be prohibitively expensive. As a consequence, some types of model reduction techniques are required to design efficient solution algorithms. For practical purpose, we are interested in mixed finite element problems as they produce solutions with certain conservative properties. Existing multiscale methods for such problems include the mixed multiscale finite element methods. We show that for complicated problems, the mixedmore » multiscale finite element methods may not be able to produce reliable approximations. This motivates the need of enrichment for coarse spaces. Two enrichment approaches are proposed, one is based on generalized multiscale finte element metthods (GMsFEM), while the other is based on spectral element-based algebraic multigrid (rAMGe). The former one, which is called mixed GMsFEM, is developed for both Darcy’s flow and linear elasticity. Application of the algorithm in two-phase flow simulations are demonstrated. For linear elasticity, the algorithm is subtly modified due to the symmetry requirement of the stress tensor. The latter enrichment approach is based on rAMGe. The algorithm differs from GMsFEM in that both of the velocity and pressure spaces are coarsened. Due the multigrid nature of the algorithm, recursive application is available, which results in an efficient multilevel construction of the coarse spaces. Stability, convergence analysis, and exhaustive numerical experiments are carried out to validate the proposed enrichment approaches. iii« less

Implicit approximate-factorization schemes for the low-frequency transonic equation

NASA Technical Reports Server (NTRS)

Ballhaus, W. F.; Steger, J. L.

1975-01-01

Two- and three-level implicit finite-difference algorithms for the low-frequency transonic small disturbance-equation are constructed using approximate factorization techniques. The schemes are unconditionally stable for the model linear problem. For nonlinear mixed flows, the schemes maintain stability by the use of conservatively switched difference operators for which stability is maintained only if shock propagation is restricted to be less than one spatial grid point per time step. The shock-capturing properties of the schemes were studied for various shock motions that might be encountered in problems of engineering interest. Computed results for a model airfoil problem that produces a flow field similar to that about a helicopter rotor in forward flight show the development of a shock wave and its subsequent propagation upstream off the front of the airfoil.

A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations

NASA Astrophysics Data System (ADS)

Li, Meng; Gu, Xian-Ming; Huang, Chengming; Fei, Mingfa; Zhang, Guoyu

2018-04-01

In this paper, a fast linearized conservative finite element method is studied for solving the strongly coupled nonlinear fractional Schrödinger equations. We prove that the scheme preserves both the mass and energy, which are defined by virtue of some recursion relationships. Using the Sobolev inequalities and then employing the mathematical induction, the discrete scheme is proved to be unconditionally convergent in the sense of L2-norm and H α / 2-norm, which means that there are no any constraints on the grid ratios. Then, the prior bound of the discrete solution in L2-norm and L∞-norm are also obtained. Moreover, we propose an iterative algorithm, by which the coefficient matrix is independent of the time level, and thus it leads to Toeplitz-like linear systems that can be efficiently solved by Krylov subspace solvers with circulant preconditioners. This method can reduce the memory requirement of the proposed linearized finite element scheme from O (M2) to O (M) and the computational complexity from O (M3) to O (Mlog ⁡ M) in each iterative step, where M is the number of grid nodes. Finally, numerical results are carried out to verify the correction of the theoretical analysis, simulate the collision of two solitary waves, and show the utility of the fast numerical solution techniques.

The unstaggered extension to GFDL's FV3 dynamical core on the cubed-sphere

NASA Astrophysics Data System (ADS)

Chen, X.; Lin, S. J.; Harris, L.

2017-12-01

Finite-volume schemes have become popular for atmospheric transport since they provide intrinsic mass conservation to constituent species. Many CFD codes use unstaggered discretizations for finite volume methods with an approximate Riemann solver. However, this approach is inefficient for geophysical flows due to the complexity of the Riemann solver. We introduce a Low Mach number Approximate Riemann Solver (LMARS) simplified using assumptions appropriate for atmospheric flows: the wind speed is much slower than the sound speed, weak discontinuities, and locally uniform sound wave velocity. LMARS makes possible a Riemann-solver-based dynamical core comparable in computational efficiency to many current dynamical cores. We will present a 3D finite-volume dynamical core using LMARS in a cubed-sphere geometry with a vertically Lagrangian discretization. Results from standard idealized test cases will be discussed.

Improving a complex finite-difference ground water flow model through the use of an analytic element screening model

USGS Publications Warehouse

Hunt, R.J.; Anderson, M.P.; Kelson, V.A.

1998-01-01

This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.

Temporal Specification and Verification of Real-Time Systems.

DTIC Science & Technology

1991-08-30

of concrete real - time systems can be modeled adequately. Specification: We present two conservative extensions of temporal logic that allow for the...logic. We present both model-checking algorithms for the automatic verification of finite-state real - time systems and proof methods for the deductive verification of real - time systems .

Inverse transonic airfoil design methods including boundary layer and viscous interaction effects

NASA Technical Reports Server (NTRS)

Carlson, L. A.

1979-01-01

The development and incorporation into TRANDES of a fully conservative analysis method utilizing the artificial compressibility approach is described. The method allows for lifting cases and finite thickness airfoils and utilizes a stretched coordinate system. Wave drag and massive separation studies are also discussed.

Advanced bridge safety initiative, task 3 : slab bridge load rating using AASHTO methodology and finite element analysis - an analysis of 20 bridges.

DOT National Transportation Integrated Search

2011-12-01

Current AASHTO provisions for the conventional load rating of flat slab bridges rely on the equivalent strip method : of analysis for determining live load effects, this is generally regarded as overly conservative by many professional : engineers. A...

Edge gradients evaluation for 2D hybrid finite volume method model

USDA-ARS?s Scientific Manuscript database

In this study, a two-dimensional depth-integrated hydrodynamic model was developed using FVM on a hybrid unstructured collocated mesh system. To alleviate the negative effects of mesh irregularity and non-uniformity, a conservative evaluation method for edge gradients based on the second-order Tayl...

Adaptive finite-volume WENO schemes on dynamically redistributed grids for compressible Euler equations

NASA Astrophysics Data System (ADS)

Pathak, Harshavardhana S.; Shukla, Ratnesh K.

2016-08-01

A high-order adaptive finite-volume method is presented for simulating inviscid compressible flows on time-dependent redistributed grids. The method achieves dynamic adaptation through a combination of time-dependent mesh node clustering in regions characterized by strong solution gradients and an optimal selection of the order of accuracy and the associated reconstruction stencil in a conservative finite-volume framework. This combined approach maximizes spatial resolution in discontinuous regions that require low-order approximations for oscillation-free shock capturing. Over smooth regions, high-order discretization through finite-volume WENO schemes minimizes numerical dissipation and provides excellent resolution of intricate flow features. The method including the moving mesh equations and the compressible flow solver is formulated entirely on a transformed time-independent computational domain discretized using a simple uniform Cartesian mesh. Approximations for the metric terms that enforce discrete geometric conservation law while preserving the fourth-order accuracy of the two-point Gaussian quadrature rule are developed. Spurious Cartesian grid induced shock instabilities such as carbuncles that feature in a local one-dimensional contact capturing treatment along the cell face normals are effectively eliminated through upwind flux calculation using a rotated Hartex-Lax-van Leer contact resolving (HLLC) approximate Riemann solver for the Euler equations in generalized coordinates. Numerical experiments with the fifth and ninth-order WENO reconstructions at the two-point Gaussian quadrature nodes, over a range of challenging test cases, indicate that the redistributed mesh effectively adapts to the dynamic flow gradients thereby improving the solution accuracy substantially even when the initial starting mesh is non-adaptive. The high adaptivity combined with the fifth and especially the ninth-order WENO reconstruction allows remarkably sharp capture of discontinuous propagating shocks with simultaneous resolution of smooth yet complex small scale unsteady flow features to an exceptional detail.

A structure-preserving method for a class of nonlinear dissipative wave equations with Riesz space-fractional derivatives

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

2017-12-01

In this manuscript, we consider an initial-boundary-value problem governed by a (1 + 1)-dimensional hyperbolic partial differential equation with constant damping that generalizes many nonlinear wave equations from mathematical physics. The model considers the presence of a spatial Laplacian of fractional order which is defined in terms of Riesz fractional derivatives, as well as the inclusion of a generic continuously differentiable potential. It is known that the undamped regime has an associated positive energy functional, and we show here that it is preserved throughout time under suitable boundary conditions. To approximate the solutions of this model, we propose a finite-difference discretization based on fractional centered differences. Some discrete quantities are proposed in this work to estimate the energy functional, and we show that the numerical method is capable of conserving the discrete energy under the same boundary conditions for which the continuous model is conservative. Moreover, we establish suitable computational constraints under which the discrete energy of the system is positive. The method is consistent of second order, and is both stable and convergent. The numerical simulations shown here illustrate the most important features of our numerical methodology.

Smoothed Particle Hydrodynamics Continuous Boundary Force method for Navier-Stokes equations subject to Robin boundary condition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pan, Wenxiao; Bao, Jie; Tartakovsky, Alexandre M.

2014-02-15

Robin boundary condition for the Navier-Stokes equations is used to model slip conditions at the fluid-solid boundaries. A novel Continuous Boundary Force (CBF) method is proposed for solving the Navier-Stokes equations subject to Robin boundary condition. In the CBF method, the Robin boundary condition at boundary is replaced by the homogeneous Neumann boundary condition at the boundary and a volumetric force term added to the momentum conservation equation. Smoothed Particle Hydrodynamics (SPH) method is used to solve the resulting Navier-Stokes equations. We present solutions for two-dimensional and three-dimensional flows in domains bounded by flat and curved boundaries subject to variousmore » forms of the Robin boundary condition. The numerical accuracy and convergence are examined through comparison of the SPH-CBF results with the solutions of finite difference or finite element method. Taken the no-slip boundary condition as a special case of slip boundary condition, we demonstrate that the SPH-CBF method describes accurately both no-slip and slip conditions.« less

An ultra-accurate numerical method in the design of liquid phononic crystals with hard inclusion

NASA Astrophysics Data System (ADS)

Li, Eric; He, Z. C.; Wang, G.; Liu, G. R.

2017-12-01

The phononics crystals (PCs) are periodic man-made composite materials. In this paper, a mass-redistributed finite element method (MR-FEM) is formulated to study the wave propagation within liquid PCs with hard inclusion. With a perfect balance between stiffness and mass in the MR-FEM model, the dispersion error of longitudinal wave is minimized by redistribution of mass. Such tuning can be easily achieved by adjusting the parameter r that controls the location of integration points of mass matrix. More importantly, the property of mass conservation in the MR-FEM model indicates that the locations of integration points inside or outside the element are immaterial. Four numerical examples are studied in this work, including liquid PCs with cross and circle hard inclusions, different size of inclusion and defect. Compared with standard finite element method, the numerical results have verified the accuracy and effectiveness of MR-FEM. The proposed MR-FEM is a unique and innovative numerical approach with its outstanding features, which has strong potentials to study the stress wave within multi-physics PCs.

HYDRA-II: A hydrothermal analysis computer code: Volume 2, User's manual

DOE Office of Scientific and Technical Information (OSTI.GOV)

McCann, R.A.; Lowery, P.S.; Lessor, D.L.

1987-09-01

HYDRA-II is a hydrothermal computer code capable of three-dimensional analysis of coupled conduction, convection, and thermal radiation problems. This code is especially appropriate for simulating the steady-state performance of spent fuel storage systems. The code has been evaluated for this application for the US Department of Energy's Commercial Spent Fuel Management Program. HYDRA-II provides a finite-difference solution in cartesian coordinates to the equations governing the conservation of mass, momentum, and energy. A cylindrical coordinate system may also be used to enclose the cartesian coordinate system. This exterior coordinate system is useful for modeling cylindrical cask bodies. The difference equations formore » conservation of momentum incorporate directional porosities and permeabilities that are available to model solid structures whose dimensions may be smaller than the computational mesh. The equation for conservation of energy permits modeling of orthotropic physical properties and film resistances. Several automated methods are available to model radiation transfer within enclosures and from fuel rod to fuel rod. The documentation of HYDRA-II is presented in three separate volumes. Volume 1 - Equations and Numerics describes the basic differential equations, illustrates how the difference equations are formulated, and gives the solution procedures employed. This volume, Volume 2 - User's Manual, contains code flow charts, discusses the code structure, provides detailed instructions for preparing an input file, and illustrates the operation of the code by means of a sample problem. The final volume, Volume 3 - Verification/Validation Assessments, provides a comparison between the analytical solution and the numerical simulation for problems with a known solution. 6 refs.« less

Numerical Methods for Nonlinear Fokker-Planck Collision Operator in TEMPEST

NASA Astrophysics Data System (ADS)

Kerbel, G.; Xiong, Z.

2006-10-01

Early implementations of Fokker-Planck collision operator and moment computations in TEMPEST used low order polynomial interpolation schemes to reuse conservative operators developed for speed/pitch-angle (v, θ) coordinates. When this approach proved to be too inaccurate we developed an alternative higher order interpolation scheme for the Rosenbluth potentials and a high order finite volume method in TEMPEST (,) coordinates. The collision operator is thus generated by using the expansion technique in (v, θ) coordinates for the diffusion coefficients only, and then the fluxes for the conservative differencing are computed directly in the TEMPEST (,) coordinates. Combined with a cut-cell treatment at the turning-point boundary, this new approach is shown to have much better accuracy and conservation properties.

Exactly energy conserving semi-implicit particle in cell formulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lapenta, Giovanni, E-mail: giovanni.lapenta@kuleuven.be

We report a new particle in cell (PIC) method based on the semi-implicit approach. The novelty of the new method is that unlike any of its semi-implicit predecessors at the same time it retains the explicit computational cycle and conserves energy exactly. Recent research has presented fully implicit methods where energy conservation is obtained as part of a non-linear iteration procedure. The new method (referred to as Energy Conserving Semi-Implicit Method, ECSIM), instead, does not require any non-linear iteration and its computational cycle is similar to that of explicit PIC. The properties of the new method are: i) it conservesmore » energy exactly to round-off for any time step or grid spacing; ii) it is unconditionally stable in time, freeing the user from the need to resolve the electron plasma frequency and allowing the user to select any desired time step; iii) it eliminates the constraint of the finite grid instability, allowing the user to select any desired resolution without being forced to resolve the Debye length; iv) the particle mover has a computational complexity identical to that of the explicit PIC, only the field solver has an increased computational cost. The new ECSIM is tested in a number of benchmarks where accuracy and computational performance are tested. - Highlights: • We present a new fully energy conserving semi-implicit particle in cell (PIC) method based on the implicit moment method (IMM). The new method is called Energy Conserving Implicit Moment Method (ECIMM). • The novelty of the new method is that unlike any of its predecessors at the same time it retains the explicit computational cycle and conserves energy exactly. • The new method is unconditionally stable in time, freeing the user from the need to resolve the electron plasma frequency. • The new method eliminates the constraint of the finite grid instability, allowing the user to select any desired resolution without being forced to resolve the Debye length. • These features are achieved at a reduced cost compared with either previous IMM or fully implicit implementation of PIC.« less

The problem of the second wind turbine - a note on a common but flawed wind power estimation method

NASA Astrophysics Data System (ADS)

Gans, F.; Miller, L. M.; Kleidon, A.

2010-06-01

Several recent wind power estimates suggest how this renewable resource can meet all of the current and future global energy demand with little impact on the atmosphere. These estimates are calculated using observed wind speeds in combination with specifications of wind turbine size and density to quantify the extractable wind power. Here we show that this common methodology is flawed because it does not account for energy removal by the turbines that is necessary to ensure the conservation of energy. We will first illustrate the common but flawed methodology using parameters from a recent global quantification of wind power in a simple experimental setup. For a small number of turbines at small scales, the conservation of energy hardly results in a difference when compared to the common method. However, when applied at large to global scales, the ability of radiative gradients to generate a finite amount of kinetic energy needs to be taken into account. Using the same experimental setup, we use the simplest method to ensure the conservation of energy to show a non-negligble decrease in wind velocity after the first turbine that will successively result in lower extraction of the downwind turbines. We then show how the conservation of energy inevitably results in substantially lower estimates of wind power at the global scale. Because conservation of energy is fundamental, we conclude that ultimately environmental constraints set the upper limit for wind power availability at the larger scale rather than detailed engineering specifications of the wind turbine design and placement.

ICASE Semiannual Report, October 1, 1992 through March 31, 1993

DTIC Science & Technology

1993-06-01

NUMERICAL MATHEMATICS Saul Abarbanel Further results have been obtained regarding long time integration of high order compact finite difference schemes...overall accuracy. These problems are common to all numerical methods: finite differences , finite elements and spectral methods. It should be noted that...fourth order finite difference scheme. * In the same case, the D6 wavelets provide a sixth order finite difference , noncompact formula. * The wavelets

Applications and Improvement of a Coupled, Global and Cloud-Resolving Modeling System

NASA Technical Reports Server (NTRS)

Tao, W.-K.; Chern, J.; Atlas, R.

2005-01-01

Recently Grabowski (2001) and Khairoutdinov and Randall (2001) have proposed the use of 2D CFWs as a "super parameterization" [or multi-scale modeling framework (MMF)] to represent cloud processes within atmospheric general circulation models (GCMs). In the MMF, a fine-resolution 2D CRM takes the place of the single-column parameterization used in conventional GCMs. A prototype Goddard MMF based on the 2D Goddard Cumulus Ensemble (GCE) model and the Goddard finite volume general circulation model (fvGCM) is now being developed. The prototype includes the fvGCM run at 2.50 x 20 horizontal resolution with 32 vertical layers from the surface to 1 mb and the 2D (x-z) GCE using 64 horizontal and 32 vertical grid points with 4 km horizontal resolution and a cyclic lateral boundary. The time step for the 2D GCE would be 15 seconds, and the fvGCM-GCE coupling frequency would be 30 minutes (i.e. the fvGCM physical time step). We have successfully developed an fvGCM-GCE coupler for this prototype. Because the vertical coordinate of the fvGCM (a terrain-following floating Lagrangian coordinate) is different from that of the GCE (a z coordinate), vertical interpolations between the two coordinates are needed in the coupler. In interpolating fields from the GCE to fvGCM, we use an existing fvGCM finite- volume piecewise parabolic mapping (PPM) algorithm, which conserves the mass, momentum, and total energy. A new finite-volume PPM algorithm, which conserves the mass, momentum and moist static energy in the z coordinate, is being developed for interpolating fields from the fvGCM to the GCE. In the meeting, we will discuss the major differences between the two MMFs (i.e., the CSU MMF and the Goddard MMF). We will also present performance and critical issues related to the MMFs. In addition, we will present multi-dimensional cloud datasets (i.e., a cloud data library) generated by the Goddard MMF that will be provided to the global modeling community to help improve the representation and performance of moist processes in climate models and to improve our understanding of cloud processes globally (the software tools needed to produce cloud statistics and to identify various types of clouds and cloud systems from both high-resolution satellite and model data will be also presented).

Semi-implicit finite difference methods for three-dimensional shallow water flow

USGS Publications Warehouse

Casulli, Vincenzo; Cheng, Ralph T.

1992-01-01

A semi-implicit finite difference method for the numerical solution of three-dimensional shallow water flows is presented and discussed. The governing equations are the primitive three-dimensional turbulent mean flow equations where the pressure distribution in the vertical has been assumed to be hydrostatic. In the method of solution a minimal degree of implicitness has been adopted in such a fashion that the resulting algorithm is stable and gives a maximal computational efficiency at a minimal computational cost. At each time step the numerical method requires the solution of one large linear system which can be formally decomposed into a set of small three-diagonal systems coupled with one five-diagonal system. All these linear systems are symmetric and positive definite. Thus the existence and uniquencess of the numerical solution are assured. When only one vertical layer is specified, this method reduces as a special case to a semi-implicit scheme for solving the corresponding two-dimensional shallow water equations. The resulting two- and three-dimensional algorithm has been shown to be fast, accurate and mass-conservative and can also be applied to simulate flooding and drying of tidal mud-flats in conjunction with three-dimensional flows. Furthermore, the resulting algorithm is fully vectorizable for an efficient implementation on modern vector computers.

Solvable continuous-time random walk model of the motion of tracer particles through porous media.

PubMed

Fouxon, Itzhak; Holzner, Markus

2016-08-01

We consider the continuous-time random walk (CTRW) model of tracer motion in porous medium flows based on the experimentally determined distributions of pore velocity and pore size reported by Holzner et al. [M. Holzner et al., Phys. Rev. E 92, 013015 (2015)PLEEE81539-375510.1103/PhysRevE.92.013015]. The particle's passing through one channel is modeled as one step of the walk. The step (channel) length is random and the walker's velocity at consecutive steps of the walk is conserved with finite probability, mimicking that at the turning point there could be no abrupt change of velocity. We provide the Laplace transform of the characteristic function of the walker's position and reductions for different cases of independence of the CTRW's step duration τ, length l, and velocity v. We solve our model with independent l and v. The model incorporates different forms of the tail of the probability density of small velocities that vary with the model parameter α. Depending on that parameter, all types of anomalous diffusion can hold, from super- to subdiffusion. In a finite interval of α, ballistic behavior with logarithmic corrections holds, which was observed in a previously introduced CTRW model with independent l and τ. Universality of tracer diffusion in the porous medium is considered.

Biomechanical investigation of different surgical strategies for the treatment of rib fractures using a three-dimensional human respiratory model.

PubMed

Shih, Kao-Shang; Truong, Thanh An; Hsu, Ching-Chi; Hou, Sheng-Mou

2017-11-02

Rib fracture is a common injury and can result in pain during respiration. Conservative treatment of rib fracture is applied via mechanical ventilation. However, ventilator-associated complications frequently occur. Surgical fixation is another approach to treat rib fractures. Unfortunately, this surgical treatment is still not completely defined. Past studies have evaluated the biomechanics of the rib cage during respiration using a finite element method, but only intact conditions were modelled. Thus, the purpose of this study was to develop a realistic numerical model of the human rib cage and to analyse the biomechanical performance of intact, injured and treated rib cages. Three-dimensional finite element models of the human rib cage were developed. Respiratory movement of the human rib cage was simulated to evaluate the strengths and limitations of different scenarios. The results show that a realistic human respiratory movement can be simulated and the predicted results were closely related to previous study (correlation coefficient>0.92). Fixation of two fractured ribs significantly decreased the fixation index (191%) compared to the injured model. This fixation may provide adequate fixation stability as well as reveal lower bone stress and implant stress compared with the fixation of three or more fractured ribs.

Large-eddy simulation of flow past a circular cylinder

NASA Technical Reports Server (NTRS)

Mittal, R.

1995-01-01

Some of the most challenging applications of large-eddy simulation are those in complex geometries where spectral methods are of limited use. For such applications more conventional methods such as finite difference or finite element have to be used. However, it has become clear in recent years that dissipative numerical schemes which are routinely used in viscous flow simulations are not good candidates for use in LES of turbulent flows. Except in cases where the flow is extremely well resolved, it has been found that upwind schemes tend to damp out a significant portion of the small scales that can be resolved on the grid. Furthermore, it has been found that even specially designed higher-order upwind schemes that have been used successfully in the direct numerical simulation of turbulent flows produce too much dissipation when used in conjunction with large-eddy simulation. The objective of the current study is to perform a LES of incompressible flow past a circular cylinder at a Reynolds number of 3900 using a solver which employs an energy-conservative second-order central difference scheme for spatial discretization and compare the results obtained with those of Beaudan & Moin (1994) and with the experiments in order to assess the performance of the central scheme for this relatively complex geometry.

A solution to the Navier-Stokes equations based upon the Newton Kantorovich method

NASA Technical Reports Server (NTRS)

Davis, J. E.; Gabrielsen, R. E.; Mehta, U. B.

1977-01-01

An implicit finite difference scheme based on the Newton-Kantorovich technique was developed for the numerical solution of the nonsteady, incompressible, two-dimensional Navier-Stokes equations in conservation-law form. The algorithm was second-order-time accurate, noniterative with regard to the nonlinear terms in the vorticity transport equation except at the earliest few time steps, and spatially factored. Numerical results were obtained with the technique for a circular cylinder at Reynolds number 15. Results indicate that the technique is in excellent agreement with other numerical techniques for all geometries and Reynolds numbers investigated, and indicates a potential for significant reduction in computation time over current iterative techniques.

Numerical simulation of convective motion in an anisotropic porous medium and cosymmetry conservation

NASA Astrophysics Data System (ADS)

Abdelhafez, M. A.; Tsybulin, V. G.

2017-10-01

The onset of convection in a porous anisotropic rectangle occupied by a heat-conducting fluid heated from below is analyzed on the basis of the Darcy-Boussinesq model. It is shown that there are combinations of control parameters for which the system has a nontrivial cosymmetry and a one-parameter family of stationary convective regimes branches off from the mechanical equilibrium. For the two-dimensional convection equations in a porous medium, finite-difference approximations preserving the cosymmetry of the original system are developed. Numerical results are presented that demonstrate the formation of a family of convective regimes and its disappearance when the approximations do not inherit the cosymmetry property.

NUMERICAL ANALYSES FOR TREATING DIFFUSION IN SINGLE-, TWO-, AND THREE-PHASE BINARY ALLOY SYSTEMS

NASA Technical Reports Server (NTRS)

Tenney, D. R.

1994-01-01

This package consists of a series of three computer programs for treating one-dimensional transient diffusion problems in single and multiple phase binary alloy systems. An accurate understanding of the diffusion process is important in the development and production of binary alloys. Previous solutions of the diffusion equations were highly restricted in their scope and application. The finite-difference solutions developed for this package are applicable for planar, cylindrical, and spherical geometries with any diffusion-zone size and any continuous variation of the diffusion coefficient with concentration. Special techniques were included to account for differences in modal volumes, initiation and growth of an intermediate phase, disappearance of a phase, and the presence of an initial composition profile in the specimen. In each analysis, an effort was made to achieve good accuracy while minimizing computation time. The solutions to the diffusion equations for single-, two-, and threephase binary alloy systems are numerically calculated by the three programs NAD1, NAD2, and NAD3. NAD1 treats the diffusion between pure metals which belong to a single-phase system. Diffusion in this system is described by a one-dimensional Fick's second law and will result in a continuous composition variation. For computational purposes, Fick's second law is expressed as an explicit second-order finite difference equation. Finite difference calculations are made by choosing the grid spacing small enough to give convergent solutions of acceptable accuracy. NAD2 treats diffusion between pure metals which form a two-phase system. Diffusion in the twophase system is described by two partial differential equations (a Fick's second law for each phase) and an interface-flux-balance equation which describes the location of the interface. Actual interface motion is obtained by a mass conservation procedure. To account for changes in the thicknesses of the two phases as diffusion progresses, a variable grid technique developed by Murray and Landis is employed. These equations are expressed in finite difference form and solved numerically. Program NAD3 treats diffusion between pure metals which form a two-phase system with an intermediate third phase. Diffusion in the three-phase system is described by three partial differential expressions of Fick's second law and two interface-flux-balance equations. As with the two-phase case, a variable grid finite difference is used to numerically solve the diffusion equations. Computation time is minimized without sacrificing solution accuracy by treating the three-phase problem as a two-phase problem when the thickness of the intermediate phase is less than a preset value. Comparisons between these programs and other solutions have shown excellent agreement. The programs are written in FORTRAN IV for batch execution on the CDC 6600 with a central memory requirement of approximately 51K (octal) 60 bit words.

Numerical compliance testing of human exposure to electromagnetic radiation from smart-watches.

PubMed

Hong, Seon-Eui; Lee, Ae-Kyoung; Kwon, Jong-Hwa; Pack, Jeong-Ki

2016-10-07

In this study, we investigated the electromagnetic dosimetry for smart-watches. At present, the standard for compliance testing of body-mounted and handheld devices specifies the use of a flat phantom to provide conservative estimates of the peak spatial-averaged specific absorption rate (SAR). This means that the estimated SAR using a flat phantom should be higher than the SAR in the exposure part of an anatomical human-body model. To verify this, we numerically calculated the SAR for a flat phantom and compared it with the numerical calculation of the SAR for four anatomical human-body models of different ages. The numerical analysis was performed using the finite difference time domain method (FDTD). The smart-watch models were used in the three antennas: the shorted planar inverted-F antenna (PIFA), loop antenna, and monopole antenna. Numerical smart-watch models were implemented for cellular commutation and wireless local-area network operation at 835, 1850, and 2450 MHz. The peak spatial-averaged SARs of the smart-watch models are calculated for the flat phantom and anatomical human-body model for the wrist-worn and next to mouth positions. The results show that the flat phantom does not provide a consistent conservative SAR estimate. We concluded that the difference in the SAR results between an anatomical human-body model and a flat phantom can be attributed to the different phantom shapes and tissue structures.

Numerical compliance testing of human exposure to electromagnetic radiation from smart-watches

NASA Astrophysics Data System (ADS)

Hong, Seon-Eui; Lee, Ae-Kyoung; Kwon, Jong-Hwa; Pack, Jeong-Ki

2016-10-01

In this study, we investigated the electromagnetic dosimetry for smart-watches. At present, the standard for compliance testing of body-mounted and handheld devices specifies the use of a flat phantom to provide conservative estimates of the peak spatial-averaged specific absorption rate (SAR). This means that the estimated SAR using a flat phantom should be higher than the SAR in the exposure part of an anatomical human-body model. To verify this, we numerically calculated the SAR for a flat phantom and compared it with the numerical calculation of the SAR for four anatomical human-body models of different ages. The numerical analysis was performed using the finite difference time domain method (FDTD). The smart-watch models were used in the three antennas: the shorted planar inverted-F antenna (PIFA), loop antenna, and monopole antenna. Numerical smart-watch models were implemented for cellular commutation and wireless local-area network operation at 835, 1850, and 2450 MHz. The peak spatial-averaged SARs of the smart-watch models are calculated for the flat phantom and anatomical human-body model for the wrist-worn and next to mouth positions. The results show that the flat phantom does not provide a consistent conservative SAR estimate. We concluded that the difference in the SAR results between an anatomical human-body model and a flat phantom can be attributed to the different phantom shapes and tissue structures.

A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal-icosahedral and cubed sphere grids

NASA Astrophysics Data System (ADS)

Thuburn, J.; Cotter, C. J.; Dubos, T.

2013-12-01

A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a Crank-Nicolson time discretization of fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity (PV). The algorithm is implemented and tested on two families of grids: hexagonal-icosahedral Voronoi grids, and modified equiangular cubed-sphere grids. Results of a variety of tests are presented, including convergence of the discrete scalar Laplacian and Coriolis operators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of balance including vanishing ∇ × ∇, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1. In the most idealized tests the overall accuracy of the scheme appears to be limited by the accuracy of the Coriolis and other mimetic spatial operators, particularly on the cubed sphere grid. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.

A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal-icosahedral and cubed-sphere grids

NASA Astrophysics Data System (ADS)

Thuburn, J.; Cotter, C. J.; Dubos, T.

2014-05-01

A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a Crank-Nicolson time discretization of fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity (PV). The algorithm is implemented and tested on two families of grids: hexagonal-icosahedral Voronoi grids, and modified equiangular cubed-sphere grids. Results of a variety of tests are presented, including convergence of the discrete scalar Laplacian and Coriolis operators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of balance including vanishing ∇ × ∇, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1. In the most idealized tests the overall accuracy of the scheme appears to be limited by the accuracy of the Coriolis and other mimetic spatial operators, particularly on the cubed-sphere grid. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.

An arbitrary-order Runge–Kutta discontinuous Galerkin approach to reinitialization for banded conservative level sets

DOE PAGES

Jibben, Zechariah Joel; Herrmann, Marcus

2017-08-24

Here, we present a Runge-Kutta discontinuous Galerkin method for solving conservative reinitialization in the context of the conservative level set method. This represents an extension of the method recently proposed by Owkes and Desjardins [21], by solving the level set equations on the refined level set grid and projecting all spatially-dependent variables into the full basis used by the discontinuous Galerkin discretization. By doing so, we achieve the full k+1 order convergence rate in the L1 norm of the level set field predicted for RKDG methods given kth degree basis functions when the level set profile thickness is held constantmore » with grid refinement. Shape and volume errors for the 0.5-contour of the level set, on the other hand, are found to converge between first and second order. We show a variety of test results, including the method of manufactured solutions, reinitialization of a circle and sphere, Zalesak's disk, and deforming columns and spheres, all showing substantial improvements over the high-order finite difference traditional level set method studied for example by Herrmann. We also demonstrate the need for kth order accurate normal vectors, as lower order normals are found to degrade the convergence rate of the method.« less

Computer-Aided Engineering of Semiconductor Integrated Circuits

DTIC Science & Technology

1979-07-01

equation using a five point finite difference approximation. Section 4.3.6 describes the numerical techniques and iterative algorithms which are used...neighbor points. This is generally referred to as a five point finite difference scheme on a rectangular grid, as described below. The finite difference ...problems in steady state have been analyzed by the finite difference method [4. 16 ] [4.17 3 or finite element method [4. 18 3, [4. 19 3 as reported last

Program For Finite-Element Analyses Of Phase-Change Fluids

NASA Technical Reports Server (NTRS)

Viterna, L. A.

1995-01-01

PHASTRAN analyzes heat-transfer and flow behaviors of materials undergoing phase changes. Many phase changes operate over range of accelerations or effective gravitational fields. To analyze such thermal systems, it is necessary to obtain simultaneous solutions for equations of conservation of energy, momentum, and mass, and for equation of state. Written in APL2.

A cut-cell finite volume – finite element coupling approach for fluid–structure interaction in compressible flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pasquariello, Vito, E-mail: vito.pasquariello@tum.de; Hammerl, Georg; Örley, Felix

2016-02-15

We present a loosely coupled approach for the solution of fluid–structure interaction problems between a compressible flow and a deformable structure. The method is based on staggered Dirichlet–Neumann partitioning. The interface motion in the Eulerian frame is accounted for by a conservative cut-cell Immersed Boundary method. The present approach enables sub-cell resolution by considering individual cut-elements within a single fluid cell, which guarantees an accurate representation of the time-varying solid interface. The cut-cell procedure inevitably leads to non-matching interfaces, demanding for a special treatment. A Mortar method is chosen in order to obtain a conservative and consistent load transfer. Wemore » validate our method by investigating two-dimensional test cases comprising a shock-loaded rigid cylinder and a deformable panel. Moreover, the aeroelastic instability of a thin plate structure is studied with a focus on the prediction of flutter onset. Finally, we propose a three-dimensional fluid–structure interaction test case of a flexible inflated thin shell interacting with a shock wave involving large and complex structural deformations.« less

Critical spreading dynamics of parity conserving annihilating random walks with power-law branching

NASA Astrophysics Data System (ADS)

Laise, T.; dos Anjos, F. C.; Argolo, C.; Lyra, M. L.

2018-09-01

We investigate the critical spreading of the parity conserving annihilating random walks model with Lévy-like branching. The random walks are considered to perform normal diffusion with probability p on the sites of a one-dimensional lattice, annihilating in pairs by contact. With probability 1 - p, each particle can also produce two offspring which are placed at a distance r from the original site following a power-law Lévy-like distribution P(r) ∝ 1 /rα. We perform numerical simulations starting from a single particle. A finite-time scaling analysis is employed to locate the critical diffusion probability pc below which a finite density of particles is developed in the long-time limit. Further, we estimate the spreading dynamical exponents related to the increase of the average number of particles at the critical point and its respective fluctuations. The critical exponents deviate from those of the counterpart model with short-range branching for small values of α. The numerical data suggest that continuously varying spreading exponents sets up while the branching process still results in a diffusive-like spreading.

Multi-Hamiltonian structure of equations of hydrodynamic type

NASA Astrophysics Data System (ADS)

Gümral, H.; Nutku, Y.

1990-11-01

The discussion of the Hamiltonian structure of two-component equations of hydrodynamic type is completed by presenting the Hamiltonian operators for Euler's equation governing the motion of plane sound waves of finite amplitude and another quasilinear second-order wave equation. There exists a doubly infinite family of conserved Hamiltonians for the equations of gas dynamics that degenerate into one, namely, the Benney sequence, for shallow-water waves. Infinite sequences of conserved quantities for these equations are also presented. In the case of multicomponent equations of hydrodynamic type, it is shown, that Kodama's generalization of the shallow-water equations admits bi-Hamiltonian structure.

An axisymmetric PFEM formulation for bottle forming simulation

NASA Astrophysics Data System (ADS)

Ryzhakov, Pavel B.

2017-01-01

A numerical model for bottle forming simulation is proposed. It is based upon the Particle Finite Element Method (PFEM) and is developed for the simulation of bottles characterized by rotational symmetry. The PFEM strategy is adapted to suit the problem of interest. Axisymmetric version of the formulation is developed and a modified contact algorithm is applied. This results in a method characterized by excellent computational efficiency and volume conservation characteristics. The model is validated. An example modelling the final blow process is solved. Bottle wall thickness is estimated and the mass conservation of the method is analysed.

Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean.

PubMed

Beron-Vera, Francisco J; Olascoaga, María J; Haller, George; Farazmand, Mohammad; Triñanes, Joaquín; Wang, Yan

2015-08-01

Recent developments in dynamical systems theory have revealed long-lived and coherent Lagrangian (i.e., material) eddies in incompressible, satellite-derived surface ocean velocity fields. Paradoxically, observed drifting buoys and floating matter tend to create dissipative-looking patterns near oceanic eddies, which appear to be inconsistent with the conservative fluid particle patterns created by coherent Lagrangian eddies. Here, we show that inclusion of inertial effects (i.e., those produced by the buoyancy and size finiteness of an object) in a rotating two-dimensional incompressible flow context resolves this paradox. Specifically, we obtain that anticyclonic coherent Lagrangian eddies attract (repel) negatively (positively) buoyant finite-size particles, while cyclonic coherent Lagrangian eddies attract (repel) positively (negatively) buoyant finite-size particles. We show how these results explain dissipative-looking satellite-tracked surface drifter and subsurface float trajectories, as well as satellite-derived Sargassum distributions.

Renormalizability of the gradient flow in the 2D O(N) non-linear sigma model

NASA Astrophysics Data System (ADS)

Makino, Hiroki; Suzuki, Hiroshi

2015-03-01

It is known that the gauge field and its composite operators evolved by the Yang-Mills gradient flow are ultraviolet (UV) finite without any multiplicative wave function renormalization. In this paper, we prove that the gradient flow in the 2D O(N) non-linear sigma model possesses a similar property: The flowed N-vector field and its composite operators are UV finite without multiplicative wave function renormalization. Our proof in all orders of perturbation theory uses a (2+1)-dimensional field theoretical representation of the gradient flow, which possesses local gauge invariance without gauge field. As an application of the UV finiteness of the gradient flow, we construct the energy-momentum tensor in the lattice formulation of the O(N) non-linear sigma model that automatically restores the correct normalization and the conservation law in the continuum limit.

Three-Dimensional High-Order Spectral Finite Volume Method for Unstructured Grids

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel; Wang, Z. J.; Kwak, Dochan (Technical Monitor)

2002-01-01

Many areas require a very high-order accurate numerical solution of conservation laws for complex shapes. This paper deals with the extension to three dimensions of the Spectral Finite Volume (SV) method for unstructured grids, which was developed to solve such problems. We first summarize the limitations of traditional methods such as finite-difference, and finite-volume for both structured and unstructured grids. We then describe the basic formulation of the spectral finite volume method. What distinguishes the SV method from conventional high-order finite-volume methods for unstructured triangular or tetrahedral grids is the data reconstruction. Instead of using a large stencil of neighboring cells to perform a high-order reconstruction, the stencil is constructed by partitioning each grid cell, called a spectral volume (SV), into 'structured' sub-cells, called control volumes (CVs). One can show that if all the SV cells are partitioned into polygonal or polyhedral CV sub-cells in a geometrically similar manner, the reconstructions for all the SVs become universal, irrespective of their shapes, sizes, orientations, or locations. It follows that the reconstruction is reduced to a weighted sum of unknowns involving just a few simple adds and multiplies, and those weights are universal and can be pre-determined once for all. The method is thus very efficient, accurate, and yet geometrically flexible. The most critical part of the SV method is the partitioning of the SV into CVs. In this paper we present the partitioning of a tetrahedral SV into polyhedral CVs with one free parameter for polynomial reconstructions up to degree of precision five. (Note that the order of accuracy of the method is one order higher than the reconstruction degree of precision.) The free parameter will be determined by minimizing the Lebesgue constant of the reconstruction matrix or similar criteria to obtain optimized partitions. The details of an efficient, parallelizable code to solve three-dimensional problems for any order of accuracy are then presented. Important aspects of the data structure are discussed. Comparisons with the Discontinuous Galerkin (DG) method are made. Numerical examples for wave propagation problems are presented.

Moisture Transport in Composites during Repair Work,

DTIC Science & Technology

1983-09-01

4 * FINITE DIFFERENCE EQUATIONS. .. . . .. . .. .. .. .. .. 6 INI I A ANBOUNAAYYCONDITIONS................ 7 REASONABLE FIRST...DURING DRYING AND CURING . . . ........ 9 5 CONVERGENCE OF FINITE DIFFERENCE METHOD USING DIFFERENT At . . .. 12 6 CONVERGENCE OF FDA METHOD FOR SAME At...transport we will use a finite difference approach, changing the Fickian equation to a finite number of linear algebraic equations that can be solved by

Numerical Simulation of the 2004 Indian Ocean Tsunami: Accurate Flooding and drying in Banda Aceh

NASA Astrophysics Data System (ADS)

Cui, Haiyang; Pietrzak, Julie; Stelling, Guus; Androsov, Alexey; Harig, Sven

2010-05-01

The Indian Ocean Tsunami on December 26, 2004 caused one of the largest tsunamis in recent times and led to widespread devastation and loss of life. One of the worst hit regions was Banda Aceh, which is the capital of the Aceh province, located in the northern part of Sumatra, 150km from the source of the earthquake. A German-Indonesian Tsunami Early Warning System (GITEWS) (www.gitews.de) is currently under active development. The work presented here is carried out within the GITEWS framework. One of the aims of this project is the development of accurate models with which to simulate the propagation, flooding and drying, and run-up of a tsunami. In this context, TsunAWI has been developed by the Alfred Wegener Institute; it is an explicit, () finite element model. However, the accurate numerical simulation of flooding and drying requires the conservation of mass and momentum. This is not possible in the current version of TsunAWi. The P1NC - P1element guarantees mass conservation in a global sense, yet as we show here it is important to guarantee mass conservation at the local level, that is within each individual cell. Here an unstructured grid, finite volume ocean model is presented. It is derived from the P1NC - P1 element, and is shown to be mass and momentum conserving. Then a number of simulations are presented, including dam break problems flooding over both a wet and a dry bed. Excellent agreement is found. Then we present simulations for Banda Aceh, and compare the results to on-site survey data, as well as to results from the original TsunAWI code.

A Stabilized Finite Element Method for Modified Poisson-Nernst-Planck Equations to Determine Ion Flow Through a Nanopore

PubMed Central

Chaudhry, Jehanzeb Hameed; Comer, Jeffrey; Aksimentiev, Aleksei; Olson, Luke N.

2013-01-01

The conventional Poisson-Nernst-Planck equations do not account for the finite size of ions explicitly. This leads to solutions featuring unrealistically high ionic concentrations in the regions subject to external potentials, in particular, near highly charged surfaces. A modified form of the Poisson-Nernst-Planck equations accounts for steric effects and results in solutions with finite ion concentrations. Here, we evaluate numerical methods for solving the modified Poisson-Nernst-Planck equations by modeling electric field-driven transport of ions through a nanopore. We describe a novel, robust finite element solver that combines the applications of the Newton's method to the nonlinear Galerkin form of the equations, augmented with stabilization terms to appropriately handle the drift-diffusion processes. To make direct comparison with particle-based simulations possible, our method is specifically designed to produce solutions under periodic boundary conditions and to conserve the number of ions in the solution domain. We test our finite element solver on a set of challenging numerical experiments that include calculations of the ion distribution in a volume confined between two charged plates, calculations of the ionic current though a nanopore subject to an external electric field, and modeling the effect of a DNA molecule on the ion concentration and nanopore current. PMID:24363784

Comparison of finite-difference schemes for analysis of shells of revolution. [stress and free vibration analysis

NASA Technical Reports Server (NTRS)

Noor, A. K.; Stephens, W. B.

1973-01-01

Several finite difference schemes are applied to the stress and free vibration analysis of homogeneous isotropic and layered orthotropic shells of revolution. The study is based on a form of the Sanders-Budiansky first-approximation linear shell theory modified such that the effects of shear deformation and rotary inertia are included. A Fourier approach is used in which all the shell stress resultants and displacements are expanded in a Fourier series in the circumferential direction, and the governing equations reduce to ordinary differential equations in the meridional direction. While primary attention is given to finite difference schemes used in conjunction with first order differential equation formulation, comparison is made with finite difference schemes used with other formulations. These finite difference discretization models are compared with respect to simplicity of application, convergence characteristics, and computational efficiency. Numerical studies are presented for the effects of variations in shell geometry and lamination parameters on the accuracy and convergence of the solutions obtained by the different finite difference schemes. On the basis of the present study it is shown that the mixed finite difference scheme based on the first order differential equation formulation and two interlacing grids for the different fundamental unknowns combines a number of advantages over other finite difference schemes previously reported in the literature.

A projection gradient method for computing ground state of spin-2 Bose–Einstein condensates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Hanquan, E-mail: hanquan.wang@gmail.com; Yunnan Tongchang Scientific Computing and Data Mining Research Center, Kunming, Yunnan Province, 650221

In this paper, a projection gradient method is presented for computing ground state of spin-2 Bose–Einstein condensates (BEC). We first propose the general projection gradient method for solving energy functional minimization problem under multiple constraints, in which the energy functional takes real functions as independent variables. We next extend the method to solve a similar problem, where the energy functional now takes complex functions as independent variables. We finally employ the method into finding the ground state of spin-2 BEC. The key of our method is: by constructing continuous gradient flows (CGFs), the ground state of spin-2 BEC can bemore » computed as the steady state solution of such CGFs. We discretized the CGFs by a conservative finite difference method along with a proper way to deal with the nonlinear terms. We show that the numerical discretization is normalization and magnetization conservative and energy diminishing. Numerical results of the ground state and their energy of spin-2 BEC are reported to demonstrate the effectiveness of the numerical method.« less

Simulating compressible-incompressible two-phase flows

NASA Astrophysics Data System (ADS)

Denner, Fabian; van Wachem, Berend

2017-11-01

Simulating compressible gas-liquid flows, e.g. air-water flows, presents considerable numerical issues and requires substantial computational resources, particularly because of the stiff equation of state for the liquid and the different Mach number regimes. Treating the liquid phase (low Mach number) as incompressible, yet concurrently considering the gas phase (high Mach number) as compressible, can improve the computational performance of such simulations significantly without sacrificing important physical mechanisms. A pressure-based algorithm for the simulation of two-phase flows is presented, in which a compressible and an incompressible fluid are separated by a sharp interface. The algorithm is based on a coupled finite-volume framework, discretised in conservative form, with a compressive VOF method to represent the interface. The bulk phases are coupled via a novel acoustically-conservative interface discretisation method that retains the acoustic properties of the compressible phase and does not require a Riemann solver. Representative test cases are presented to scrutinize the proposed algorithm, including the reflection of acoustic waves at the compressible-incompressible interface, shock-drop interaction and gas-liquid flows with surface tension. Financial support from the EPSRC (Grant EP/M021556/1) is gratefully acknowledged.

HYDRA-II: A hydrothermal analysis computer code: Volume 3, Verification/validation assessments

DOE Office of Scientific and Technical Information (OSTI.GOV)

McCann, R.A.; Lowery, P.S.

1987-10-01

HYDRA-II is a hydrothermal computer code capable of three-dimensional analysis of coupled conduction, convection, and thermal radiation problems. This code is especially appropriate for simulating the steady-state performance of spent fuel storage systems. The code has been evaluated for this application for the US Department of Energy's Commercial Spent Fuel Management Program. HYDRA-II provides a finite difference solution in cartesian coordinates to the equations governing the conservation of mass, momentum, and energy. A cylindrical coordinate system may also be used to enclose the cartesian coordinate system. This exterior coordinate system is useful for modeling cylindrical cask bodies. The difference equationsmore » for conservation of momentum are enhanced by the incorporation of directional porosities and permeabilities that aid in modeling solid structures whose dimensions may be smaller than the computational mesh. The equation for conservation of energy permits modeling of orthotropic physical properties and film resistances. Several automated procedures are available to model radiation transfer within enclosures and from fuel rod to fuel rod. The documentation of HYDRA-II is presented in three separate volumes. Volume I - Equations and Numerics describes the basic differential equations, illustrates how the difference equations are formulated, and gives the solution procedures employed. Volume II - User's Manual contains code flow charts, discusses the code structure, provides detailed instructions for preparing an input file, and illustrates the operation of the code by means of a model problem. This volume, Volume III - Verification/Validation Assessments, provides a comparison between the analytical solution and the numerical simulation for problems with a known solution. This volume also documents comparisons between the results of simulations of single- and multiassembly storage systems and actual experimental data. 11 refs., 55 figs., 13 tabs.« less

Finite Element Methods and Multiphase Continuum Theory for Modeling 3D Air-Water-Sediment Interactions

NASA Astrophysics Data System (ADS)

Kees, C. E.; Miller, C. T.; Dimakopoulos, A.; Farthing, M.

2016-12-01

The last decade has seen an expansion in the development and application of 3D free surface flow models in the context of environmental simulation. These models are based primarily on the combination of effective algorithms, namely level set and volume-of-fluid methods, with high-performance, parallel computing. These models are still computationally expensive and suitable primarily when high-fidelity modeling near structures is required. While most research on algorithms and implementations has been conducted in the context of finite volume methods, recent work has extended a class of level set schemes to finite element methods on unstructured methods. This work considers models of three-phase flow in domains containing air, water, and granular phases. These multi-phase continuum mechanical formulations show great promise for applications such as analysis of coastal and riverine structures. This work will consider formulations proposed in the literature over the last decade as well as new formulations derived using the thermodynamically constrained averaging theory, an approach to deriving and closing macroscale continuum models for multi-phase and multi-component processes. The target applications require the ability to simulate wave breaking and structure over-topping, particularly fully three-dimensional, non-hydrostatic flows that drive these phenomena. A conservative level set scheme suitable for higher-order finite element methods is used to describe the air/water phase interaction. The interaction of these air/water flows with granular materials, such as sand and rubble, must also be modeled. The range of granular media dynamics targeted including flow and wave transmision through the solid media as well as erosion and deposition of granular media and moving bed dynamics. For the granular phase we consider volume- and time-averaged continuum mechanical formulations that are discretized with the finite element method and coupled to the underlying air/water flow via operator splitting (fractional step) schemes. Particular attention will be given to verification and validation of the numerical model and important qualitative features of the numerical methods including phase conservation, wave energy dissipation, and computational efficiency in regimes of interest.

Resource Optimization and World Peace. Occasional Paper 30.

ERIC Educational Resources Information Center

Purcell, Arthur H.

A comprehensive, international program is proposed to help nations optimize and conserve natural resources. The aim of the program is to increase the overall supply of natural resources available to improve the chances for world peace. The energy and material resources of the world are finite. We must live with and adapt to the concept of finite…

A total variation diminishing finite difference algorithm for sonic boom propagation models

NASA Technical Reports Server (NTRS)

Sparrow, Victor W.

1993-01-01

It is difficult to accurately model the rise phases of sonic boom waveforms with traditional finite difference algorithms because of finite difference phase dispersion. This paper introduces the concept of a total variation diminishing (TVD) finite difference method as a tool for accurately modeling the rise phases of sonic booms. A standard second order finite difference algorithm and its TVD modified counterpart are both applied to the one-way propagation of a square pulse. The TVD method clearly outperforms the non-TVD method, showing great potential as a new computational tool in the analysis of sonic boom propagation.

Optimal nonlinear filtering using the finite-volume method

NASA Astrophysics Data System (ADS)

Fox, Colin; Morrison, Malcolm E. K.; Norton, Richard A.; Molteno, Timothy C. A.

2018-01-01

Optimal sequential inference, or filtering, for the state of a deterministic dynamical system requires simulation of the Frobenius-Perron operator, that can be formulated as the solution of a continuity equation. For low-dimensional, smooth systems, the finite-volume numerical method provides a solution that conserves probability and gives estimates that converge to the optimal continuous-time values, while a Courant-Friedrichs-Lewy-type condition assures that intermediate discretized solutions remain positive density functions. This method is demonstrated in an example of nonlinear filtering for the state of a simple pendulum, with comparison to results using the unscented Kalman filter, and for a case where rank-deficient observations lead to multimodal probability distributions.

Progress on a Taylor weak statement finite element algorithm for high-speed aerodynamic flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Freels, J. D.

1989-01-01

A new finite element numerical Computational Fluid Dynamics (CFD) algorithm has matured to the point of efficiently solving two-dimensional high speed real-gas compressible flow problems in generalized coordinates on modern vector computer systems. The algorithm employs a Taylor Weak Statement classical Galerkin formulation, a variably implicit Newton iteration, and a tensor matrix product factorization of the linear algebra Jacobian under a generalized coordinate transformation. Allowing for a general two-dimensional conservation law system, the algorithm has been exercised on the Euler and laminar forms of the Navier-Stokes equations. Real-gas fluid properties are admitted, and numerical results verify solution accuracy, efficiency, and stability over a range of test problem parameters.

Multiple types of synchronization analysis for discontinuous Cohen-Grossberg neural networks with time-varying delays.

PubMed

Li, Jiarong; Jiang, Haijun; Hu, Cheng; Yu, Zhiyong

2018-03-01

This paper is devoted to the exponential synchronization, finite time synchronization, and fixed-time synchronization of Cohen-Grossberg neural networks (CGNNs) with discontinuous activations and time-varying delays. Discontinuous feedback controller and Novel adaptive feedback controller are designed to realize global exponential synchronization, finite time synchronization and fixed-time synchronization by adjusting the values of the parameters ω in the controller. Furthermore, the settling time of the fixed-time synchronization derived in this paper is less conservative and more accurate. Finally, some numerical examples are provided to show the effectiveness and flexibility of the results derived in this paper. Copyright © 2018 Elsevier Ltd. All rights reserved.

Accuracy of a class of concurrent algorithms for transient finite element analysis

NASA Technical Reports Server (NTRS)

Ortiz, Michael; Sotelino, Elisa D.; Nour-Omid, Bahram

1988-01-01

The accuracy of a new class of concurrent procedures for transient finite element analysis is examined. A phase error analysis is carried out which shows that wave retardation leading to unacceptable loss of accuracy may occur if a Courant condition based on the dimensions of the subdomains is violated. Numerical tests suggest that this Courant condition is conservative for typical structural applications and may lead to a marked increase in accuracy as the number of subdomains is increased. Theoretical speed-up ratios are derived which suggest that the algorithms under consideration can be expected to exhibit a performance superior to that of globally implicit methods when implemented on parallel machines.

SToRM: A Model for Unsteady Surface Hydraulics Over Complex Terrain

USGS Publications Warehouse

Simoes, Francisco J.

2014-01-01

A two-dimensional (depth-averaged) finite volume Godunov-type shallow water model developed for flow over complex topography is presented. The model is based on an unstructured cellcentered finite volume formulation and a nonlinear strong stability preserving Runge-Kutta time stepping scheme. The numerical discretization is founded on the classical and well established shallow water equations in hyperbolic conservative form, but the convective fluxes are calculated using auto-switching Riemann and diffusive numerical fluxes. The model’s implementation within a graphical user interface is discussed. Field application of the model is illustrated by utilizing it to estimate peak flow discharges in a flooding event of historic significance in Colorado, U.S.A., in 2013.

Finite Volume Algorithms for Heat Conduction

DTIC Science & Technology

2010-05-01

scalar quantity). Although (3) is relatively easy to discretize by using finite differences , its form in generalized coordinates is not. Later, we...familiar with the finite difference method for discretizing differential equations. In fact, the Newton divided difference is the numerical analog for a...expression (8) for the average derivative matches the Newton divided difference formula, so for uniform one-dimensional meshes, the finite volume and

A Kirchhoff Approach to Seismic Modeling and Prestack Depth Migration

DTIC Science & Technology

1993-05-01

continuation of sources and geophones by finite difference (S-G finite - difference migration ), are relatively slow and dip-limited. Compared to S-G... finite - difference migration , the Kirchhoff integral implements prestack migration relatively efficiently and has no dip limitation. Liu .Mlodeling and...for modeling and migration . In this paper, a finite - difference algorithm is used to calculate traveltimes and amplitudes. With the help of

Three-dimensional elastic wave analysis of the October 2, 2004 tremor at Mount St. Helens, Washington.

NASA Astrophysics Data System (ADS)

Denlinger, R. P.

2006-12-01

On October 2, 2004, three component, broad-frequency band seismometers as far as 250 km away from Mount St. Helens volcano detected a prominent low-frequency resonance associated with the onset of eruptive volcanic activity. The energy is dominantly in the 0.5 to 10 Hz range. Since gas emissions were low, I investigate a gas-free tremor mechanism generated by sudden extension of a pressurized, cylindrical, visco- elastic magma conduit beneath the mountain as it forces its way through a brittle crust. The concept is that rapid faulting of the crust around and above the magma results in a sudden drop in resistance and, consequently, a concurrent extension of the magma in the magma column at a rate greater than magma can resupply the column. The result is a rapid pressure drop in the magma, causing the column to oscillate and radiate elastic energy into the surrounding crust. The full wavefield generated by this physical mechanism is analyzed using the finite volume method of Leveque (2002), with the approximation outlined in Langseth and Leveque (2000) for hyperbolic conservation laws. In this method, the three-dimensional equations of elasticity are written as a first order set of conservation equations, with a solution vector composed of 3 velocity components and 6 stress components. The eigenvectors of the jacobian matrices of these conservation equations are used in a fourth-order Taylors series expansion of the solution vector around a small increment in time. This method is robust, allows waves to cleanly propagate off of a finite computational grid, and includes surface and interface waves. The method also allows for extremely large contrasts in elastic moduli across internal boundaries in the grid, necessary to accommodate the large variations in rigidity between a hot, visco-elastic magma at depth and the Earth's crust. Analyzing the October 2, 2004 tremor observed at Johnson Ridge Observatory, 9 km north of the mountain, for pressure drop in a 10 km long conduit, I obtain 0.3 +/- .05 MPa, which is consistent with elastic analysis of crustal deformation around the mountain during this time period. Langseth, J.O., and R.J. LeVeque, 2000, A wave propagation method for 3D hyperbolic conservation laws, J. Comp. Phys., 165, 126-166. Leveque, R.J., 2002, Finite volume methods for hyperbolic problems, Cambridge U. Press, 558 p.

Evaluation of finite difference and FFT-based solutions of the transport of intensity equation.

PubMed

Zhang, Hongbo; Zhou, Wen-Jing; Liu, Ying; Leber, Donald; Banerjee, Partha; Basunia, Mahmudunnabi; Poon, Ting-Chung

2018-01-01

A finite difference method is proposed for solving the transport of intensity equation. Simulation results show that although slower than fast Fourier transform (FFT)-based methods, finite difference methods are able to reconstruct the phase with better accuracy due to relaxed assumptions for solving the transport of intensity equation relative to FFT methods. Finite difference methods are also more flexible than FFT methods in dealing with different boundary conditions.

Distributed Relaxation for Conservative Discretizations

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2001-01-01

A multigrid method is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work that is a small (less than 10) multiple of the operation count in one target-grid residual evaluation. The way to achieve this efficiency is the distributed relaxation approach. TME solvers employing distributed relaxation have already been demonstrated for nonconservative formulations of high-Reynolds-number viscous incompressible and subsonic compressible flow regimes. The purpose of this paper is to provide foundations for applications of distributed relaxation to conservative discretizations. A direct correspondence between the primitive variable interpolations for calculating fluxes in conservative finite-volume discretizations and stencils of the discretized derivatives in the nonconservative formulation has been established. Based on this correspondence, one can arrive at a conservative discretization which is very efficiently solved with a nonconservative relaxation scheme and this is demonstrated for conservative discretization of the quasi one-dimensional Euler equations. Formulations for both staggered and collocated grid arrangements are considered and extensions of the general procedure to multiple dimensions are discussed.

Multiphase wavetrains, singular wave interactions and the emergence of the Korteweg–de Vries equation

PubMed Central

Bridges, Thomas J.

2016-01-01

Multiphase wavetrains are multiperiodic travelling waves with a set of distinct wavenumbers and distinct frequencies. In conservative systems, such families are associated with the conservation of wave action or other conservation law. At generic points (where the Jacobian of the wave action flux is non-degenerate), modulation of the wavetrain leads to the dispersionless multiphase conservation of wave action. The main result of this paper is that modulation of the multiphase wavetrain, when the Jacobian of the wave action flux vector is singular, morphs the vector-valued conservation law into the scalar Korteweg–de Vries (KdV) equation. The coefficients in the emergent KdV equation have a geometrical interpretation in terms of projection of the vector components of the conservation law. The theory herein is restricted to two phases to simplify presentation, with extensions to any finite dimension discussed in the concluding remarks. Two applications of the theory are presented: a coupled nonlinear Schrödinger equation and two-layer shallow-water hydrodynamics with a free surface. Both have two-phase solutions where criticality and the properties of the emergent KdV equation can be determined analytically. PMID:28119546

Interpolation methods and the accuracy of lattice-Boltzmann mesh refinement

DOE PAGES

Guzik, Stephen M.; Weisgraber, Todd H.; Colella, Phillip; ...

2013-12-10

A lattice-Boltzmann model to solve the equivalent of the Navier-Stokes equations on adap- tively refined grids is presented. A method for transferring information across interfaces between different grid resolutions was developed following established techniques for finite- volume representations. This new approach relies on a space-time interpolation and solving constrained least-squares problems to ensure conservation. The effectiveness of this method at maintaining the second order accuracy of lattice-Boltzmann is demonstrated through a series of benchmark simulations and detailed mesh refinement studies. These results exhibit smaller solution errors and improved convergence when compared with similar approaches relying only on spatial interpolation. Examplesmore » highlighting the mesh adaptivity of this method are also provided.« less

A modified Dodge algorithm for the parabolized Navier-Stokes equation and compressible duct flows

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1981-01-01

A revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition. Qualitive agreement with analytical predictions and experimental results was obtained for some flows with well-known solutions.

Numerical computation of space shuttle orbiter flow field

NASA Technical Reports Server (NTRS)

Tannehill, John C.

1988-01-01

A new parabolized Navier-Stokes (PNS) code has been developed to compute the hypersonic, viscous chemically reacting flow fields around 3-D bodies. The flow medium is assumed to be a multicomponent mixture of thermally perfect but calorically imperfect gases. The new PNS code solves the gas dynamic and species conservation equations in a coupled manner using a noniterative, implicit, approximately factored, finite difference algorithm. The space-marching method is made well-posed by special treatment of the streamwise pressure gradient term. The code has been used to compute hypersonic laminar flow of chemically reacting air over cones at angle of attack. The results of the computations are compared with the results of reacting boundary-layer computations and show excellent agreement.

A New Cell-Centered Implicit Numerical Scheme for Ions in the 2-D Axisymmetric Code Hall2de

NASA Technical Reports Server (NTRS)

Lopez Ortega, Alejandro; Mikellides, Ioannis G.

2014-01-01

We present a new algorithm in the Hall2De code to simulate the ion hydrodynamics in the acceleration channel and near plume regions of Hall-effect thrusters. This implementation constitutes an upgrade of the capabilities built in the Hall2De code. The equations of mass conservation and momentum for unmagnetized ions are solved using a conservative, finite-volume, cell-centered scheme on a magnetic-field-aligned grid. Major computational savings are achieved by making use of an implicit predictor/multi-corrector algorithm for time evolution. Inaccuracies in the prediction of the motion of low-energy ions in the near plume in hydrodynamics approaches are addressed by implementing a multi-fluid algorithm that tracks ions of different energies separately. A wide range of comparisons with measurements are performed to validate the new ion algorithms. Several numerical experiments with the location and value of the anomalous collision frequency are also presented. Differences in the plasma properties in the near-plume between the single fluid and multi-fluid approaches are discussed. We complete our validation by comparing predicted erosion rates at the channel walls of the thruster with measurements. Erosion rates predicted by the plasma properties obtained from simulations replicate accurately measured rates of erosion within the uncertainty range of the sputtering models employed.

A comparative study of finite element and finite difference methods for Cauchy-Riemann type equations

NASA Technical Reports Server (NTRS)

Fix, G. J.; Rose, M. E.

1983-01-01

A least squares formulation of the system divu = rho, curlu = zeta is surveyed from the viewpoint of both finite element and finite difference methods. Closely related arguments are shown to establish convergence estimates.

A-Posteriori Error Estimation for Hyperbolic Conservation Laws with Constraint

NASA Technical Reports Server (NTRS)

Barth, Timothy

2004-01-01

This lecture considers a-posteriori error estimates for the numerical solution of conservation laws with time invariant constraints such as those arising in magnetohydrodynamics (MHD) and gravitational physics. Using standard duality arguments, a-posteriori error estimates for the discontinuous Galerkin finite element method are then presented for MHD with solenoidal constraint. From these estimates, a procedure for adaptive discretization is outlined. A taxonomy of Green's functions for the linearized MHD operator is given which characterizes the domain of dependence for pointwise errors. The extension to other constrained systems such as the Einstein equations of gravitational physics are then considered. Finally, future directions and open problems are discussed.

A staggered-grid finite-difference scheme optimized in the time–space domain for modeling scalar-wave propagation in geophysical problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tan, Sirui, E-mail: siruitan@hotmail.com; Huang, Lianjie, E-mail: ljh@lanl.gov

For modeling scalar-wave propagation in geophysical problems using finite-difference schemes, optimizing the coefficients of the finite-difference operators can reduce numerical dispersion. Most optimized finite-difference schemes for modeling seismic-wave propagation suppress only spatial but not temporal dispersion errors. We develop a novel optimized finite-difference scheme for numerical scalar-wave modeling to control dispersion errors not only in space but also in time. Our optimized scheme is based on a new stencil that contains a few more grid points than the standard stencil. We design an objective function for minimizing relative errors of phase velocities of waves propagating in all directions within amore » given range of wavenumbers. Dispersion analysis and numerical examples demonstrate that our optimized finite-difference scheme is computationally up to 2.5 times faster than the optimized schemes using the standard stencil to achieve the similar modeling accuracy for a given 2D or 3D problem. Compared with the high-order finite-difference scheme using the same new stencil, our optimized scheme reduces 50 percent of the computational cost to achieve the similar modeling accuracy. This new optimized finite-difference scheme is particularly useful for large-scale 3D scalar-wave modeling and inversion.« less

Valence-bond theory of linear Hubbard and Pariser-Parr-Pople models

NASA Astrophysics Data System (ADS)

Soos, Z. G.; Ramasesha, S.

1984-05-01

The ground and low-lying states of finite quantum-cell models with one state per site are obtained exactly through a real-space basis of valence-bond (VB) diagrams that explicitly conserve the total spin. Regular and alternating Hubbard and Pariser-Parr-Pople (PPP) chains and rings with Ne electrons on N(<=12) sites are extrapolated to infinite arrays. The ground-state energy and optical gap of regular U=4|t| Hubbard chains agree with exact results, suggesting comparable accuracy for alternating Hubbard and PPP models, but differ from mean-field results. Molecular PPP parameters describe well the excitations of finite polyenes, odd polyene ions, linear cyanine dyes, and slightly overestimate the absorption peaks in polyacetylene (CH)x. Molecular correlations contrast sharply with uncorrelated descriptions of topological solitons, which are modeled by regular polyene radicals and their ions for both wide and narrow alternation crossovers. Neutral solitons have no midgap absorption and negative spin densities, while the intensity of the in-gap excitation of charged solitons is not enhanced. The properties of correlated states in quantum-cell models with one valence state per site are discussed in the adiabatic limit for excited-state geometries and instabilities to dimerization.

A WENO-solver combined with adaptive momentum discretization for the Wigner transport equation and its application to resonant tunneling diodes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dorda, Antonius, E-mail: dorda@tugraz.at; Schürrer, Ferdinand, E-mail: ferdinand.schuerrer@tugraz.at

2015-03-01

We present a novel numerical scheme for the deterministic solution of the Wigner transport equation, especially suited to deal with situations in which strong quantum effects are present. The unique feature of the algorithm is the expansion of the Wigner function in local basis functions, similar to finite element or finite volume methods. This procedure yields a discretization of the pseudo-differential operator that conserves the particle density on arbitrarily chosen grids. The high flexibility in refining the grid spacing together with the weighted essentially non-oscillatory (WENO) scheme for the advection term allows for an accurate and well-resolved simulation of themore » phase space dynamics. A resonant tunneling diode is considered as test case and a detailed convergence study is given by comparing the results to a non-equilibrium Green's functions calculation. The impact of the considered domain size and of the grid spacing is analyzed. The obtained convergence of the results towards a quasi-exact agreement of the steady state Wigner and Green's functions computations demonstrates the accuracy of the scheme, as well as the high flexibility to adjust to different physical situations.« less

A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models

DOE PAGES

Guerra, Jorge E.; Ullrich, Paul A.

2016-06-01

Atmospheric modeling systems require economical methods to solve the non-hydrostatic Euler equations. Two major differences between hydrostatic models and a full non-hydrostatic description lies in the vertical velocity tendency and numerical stiffness associated with sound waves. In this work we introduce a new arbitrary-order vertical discretization entitled the staggered nodal finite-element method (SNFEM). Our method uses a generalized discrete derivative that consistently combines the discontinuous Galerkin and spectral element methods on a staggered grid. Our combined method leverages the accurate wave propagation and conservation properties of spectral elements with staggered methods that eliminate stationary (2Δ x) modes. Furthermore, high-order accuracymore » also eliminates the need for a reference state to maintain hydrostatic balance. In this work we demonstrate the use of high vertical order as a means of improving simulation quality at relatively coarse resolution. We choose a test case suite that spans the range of atmospheric flows from predominantly hydrostatic to nonlinear in the large-eddy regime. Lastly, our results show that there is a distinct benefit in using the high-order vertical coordinate at low resolutions with the same robust properties as the low-order alternative.« less

A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guerra, Jorge E.; Ullrich, Paul A.

Atmospheric modeling systems require economical methods to solve the non-hydrostatic Euler equations. Two major differences between hydrostatic models and a full non-hydrostatic description lies in the vertical velocity tendency and numerical stiffness associated with sound waves. In this work we introduce a new arbitrary-order vertical discretization entitled the staggered nodal finite-element method (SNFEM). Our method uses a generalized discrete derivative that consistently combines the discontinuous Galerkin and spectral element methods on a staggered grid. Our combined method leverages the accurate wave propagation and conservation properties of spectral elements with staggered methods that eliminate stationary (2Δ x) modes. Furthermore, high-order accuracymore » also eliminates the need for a reference state to maintain hydrostatic balance. In this work we demonstrate the use of high vertical order as a means of improving simulation quality at relatively coarse resolution. We choose a test case suite that spans the range of atmospheric flows from predominantly hydrostatic to nonlinear in the large-eddy regime. Lastly, our results show that there is a distinct benefit in using the high-order vertical coordinate at low resolutions with the same robust properties as the low-order alternative.« less

CAM-SE: A scalable spectral element dynamical core for the Community Atmosphere Model.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dennis, John; Edwards, Jim; Evans, Kate J

2012-01-01

The Community Atmosphere Model (CAM) version 5 includes a spectral element dynamical core option from NCAR's High-Order Method Modeling Environment. It is a continuous Galerkin spectral finite element method designed for fully unstructured quadrilateral meshes. The current configurations in CAM are based on the cubed-sphere grid. The main motivation for including a spectral element dynamical core is to improve the scalability of CAM by allowing quasi-uniform grids for the sphere that do not require polar filters. In addition, the approach provides other state-of-the-art capabilities such as improved conservation properties. Spectral elements are used for the horizontal discretization, while most othermore » aspects of the dynamical core are a hybrid of well tested techniques from CAM's finite volume and global spectral dynamical core options. Here we first give a overview of the spectral element dynamical core as used in CAM. We then give scalability and performance results from CAM running with three different dynamical core options within the Community Earth System Model, using a pre-industrial time-slice configuration. We focus on high resolution simulations of 1/4 degree, 1/8 degree, and T340 spectral truncation.« less

Molecular finite-size effects in stochastic models of equilibrium chemical systems.

PubMed

Cianci, Claudia; Smith, Stephen; Grima, Ramon

2016-02-28

The reaction-diffusion master equation (RDME) is a standard modelling approach for understanding stochastic and spatial chemical kinetics. An inherent assumption is that molecules are point-like. Here, we introduce the excluded volume reaction-diffusion master equation (vRDME) which takes into account volume exclusion effects on stochastic kinetics due to a finite molecular radius. We obtain an exact closed form solution of the RDME and of the vRDME for a general chemical system in equilibrium conditions. The difference between the two solutions increases with the ratio of molecular diameter to the compartment length scale. We show that an increase in the fraction of excluded space can (i) lead to deviations from the classical inverse square root law for the noise-strength, (ii) flip the skewness of the probability distribution from right to left-skewed, (iii) shift the equilibrium of bimolecular reactions so that more product molecules are formed, and (iv) strongly modulate the Fano factors and coefficients of variation. These volume exclusion effects are found to be particularly pronounced for chemical species not involved in chemical conservation laws. Finally, we show that statistics obtained using the vRDME are in good agreement with those obtained from Brownian dynamics with excluded volume interactions.

A WENO-solver combined with adaptive momentum discretization for the Wigner transport equation and its application to resonant tunneling diodes

PubMed Central

Dorda, Antonius; Schürrer, Ferdinand

2015-01-01

We present a novel numerical scheme for the deterministic solution of the Wigner transport equation, especially suited to deal with situations in which strong quantum effects are present. The unique feature of the algorithm is the expansion of the Wigner function in local basis functions, similar to finite element or finite volume methods. This procedure yields a discretization of the pseudo-differential operator that conserves the particle density on arbitrarily chosen grids. The high flexibility in refining the grid spacing together with the weighted essentially non-oscillatory (WENO) scheme for the advection term allows for an accurate and well-resolved simulation of the phase space dynamics. A resonant tunneling diode is considered as test case and a detailed convergence study is given by comparing the results to a non-equilibrium Green's functions calculation. The impact of the considered domain size and of the grid spacing is analyzed. The obtained convergence of the results towards a quasi-exact agreement of the steady state Wigner and Green's functions computations demonstrates the accuracy of the scheme, as well as the high flexibility to adjust to different physical situations. PMID:25892748

A WENO-solver combined with adaptive momentum discretization for the Wigner transport equation and its application to resonant tunneling diodes.

PubMed

Dorda, Antonius; Schürrer, Ferdinand

2015-03-01

We present a novel numerical scheme for the deterministic solution of the Wigner transport equation, especially suited to deal with situations in which strong quantum effects are present. The unique feature of the algorithm is the expansion of the Wigner function in local basis functions, similar to finite element or finite volume methods. This procedure yields a discretization of the pseudo-differential operator that conserves the particle density on arbitrarily chosen grids. The high flexibility in refining the grid spacing together with the weighted essentially non-oscillatory (WENO) scheme for the advection term allows for an accurate and well-resolved simulation of the phase space dynamics. A resonant tunneling diode is considered as test case and a detailed convergence study is given by comparing the results to a non-equilibrium Green's functions calculation. The impact of the considered domain size and of the grid spacing is analyzed. The obtained convergence of the results towards a quasi-exact agreement of the steady state Wigner and Green's functions computations demonstrates the accuracy of the scheme, as well as the high flexibility to adjust to different physical situations.

Linear and nonlinear 2D finite element analysis of sloshing modes and pressures in rectangular tanks subject to horizontal harmonic motions

NASA Astrophysics Data System (ADS)

Virella, Juan C.; Prato, Carlos A.; Godoy, Luis A.

2008-05-01

The influence of nonlinear wave theory on the sloshing natural periods and their modal pressure distributions are investigated for rectangular tanks under the assumption of two-dimensional behavior. Natural periods and mode shapes are computed and compared for both linear wave theory (LWT) and nonlinear wave theory (NLWT) models, using the finite element package ABAQUS. Linear wave theory is implemented in an acoustic model, whereas a plane strain problem with large displacements is used in NLWT. Pressure distributions acting on the tank walls are obtained for the first three sloshing modes using both linear and nonlinear wave theory. It is found that the nonlinearity does not have significant effects on the natural sloshing periods. For the sloshing pressures on the tank walls, different distributions were found using linear and nonlinear wave theory models. However, in all cases studied, the linear wave theory conservatively estimated the magnitude of the pressure distribution, whereas larger pressures resultant heights were obtained when using the nonlinear theory. It is concluded that the nonlinearity of the surface wave does not have major effects in the pressure distribution on the walls for rectangular tanks.

Statistical mechanical foundation of the peridynamic nonlocal continuum theory: energy and momentum conservation laws.

PubMed

Lehoucq, R B; Sears, Mark P

2011-09-01

The purpose of this paper is to derive the energy and momentum conservation laws of the peridynamic nonlocal continuum theory using the principles of classical statistical mechanics. The peridynamic laws allow the consideration of discontinuous motion, or deformation, by relying on integral operators. These operators sum forces and power expenditures separated by a finite distance and so represent nonlocal interaction. The integral operators replace the differential divergence operators conventionally used, thereby obviating special treatment at points of discontinuity. The derivation presented employs a general multibody interatomic potential, avoiding the standard assumption of a pairwise decomposition. The integral operators are also expressed in terms of a stress tensor and heat flux vector under the assumption that these fields are differentiable, demonstrating that the classical continuum energy and momentum conservation laws are consequences of the more general peridynamic laws. An important conclusion is that nonlocal interaction is intrinsic to continuum conservation laws when derived using the principles of statistical mechanics.

Numerical Modeling of Saturated Boiling in a Heated Tube

NASA Technical Reports Server (NTRS)

Majumdar, Alok; LeClair, Andre; Hartwig, Jason

2017-01-01

This paper describes a mathematical formulation and numerical solution of boiling in a heated tube. The mathematical formulation involves a discretization of the tube into a flow network consisting of fluid nodes and branches and a thermal network consisting of solid nodes and conductors. In the fluid network, the mass, momentum and energy conservation equations are solved and in the thermal network, the energy conservation equation of solids is solved. A pressure-based, finite-volume formulation has been used to solve the equations in the fluid network. The system of equations is solved by a hybrid numerical scheme which solves the mass and momentum conservation equations by a simultaneous Newton-Raphson method and the energy conservation equation by a successive substitution method. The fluid network and thermal network are coupled through heat transfer between the solid and fluid nodes which is computed by Chen's correlation of saturated boiling heat transfer. The computer model is developed using the Generalized Fluid System Simulation Program and the numerical predictions are compared with test data.

Higher-order jump conditions for conservation laws

NASA Astrophysics Data System (ADS)

Oksuzoglu, Hakan

2018-04-01

The hyperbolic conservation laws admit discontinuous solutions where the solution variables can have finite jumps in space and time. The jump conditions for conservation laws are expressed in terms of the speed of the discontinuity and the state variables on both sides. An example from the Gas Dynamics is the Rankine-Hugoniot conditions for the shock speed. Here, we provide an expression for the acceleration of the discontinuity in terms of the state variables and their spatial derivatives on both sides. We derive a jump condition for the shock acceleration. Using this general expression, we show how to obtain explicit shock acceleration formulas for nonlinear hyperbolic conservation laws. We start with the Burgers' equation and check the derived formula with an analytical solution. We next derive formulas for the Shallow Water Equations and the Euler Equations of Gas Dynamics. We will verify our formulas for the Euler Equations using an exact solution for the spherically symmetric blast wave problem. In addition, we discuss the potential use of these formulas for the implementation of shock fitting methods.

Inverse Jacobi multiplier as a link between conservative systems and Poisson structures

NASA Astrophysics Data System (ADS)

García, Isaac A.; Hernández-Bermejo, Benito

2017-08-01

Some aspects of the relationship between conservativeness of a dynamical system (namely the preservation of a finite measure) and the existence of a Poisson structure for that system are analyzed. From the local point of view, due to the flow-box theorem we restrict ourselves to neighborhoods of singularities. In this sense, we characterize Poisson structures around the typical zero-Hopf singularity in dimension 3 under the assumption of having a local analytic first integral with non-vanishing first jet by connecting with the classical Poincaré center problem. From the global point of view, we connect the property of being strictly conservative (the invariant measure must be positive) with the existence of a Poisson structure depending on the phase space dimension. Finally, weak conservativeness in dimension two is introduced by the extension of inverse Jacobi multipliers as weak solutions of its defining partial differential equation and some of its applications are developed. Examples including Lotka-Volterra systems, quadratic isochronous centers, and non-smooth oscillators are provided.

Quantum reference frames and their applications to thermodynamics.

PubMed

Popescu, Sandu; Sainz, Ana Belén; Short, Anthony J; Winter, Andreas

2018-07-13

We construct a quantum reference frame, which can be used to approximately implement arbitrary unitary transformations on a system in the presence of any number of extensive conserved quantities, by absorbing any back action provided by the conservation laws. Thus, the reference frame at the same time acts as a battery for the conserved quantities. Our construction features a physically intuitive, clear and implementation-friendly realization. Indeed, the reference system is composed of the same types of subsystems as the original system and is finite for any desired accuracy. In addition, the interaction with the reference frame can be broken down into two-body terms coupling the system to one of the reference frame subsystems at a time. We apply this construction to quantum thermodynamic set-ups with multiple, possibly non-commuting conserved quantities, which allows for the definition of explicit batteries in such cases.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

A point-value enhanced finite volume method based on approximate delta functions

NASA Astrophysics Data System (ADS)

Xuan, Li-Jun; Majdalani, Joseph

2018-02-01

We revisit the concept of an approximate delta function (ADF), introduced by Huynh (2011) [1], in the form of a finite-order polynomial that holds identical integral properties to the Dirac delta function when used in conjunction with a finite-order polynomial integrand over a finite domain. We show that the use of generic ADF polynomials can be effective at recovering and generalizing several high-order methods, including Taylor-based and nodal-based Discontinuous Galerkin methods, as well as the Correction Procedure via Reconstruction. Based on the ADF concept, we then proceed to formulate a Point-value enhanced Finite Volume (PFV) method, which stores and updates the cell-averaged values inside each element as well as the unknown quantities and, if needed, their derivatives on nodal points. The sharing of nodal information with surrounding elements saves the number of degrees of freedom compared to other compact methods at the same order. To ensure conservation, cell-averaged values are updated using an identical approach to that adopted in the finite volume method. Here, the updating of nodal values and their derivatives is achieved through an ADF concept that leverages all of the elements within the domain of integration that share the same nodal point. The resulting scheme is shown to be very stable at successively increasing orders. Both accuracy and stability of the PFV method are verified using a Fourier analysis and through applications to the linear wave and nonlinear Burgers' equations in one-dimensional space.

An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kühnlein, Christian, E-mail: christian.kuehnlein@ecmwf.int; Smolarkiewicz, Piotr K., E-mail: piotr.smolarkiewicz@ecmwf.int

An advancement of the unstructured-mesh finite-volume MPDATA (Multidimensional Positive Definite Advection Transport Algorithm) is presented that formulates the error-compensative pseudo-velocity of the scheme to rely only on face-normal advective fluxes to the dual cells, in contrast to the full vector employed in previous implementations. This is essentially achieved by expressing the temporal truncation error underlying the pseudo-velocity in a form consistent with the flux-divergence of the governing conservation law. The development is especially important for integrating fluid dynamics equations on non-rectilinear meshes whenever face-normal advective mass fluxes are employed for transport compatible with mass continuity—the latter being essential for flux-formmore » schemes. In particular, the proposed formulation enables large-time-step semi-implicit finite-volume integration of the compressible Euler equations using MPDATA on arbitrary hybrid computational meshes. Furthermore, it facilitates multiple error-compensative iterations of the finite-volume MPDATA and improved overall accuracy. The advancement combines straightforwardly with earlier developments, such as the nonoscillatory option, the infinite-gauge variant, and moving curvilinear meshes. A comprehensive description of the scheme is provided for a hybrid horizontally-unstructured vertically-structured computational mesh for efficient global atmospheric flow modelling. The proposed finite-volume MPDATA is verified using selected 3D global atmospheric benchmark simulations, representative of hydrostatic and non-hydrostatic flow regimes. Besides the added capabilities, the scheme retains fully the efficacy of established finite-volume MPDATA formulations.« less

Application of a trigonometric finite difference procedure to numerical analysis of compressive and shear buckling of orthotropic panels

NASA Technical Reports Server (NTRS)

Stein, M.; Housner, J. D.

1978-01-01

A numerical analysis developed for the buckling of rectangular orthotropic layered panels under combined shear and compression is described. This analysis uses a central finite difference procedure based on trigonometric functions instead of using the conventional finite differences which are based on polynomial functions. Inasmuch as the buckle mode shape is usually trigonometric in nature, the analysis using trigonometric finite differences can be made to exhibit a much faster convergence rate than that using conventional differences. Also, the trigonometric finite difference procedure leads to difference equations having the same form as conventional finite differences; thereby allowing available conventional finite difference formulations to be converted readily to trigonometric form. For two-dimensional problems, the procedure introduces two numerical parameters into the analysis. Engineering approaches for the selection of these parameters are presented and the analysis procedure is demonstrated by application to several isotropic and orthotropic panel buckling problems. Among these problems is the shear buckling of stiffened isotropic and filamentary composite panels in which the stiffener is broken. Results indicate that a break may degrade the effect of the stiffener to the extent that the panel will not carry much more load than if the stiffener were absent.

Efficiency trade-offs of steady-state methods using FEM and FDM. [iterative solutions for nonlinear flow equations

NASA Technical Reports Server (NTRS)

Gartling, D. K.; Roache, P. J.

1978-01-01

The efficiency characteristics of finite element and finite difference approximations for the steady-state solution of the Navier-Stokes equations are examined. The finite element method discussed is a standard Galerkin formulation of the incompressible, steady-state Navier-Stokes equations. The finite difference formulation uses simple centered differences that are O(delta x-squared). Operation counts indicate that a rapidly converging Newton-Raphson-Kantorovitch iteration scheme is generally preferable over a Picard method. A split NOS Picard iterative algorithm for the finite difference method was most efficient.

Targeted ENO schemes with tailored resolution property for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Fu, Lin; Hu, Xiangyu Y.; Adams, Nikolaus A.

2017-11-01

In this paper, we extend the range of targeted ENO (TENO) schemes (Fu et al. (2016) [18]) by proposing an eighth-order TENO8 scheme. A general formulation to construct the high-order undivided difference τK within the weighting strategy is proposed. With the underlying scale-separation strategy, sixth-order accuracy for τK in the smooth solution regions is designed for good performance and robustness. Furthermore, a unified framework to optimize independently the dispersion and dissipation properties of high-order finite-difference schemes is proposed. The new framework enables tailoring of dispersion and dissipation as function of wavenumber. The optimal linear scheme has minimum dispersion error and a dissipation error that satisfies a dispersion-dissipation relation. Employing the optimal linear scheme, a sixth-order TENO8-opt scheme is constructed. A set of benchmark cases involving strong discontinuities and broadband fluctuations is computed to demonstrate the high-resolution properties of the new schemes.

Radiation-stimulated explosive evaporation and burning of hydrogen droplets in hot aerosol mixtures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Osipov, V. V.; Marchenko, M. P.; Khasin, M.

2016-06-13

We present results of analytical and numerical investigation of explosive evaporation and burning scenarios of hydrogen droplets in hydrogen/oxygen aerosols. The following two scenarios have been elucidated. The first scenario, corresponding to sufficiently large droplets, is characterized by three stages: (i) an essentially homogeneous heating of a droplet to a near-critical temperature by IR radiation from the hot gas; (ii) explosive evaporation; and (iii) burning of hydrogen cloud formed by evaporation. The second scenario, corresponding to small droplets, differs in that a droplet is heated mainly by thermal conduction from the hot gas. The heating is accompanied by evaporation whichmore » can become explosive at the final stage of evaporation. The crossover droplet size separating the two scenarios is calculated. Conservative finite-difference numerical analysis is used to explore the predicted scenarios and verify analytical estimates.« less

The Benard problem: A comparison of finite difference and spectral collocation eigen value solutions

NASA Technical Reports Server (NTRS)

Skarda, J. Raymond Lee; Mccaughan, Frances E.; Fitzmaurice, Nessan

1995-01-01

The application of spectral methods, using a Chebyshev collocation scheme, to solve hydrodynamic stability problems is demonstrated on the Benard problem. Implementation of the Chebyshev collocation formulation is described. The performance of the spectral scheme is compared with that of a 2nd order finite difference scheme. An exact solution to the Marangoni-Benard problem is used to evaluate the performance of both schemes. The error of the spectral scheme is at least seven orders of magnitude smaller than finite difference error for a grid resolution of N = 15 (number of points used). The performance of the spectral formulation far exceeded the performance of the finite difference formulation for this problem. The spectral scheme required only slightly more effort to set up than the 2nd order finite difference scheme. This suggests that the spectral scheme may actually be faster to implement than higher order finite difference schemes.

A Space-Time Conservation Element and Solution Element Method for Solving the Two- and Three-Dimensional Unsteady Euler Equations Using Quadrilateral and Hexahedral Meshes

NASA Technical Reports Server (NTRS)

Zhang, Zeng-Chan; Yu, S. T. John; Chang, Sin-Chung; Jorgenson, Philip (Technical Monitor)

2001-01-01

In this paper, we report a version of the Space-Time Conservation Element and Solution Element (CE/SE) Method in which the 2D and 3D unsteady Euler equations are simulated using structured or unstructured quadrilateral and hexahedral meshes, respectively. In the present method, mesh values of flow variables and their spatial derivatives are treated as independent unknowns to be solved for. At each mesh point, the value of a flow variable is obtained by imposing a flux conservation condition. On the other hand, the spatial derivatives are evaluated using a finite-difference/weighted-average procedure. Note that the present extension retains many key advantages of the original CE/SE method which uses triangular and tetrahedral meshes, respectively, for its 2D and 3D applications. These advantages include efficient parallel computing ease of implementing non-reflecting boundary conditions, high-fidelity resolution of shocks and waves, and a genuinely multidimensional formulation without using a dimensional-splitting approach. In particular, because Riemann solvers, the cornerstones of the Godunov-type upwind schemes, are not needed to capture shocks, the computational logic of the present method is considerably simpler. To demonstrate the capability of the present method, numerical results are presented for several benchmark problems including oblique shock reflection, supersonic flow over a wedge, and a 3D detonation flow.

77 FR 24539 - Virginia Electric and Power Company; Surry Power Station Units 1 and 2; Independent Spent Fuel...

Federal Register 2010, 2011, 2012, 2013, 2014

2012-04-24

... bounding thermal analysis using ANSYS finite element software to evaluate the misloading events. The ANSYS analysis consists of a half-symmetric, three-dimensional model of a 32PTH DSC with a number of conservative... the maximum fuel cladding temperature presented in the UFSAR analysis dated October 2, 2009, with the...

Ash3d: A finite-volume, conservative numerical model for ash transport and tephra deposition

USGS Publications Warehouse

Schwaiger, Hans F.; Denlinger, Roger P.; Mastin, Larry G.

2012-01-01

We develop a transient, 3-D Eulerian model (Ash3d) to predict airborne volcanic ash concentration and tephra deposition during volcanic eruptions. This model simulates downwind advection, turbulent diffusion, and settling of ash injected into the atmosphere by a volcanic eruption column. Ash advection is calculated using time-varying pre-existing wind data and a robust, high-order, finite-volume method. Our routine is mass-conservative and uses the coordinate system of the wind data, either a Cartesian system local to the volcano or a global spherical system for the Earth. Volcanic ash is specified with an arbitrary number of grain sizes, which affects the fall velocity, distribution and duration of transport. Above the source volcano, the vertical mass distribution with elevation is calculated using a Suzuki distribution for a given plume height, eruptive volume, and eruption duration. Multiple eruptions separated in time may be included in a single simulation. We test the model using analytical solutions for transport. Comparisons of the predicted and observed ash distributions for the 18 August 1992 eruption of Mt. Spurr in Alaska demonstrate to the efficacy and efficiency of the routine.

A Second Law Based Unstructured Finite Volume Procedure for Generalized Flow Simulation

NASA Technical Reports Server (NTRS)

Majumdar, Alok

1998-01-01

An unstructured finite volume procedure has been developed for steady and transient thermo-fluid dynamic analysis of fluid systems and components. The procedure is applicable for a flow network consisting of pipes and various fittings where flow is assumed to be one dimensional. It can also be used to simulate flow in a component by modeling a multi-dimensional flow using the same numerical scheme. The flow domain is discretized into a number of interconnected control volumes located arbitrarily in space. The conservation equations for each control volume account for the transport of mass, momentum and entropy from the neighboring control volumes. In addition, they also include the sources of each conserved variable and time dependent terms. The source term of entropy equation contains entropy generation due to heat transfer and fluid friction. Thermodynamic properties are computed from the equation of state of a real fluid. The system of equations is solved by a hybrid numerical method which is a combination of simultaneous Newton-Raphson and successive substitution schemes. The paper also describes the application and verification of the procedure by comparing its predictions with the analytical and numerical solution of several benchmark problems.

Nonconservative and reverse spectral transfer in Hasegawa-Mima turbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Terry, P.W.; Newman, D.E.

1993-01-01

The dual cascade is generally represented as a conservative cascade of enstrophy to short wavelengths through an enstrophy similarity range and an inverse cascade of energy to long wavelengths through an energy similarity range. This picture, based on a proof due to Kraichnan [Phys. Fluids 10, 1417 (1967)], is found to be significantly modified for a spectra of finite extent. Dimensional arguments and direct measurement of spectral flow in Hasegawa-Mima turbulence indicate that for both the energy and enstrophy cascades, transfer of the conserved quantity is accompanied by a nonconservative transfer of the other quantity. The decrease of a givenmore » invariant (energy or enstrophy) in the nonconservative transfer in one similarity range is balanced by the increase of that quantity in the other similarity range, thus maintaining net invariance. The increase or decrease of a given invariant quantity in one similarity range depends on the injection scale and is consistent with that quantity being carried in a self-similar transfer of the other invariant quantity. This leads, in an inertial range of finite size, to some energy being carried to small scales and some enstrophy being carried to large scales.« less

Nonconservative and reverse spectral transfer in Hasegawa--Mima turbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Terry, P.W.; Newman, D.E.

1993-07-01

The dual cascade is generally represented as a conservative cascade of enstrophy to short wavelengths through an enstrophy similarity range and an inverse cascade of energy to long wavelengths through an energy similarity range. This picture, based on a proof due to Kraichnan [Phys. Fluids [bold 10], 1417 (1967)], is found to be significantly modified for spectra of finite extent. Dimensional arguments and direct measurement of spectral flow in Hasegawa--Mima turbulence indicate that for both the energy and enstrophy cascades, transfer of the conserved quantity is accompanied by a nonconservative transfer of the other quantity. The decrease of a givenmore » invariant (energy or enstrophy) in the nonconservative transfer in one similarity range is balanced by the increase of that quantity in the other similarity range, thus maintaining net invariance. The increase or decrease of a given invariant quantity in one similarity range depends on the injection scale and is consistent with that quantity being carried in a self-similar transfer of the other invariant quantity. This leads, in an inertial range of finite size, to some energy being carried to small scales and some enstrophy being carried to large scales.« less

ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Fambri, F.; Dumbser, M.; Köppel, S.; Rezzolla, L.; Zanotti, O.

2018-07-01

We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved space-times. In this paper, we assume the background space-time to be given and static, i.e. we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local time-stepping. In order to deal with shock waves and other discontinuities, the high-order DG schemes are supplemented with a novel a posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed space-times. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.

ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Fambri, F.; Dumbser, M.; Köppel, S.; Rezzolla, L.; Zanotti, O.

2018-03-01

We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved spacetimes. In this paper we assume the background spacetime to be given and static, i.e. we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully-discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local timestepping. In order to deal with shock waves and other discontinuities, the high-order DG schemes are supplemented with a novel a-posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed spacetimes. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.

Accurate, meshless methods for magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Hopkins, Philip F.; Raives, Matthias J.

2016-01-01

Recently, we explored new meshless finite-volume Lagrangian methods for hydrodynamics: the `meshless finite mass' (MFM) and `meshless finite volume' (MFV) methods; these capture advantages of both smoothed particle hydrodynamics (SPH) and adaptive mesh refinement (AMR) schemes. We extend these to include ideal magnetohydrodynamics (MHD). The MHD equations are second-order consistent and conservative. We augment these with a divergence-cleaning scheme, which maintains nabla \\cdot B≈ 0. We implement these in the code GIZMO, together with state-of-the-art SPH MHD. We consider a large test suite, and show that on all problems the new methods are competitive with AMR using constrained transport (CT) to ensure nabla \\cdot B=0. They correctly capture the growth/structure of the magnetorotational instability, MHD turbulence, and launching of magnetic jets, in some cases converging more rapidly than state-of-the-art AMR. Compared to SPH, the MFM/MFV methods exhibit convergence at fixed neighbour number, sharp shock-capturing, and dramatically reduced noise, divergence errors, and diffusion. Still, `modern' SPH can handle most test problems, at the cost of larger kernels and `by hand' adjustment of artificial diffusion. Compared to non-moving meshes, the new methods exhibit enhanced `grid noise' but reduced advection errors and diffusion, easily include self-gravity, and feature velocity-independent errors and superior angular momentum conservation. They converge more slowly on some problems (smooth, slow-moving flows), but more rapidly on others (involving advection/rotation). In all cases, we show divergence control beyond the Powell 8-wave approach is necessary, or all methods can converge to unphysical answers even at high resolution.

Effect of finite particle number sampling on baryon number fluctuations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Steinheimer, Jan; Koch, Volker

The effects of finite particle number sampling on the net baryon number cumulants, extracted from fluid dynamical simulations, are studied. The commonly used finite particle number sampling procedure introduces an additional Poissonian (or multinomial if global baryon number conservation is enforced) contribution which increases the extracted moments of the baryon number distribution. If this procedure is applied to a fluctuating fluid dynamics framework, one severely overestimates the actual cumulants. We show that the sampling of so-called test particles suppresses the additional contribution to the moments by at least one power of the number of test particles. We demonstrate this methodmore » in a numerical fluid dynamics simulation that includes the effects of spinodal decomposition due to a first-order phase transition. Furthermore, in the limit where antibaryons can be ignored, we derive analytic formulas which capture exactly the effect of particle sampling on the baryon number cumulants. These formulas may be used to test the various numerical particle sampling algorithms.« less

Numerical simulation of a flow-like landslide using the particle finite element method

NASA Astrophysics Data System (ADS)

Zhang, Xue; Krabbenhoft, Kristian; Sheng, Daichao; Li, Weichao

2015-01-01

In this paper, an actual landslide process that occurred in Southern China is simulated by a continuum approach, the particle finite element method (PFEM). The PFEM attempts to solve the boundary-value problems in the framework of solid mechanics, satisfying the governing equations including momentum conservation, displacement-strain relation, constitutive relation as well as the frictional contact between the sliding mass and the slip surface. To warrant the convergence behaviour of solutions, the problem is formulated as a mathematical programming problem, while the particle finite element procedure is employed to tackle the issues of mesh distortion and free-surface evolution. The whole procedure of the landslide, from initiation, sliding to deposition, is successfully reproduced by the continuum approach. It is shown that the density of the mass has little influence on the sliding process in the current landslide, whereas both the geometry and the roughness of the slip surface play important roles. Comparative studies are also conducted where a satisfactory agreement is obtained.

Effect of finite particle number sampling on baryon number fluctuations

DOE PAGES

Steinheimer, Jan; Koch, Volker

2017-09-28

The effects of finite particle number sampling on the net baryon number cumulants, extracted from fluid dynamical simulations, are studied. The commonly used finite particle number sampling procedure introduces an additional Poissonian (or multinomial if global baryon number conservation is enforced) contribution which increases the extracted moments of the baryon number distribution. If this procedure is applied to a fluctuating fluid dynamics framework, one severely overestimates the actual cumulants. We show that the sampling of so-called test particles suppresses the additional contribution to the moments by at least one power of the number of test particles. We demonstrate this methodmore » in a numerical fluid dynamics simulation that includes the effects of spinodal decomposition due to a first-order phase transition. Furthermore, in the limit where antibaryons can be ignored, we derive analytic formulas which capture exactly the effect of particle sampling on the baryon number cumulants. These formulas may be used to test the various numerical particle sampling algorithms.« less

Weak form of Stokes-Dirac structures and geometric discretization of port-Hamiltonian systems

NASA Astrophysics Data System (ADS)

Kotyczka, Paul; Maschke, Bernhard; Lefèvre, Laurent

2018-05-01

We present the mixed Galerkin discretization of distributed parameter port-Hamiltonian systems. On the prototypical example of hyperbolic systems of two conservation laws in arbitrary spatial dimension, we derive the main contributions: (i) A weak formulation of the underlying geometric (Stokes-Dirac) structure with a segmented boundary according to the causality of the boundary ports. (ii) The geometric approximation of the Stokes-Dirac structure by a finite-dimensional Dirac structure is realized using a mixed Galerkin approach and power-preserving linear maps, which define minimal discrete power variables. (iii) With a consistent approximation of the Hamiltonian, we obtain finite-dimensional port-Hamiltonian state space models. By the degrees of freedom in the power-preserving maps, the resulting family of structure-preserving schemes allows for trade-offs between centered approximations and upwinding. We illustrate the method on the example of Whitney finite elements on a 2D simplicial triangulation and compare the eigenvalue approximation in 1D with a related approach.

Split Space-Marching Finite-Volume Method for Chemically Reacting Supersonic Flow

NASA Technical Reports Server (NTRS)

Rizzi, Arthur W.; Bailey, Harry E.

1976-01-01

A space-marching finite-volume method employing a nonorthogonal coordinate system and using a split differencing scheme for calculating steady supersonic flow over aerodynamic shapes is presented. It is a second-order-accurate mixed explicit-implicit procedure that solves the inviscid adiabatic and nondiffusive equations for chemically reacting flow in integral conservation-law form. The relationship between the finite-volume and differential forms of the equations is examined and the relative merits of each discussed. The method admits initial Cauchy data situated on any arbitrary surface and integrates them forward along a general curvilinear coordinate, distorting and deforming the surface as it advances. The chemical kinetics term is split from the convective terms which are themselves dimensionally split, thereby freeing the fluid operators from the restricted step size imposed by the chemical reactions and increasing the computational efficiency. The accuracy of this splitting technique is analyzed, a sufficient stability criterion is established, a representative flow computation is discussed, and some comparisons are made with another method.

A high-order positivity-preserving single-stage single-step method for the ideal magnetohydrodynamic equations

NASA Astrophysics Data System (ADS)

Christlieb, Andrew J.; Feng, Xiao; Seal, David C.; Tang, Qi

2016-07-01

We propose a high-order finite difference weighted ENO (WENO) method for the ideal magnetohydrodynamics (MHD) equations. The proposed method is single-stage (i.e., it has no internal stages to store), single-step (i.e., it has no time history that needs to be stored), maintains a discrete divergence-free condition on the magnetic field, and has the capacity to preserve the positivity of the density and pressure. To accomplish this, we use a Taylor discretization of the Picard integral formulation (PIF) of the finite difference WENO method proposed in Christlieb et al. (2015) [23], where the focus is on a high-order discretization of the fluxes (as opposed to the conserved variables). We use the version where fluxes are expanded to third-order accuracy in time, and for the fluid variables space is discretized using the classical fifth-order finite difference WENO discretization. We use constrained transport in order to obtain divergence-free magnetic fields, which means that we simultaneously evolve the magnetohydrodynamic (that has an evolution equation for the magnetic field) and magnetic potential equations alongside each other, and set the magnetic field to be the (discrete) curl of the magnetic potential after each time step. In this work, we compute these derivatives to fourth-order accuracy. In order to retain a single-stage, single-step method, we develop a novel Lax-Wendroff discretization for the evolution of the magnetic potential, where we start with technology used for Hamilton-Jacobi equations in order to construct a non-oscillatory magnetic field. The end result is an algorithm that is similar to our previous work Christlieb et al. (2014) [8], but this time the time stepping is replaced through a Taylor method with the addition of a positivity-preserving limiter. Finally, positivity preservation is realized by introducing a parameterized flux limiter that considers a linear combination of high and low-order numerical fluxes. The choice of the free parameter is then given in such a way that the fluxes are limited towards the low-order solver until positivity is attained. Given the lack of additional degrees of freedom in the system, this positivity limiter lacks energy conservation where the limiter turns on. However, this ingredient can be dropped for problems where the pressure does not become negative. We present two and three dimensional numerical results for several standard test problems including a smooth Alfvén wave (to verify formal order of accuracy), shock tube problems (to test the shock-capturing ability of the scheme), Orszag-Tang, and cloud shock interactions. These results assert the robustness and verify the high-order of accuracy of the proposed scheme.

Practical aspects of prestack depth migration with finite differences

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ober, C.C.; Oldfield, R.A.; Womble, D.E.

1997-07-01

Finite-difference, prestack, depth migrations offers significant improvements over Kirchhoff methods in imaging near or under salt structures. The authors have implemented a finite-difference prestack depth migration algorithm for use on massively parallel computers which is discussed. The image quality of the finite-difference scheme has been investigated and suggested improvements are discussed. In this presentation, the authors discuss an implicit finite difference migration code, called Salvo, that has been developed through an ACTI (Advanced Computational Technology Initiative) joint project. This code is designed to be efficient on a variety of massively parallel computers. It takes advantage of both frequency and spatialmore » parallelism as well as the use of nodes dedicated to data input/output (I/O). Besides giving an overview of the finite-difference algorithm and some of the parallelism techniques used, migration results using both Kirchhoff and finite-difference migration will be presented and compared. The authors start out with a very simple Cartoon model where one can intuitively see the multiple travel paths and some of the potential problems that will be encountered with Kirchhoff migration. More complex synthetic models as well as results from actual seismic data from the Gulf of Mexico will be shown.« less

The Impact of Varying the Physics Grid Resolution Relative to the Dynamical Core Resolution in CAM-SE-CSLAM

NASA Astrophysics Data System (ADS)

Herrington, A. R.; Lauritzen, P. H.; Reed, K. A.

2017-12-01

The spectral element dynamical core of the Community Atmosphere Model (CAM) has recently been coupled to an approximately isotropic, finite-volume grid per implementation of the conservative semi-Lagrangian multi-tracer transport scheme (CAM-SE-CSLAM; Lauritzen et al. 2017). In this framework, the semi-Lagrangian transport of tracers are computed on the finite-volume grid, while the adiabatic dynamics are solved using the spectral element grid. The physical parameterizations are evaluated on the finite-volume grid, as opposed to the unevenly spaced Gauss-Lobatto-Legendre nodes of the spectral element grid. Computing the physics on the finite-volume grid reduces numerical artifacts such as grid imprinting, possibly because the forcing terms are no longer computed at element boundaries where the resolved dynamics are least smooth. The separation of the physics grid and the dynamics grid allows for a unique opportunity to understand the resolution sensitivity in CAM-SE-CSLAM. The observed large sensitivity of CAM to horizontal resolution is a poorly understood impediment to improved simulations of regional climate using global, variable resolution grids. Here, a series of idealized moist simulations are presented in which the finite-volume grid resolution is varied relative to the spectral element grid resolution in CAM-SE-CSLAM. The simulations are carried out at multiple spectral element grid resolutions, in part to provide a companion set of simulations, in which the spectral element grid resolution is varied relative to the finite-volume grid resolution, but more generally to understand if the sensitivity to the finite-volume grid resolution is consistent across a wider spectrum of resolved scales. Results are interpreted in the context of prior ideas regarding resolution sensitivity of global atmospheric models.

Energy Flux Positivity and Unitarity in Conformal Field Theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kulaxizi, Manuela; Parnachev, Andrei

2011-01-07

We show that in most conformal field theories the condition of the energy flux positivity, proposed by Hofman and Maldacena, is equivalent to the absence of ghosts. At finite temperature and large energy and momenta, the two-point functions of the stress energy tensor develop light like poles. The residues of the poles can be computed, as long as the only spin-two conserved current, which appears in the stress energy tensor operator-product expansion and acquires a nonvanishing expectation value at finite temperature, is the stress energy tensor. The condition for the residues to stay positive and the theory to remain ghost-freemore » is equivalent to the condition of positivity of energy flux.« less

A High Order Discontinuous Galerkin Method for 2D Incompressible Flows

NASA Technical Reports Server (NTRS)

Liu, Jia-Guo; Shu, Chi-Wang

1999-01-01

In this paper we introduce a high order discontinuous Galerkin method for two dimensional incompressible flow in vorticity streamfunction formulation. The momentum equation is treated explicitly, utilizing the efficiency of the discontinuous Galerkin method The streamfunction is obtained by a standard Poisson solver using continuous finite elements. There is a natural matching between these two finite element spaces, since the normal component of the velocity field is continuous across element boundaries. This allows for a correct upwinding gluing in the discontinuous Galerkin framework, while still maintaining total energy conservation with no numerical dissipation and total enstrophy stability The method is suitable for inviscid or high Reynolds number flows. Optimal error estimates are proven and verified by numerical experiments.

A 3-D turbulent flow analysis using finite elements with k-ɛ model

NASA Astrophysics Data System (ADS)

Okuda, H.; Yagawa, G.; Eguchi, Y.

1989-03-01

This paper describes the finite element turbulent flow analysis, which is suitable for three-dimensional large scale problems. The k-ɛ turbulence model as well as the conservation equations of mass and momentum are discretized in space using rather low order elements. Resulting coefficient matrices are evaluated by one-point quadrature in order to reduce the computational storage and the CPU cost. The time integration scheme based on the velocity correction method is employed to obtain steady state solutions. For the verification of this FEM program, two-dimensional plenum flow is simulated and compared with experiment. As the application to three-dimensional practical problems, the turbulent flows in the upper plenum of the fast breeder reactor are calculated for various boundary conditions.

Extended bounds limiter for high-order finite-volume schemes on unstructured meshes

NASA Astrophysics Data System (ADS)

Tsoutsanis, Panagiotis

2018-06-01

This paper explores the impact of the definition of the bounds of the limiter proposed by Michalak and Ollivier-Gooch in [56] (2009), for higher-order Monotone-Upstream Central Scheme for Conservation Laws (MUSCL) numerical schemes on unstructured meshes in the finite-volume (FV) framework. A new modification of the limiter is proposed where the bounds are redefined by utilising all the spatial information provided by all the elements in the reconstruction stencil. Numerical results obtained on smooth and discontinuous test problems of the Euler equations on unstructured meshes, highlight that the newly proposed extended bounds limiter exhibits superior performance in terms of accuracy and mesh sensitivity compared to the cell-based or vertex-based bounds implementations.

Numerical Modelling of Three-Fluid Flow Using The Level-set Method

NASA Astrophysics Data System (ADS)

Li, Hongying; Lou, Jing; Shang, Zhi

2014-11-01

This work presents a numerical model for simulation of three-fluid flow involving two different moving interfaces. These interfaces are captured using the level-set method via two different level-set functions. A combined formulation with only one set of conservation equations for the whole physical domain, consisting of the three different immiscible fluids, is employed. Numerical solution is performed on a fixed mesh using the finite volume method. Surface tension effect is incorporated using the Continuum Surface Force model. Validation of the present model is made against available results for stratified flow and rising bubble in a container with a free surface. Applications of the present model are demonstrated by a variety of three-fluid flow systems including (1) three-fluid stratified flow, (2) two-fluid stratified flow carrying the third fluid in the form of drops and (3) simultaneous rising and settling of two drops in a stationary third fluid. The work is supported by a Thematic and Strategic Research from A*STAR, Singapore (Ref. #: 1021640075).

Comparison of COBRA III-C and SABRE-1 (wire-wrap version) computational results with steady-state data from a 19-pin internally guard heated sodium-cooled bundle with a six-channel central blockage (THORS Bundle 3C). [LMFBR

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dearing, J F; Nelson, W R; Rose, S D

Computational thermal-hydraulic models of a 19-pin, electrically heated, wire-wrap liquid-metal fast breeder reactor test bundle were developed using two well-known subchannel analysis codes, COBRA III-C and SABRE-1 (wire-wrap version). These two codes use similar subchannel control volumes for the finite difference conservation equations but vary markedly in solution strategy and modeling capability. In particular, the empirical wire-wrap-forced diversion crossflow models are different. Surprisingly, however, crossflow velocity predictions of the two codes are very similar. Both codes show generally good agreement with experimental temperature data from a test in which a large radial temperature gradient was imposed. Differences between data andmore » code results are probably caused by experimental pin bowing, which is presently the limiting factor in validating coded empirical models.« less

Three-Dimensional High-Order Spectral Volume Method for Solving Maxwell's Equations on Unstructured Grids

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel; Wang, Z. J.

2004-01-01

A three-dimensional, high-order, conservative, and efficient discontinuous spectral volume (SV) method for the solutions of Maxwell's equations on unstructured grids is presented. The concept of discontinuous 2nd high-order loca1 representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) method, but instead of using a Galerkin finite-element formulation, the SV method is based on a finite-volume approach to attain a simpler formulation. Conventional unstructured finite-volume methods require data reconstruction based on the least-squares formulation using neighboring cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In the SV method, one starts with a relatively coarse grid of triangles or tetrahedra, called spectral volumes (SVs), and partition each SV into a number of structured subcells, called control volumes (CVs), that support a polynomial expansion of a desired degree of precision. The unknowns are cell averages over CVs. If all the SVs are partitioned in a geometrically similar manner, the reconstruction becomes universal as a weighted sum of unknowns, and only a few universal coefficients need to be stored for the surface integrals over CV faces. Since the solution is discontinuous across the SV boundaries, a Riemann solver is thus necessary to maintain conservation. In the paper, multi-parameter and symmetric SV partitions, up to quartic for triangle and cubic for tetrahedron, are first presented. The corresponding weight coefficients for CV face integrals in terms of CV cell averages for each partition are analytically determined. These discretization formulas are then applied to the integral form of the Maxwell equations. All numerical procedures for outer boundary, material interface, zonal interface, and interior SV face are unified with a single characteristic formulation. The load balancing in a massive parallel computing environment is therefore easier to achieve. A parameter is introduced in the Riemann solver to control the strength of the smoothing term. Important aspects of the data structure and its effects to communication and the optimum use of cache memory are discussed. Results will be presented for plane TE and TM waves incident on a perfectly conducting cylinder for up to fifth order of accuracy, and a plane wave incident on a perfectly conducting sphere for up to fourth order of accuracy. Comparisons are made with exact solutions for these cases.

Finite-Difference Solutions for Compressible Laminar Boundary-Layer Flows of a Dusty Gas over a Semi-Infinite Flat Plate.

DTIC Science & Technology

1986-08-01

AD-A174 952 FINITE - DIFFERENCE SOLUTIONS FOR CONPRESSIBLE LANINAR 1/2 BOUNDARY-LAYER FLOUS (U) TORONTO UNIV DOWNSVIEW (ONTARIO) INST FOR AEROSPACE...dilute dusty gas over a semi-infinite flat plate. Details are given of the impliit finite , difference schemes as well as the boundary conditions... FINITE - DIFFERENCE SOLUTIONS FOR COMPRESSIBLE LAMINAR BOUNDARY-LAYER FLOWS OF A DUSTY GAS OVER A SEMI-INFINITE FLAT PLATE by B. Y. Wang and I. I

Finite Mathematics and Discrete Mathematics: Is There a Difference?

ERIC Educational Resources Information Center

Johnson, Marvin L.

Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…

Improved methods of vibration analysis of pretwisted, airfoil blades

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.

1984-01-01

Vibration analysis of pretwisted blades of asymmetric airfoil cross section is performed by using two mixed variational approaches. Numerical results obtained from these two methods are compared to those obtained from an improved finite difference method and also to those given by the ordinary finite difference method. The relative merits, convergence properties and accuracies of all four methods are studied and discussed. The effects of asymmetry and pretwist on natural frequencies and mode shapes are investigated. The improved finite difference method is shown to be far superior to the conventional finite difference method in several respects. Close lower bound solutions are provided by the improved finite difference method for untwisted blades with a relatively coarse mesh while the mixed methods have not indicated any specific bound.

Numerical Modeling of Flow Distribution in Micro-Fluidics Systems

NASA Technical Reports Server (NTRS)

Majumdar, Alok; Cole, Helen; Chen, C. P.

2005-01-01

This paper describes an application of a general purpose computer program, GFSSP (Generalized Fluid System Simulation Program) for calculating flow distribution in a network of micro-channels. GFSSP employs a finite volume formulation of mass and momentum conservation equations in a network consisting of nodes and branches. Mass conservation equation is solved for pressures at the nodes while the momentum conservation equation is solved at the branches to calculate flowrate. The system of equations describing the fluid network is solved by a numerical method that is a combination of the Newton-Raphson and successive substitution methods. The numerical results have been compared with test data and detailed CFD (computational Fluid Dynamics) calculations. The agreement between test data and predictions is satisfactory. The discrepancies between the predictions and test data can be attributed to the frictional correlation which does not include the effect of surface tension or electro-kinetic effect.

Improving sub-grid scale accuracy of boundary features in regional finite-difference models

USGS Publications Warehouse

Panday, Sorab; Langevin, Christian D.

2012-01-01

As an alternative to grid refinement, the concept of a ghost node, which was developed for nested grid applications, has been extended towards improving sub-grid scale accuracy of flow to conduits, wells, rivers or other boundary features that interact with a finite-difference groundwater flow model. The formulation is presented for correcting the regular finite-difference groundwater flow equations for confined and unconfined cases, with or without Newton Raphson linearization of the nonlinearities, to include the Ghost Node Correction (GNC) for location displacement. The correction may be applied on the right-hand side vector for a symmetric finite-difference Picard implementation, or on the left-hand side matrix for an implicit but asymmetric implementation. The finite-difference matrix connectivity structure may be maintained for an implicit implementation by only selecting contributing nodes that are a part of the finite-difference connectivity. Proof of concept example problems are provided to demonstrate the improved accuracy that may be achieved through sub-grid scale corrections using the GNC schemes.

Plasma Theory and Simulation

DTIC Science & Technology

1988-06-30

equation using finite difference methods. The distribution function is represented by a large number of particles. The particle’s velocities change as a...Small angle Coulomb collisions The FP equation for describing small angle Coulomb collisions can be solved numerically using finite difference techniques...A finite Fourrier transform (FT) is made in z, then we can solve for each k using the following finite difference scheme [5]: 2{r 1 +l1 2 (,,+ 1 - fj

Conservative and bounded volume-of-fluid advection on unstructured grids

NASA Astrophysics Data System (ADS)

Ivey, Christopher B.; Moin, Parviz

2017-12-01

This paper presents a novel Eulerian-Lagrangian piecewise-linear interface calculation (PLIC) volume-of-fluid (VOF) advection method, which is three-dimensional, unsplit, and discretely conservative and bounded. The approach is developed with reference to a collocated node-based finite-volume two-phase flow solver that utilizes the median-dual mesh constructed from non-convex polyhedra. The proposed advection algorithm satisfies conservation and boundedness of the liquid volume fraction irrespective of the underlying flux polyhedron geometry, which differs from contemporary unsplit VOF schemes that prescribe topologically complicated flux polyhedron geometries in efforts to satisfy conservation. Instead of prescribing complicated flux-polyhedron geometries, which are prone to topological failures, our VOF advection scheme, the non-intersecting flux polyhedron advection (NIFPA) method, builds the flux polyhedron iteratively such that its intersection with neighboring flux polyhedra, and any other unavailable volume, is empty and its total volume matches the calculated flux volume. During each iteration, a candidate nominal flux polyhedron is extruded using an iteration dependent scalar. The candidate is subsequently intersected with the volume guaranteed available to it at the time of the flux calculation to generate the candidate flux polyhedron. The difference in the volume of the candidate flux polyhedron and the actual flux volume is used to calculate extrusion during the next iteration. The choice in nominal flux polyhedron impacts the cost and accuracy of the scheme; however, it does not impact the methods underlying conservation and boundedness. As such, various robust nominal flux polyhedron are proposed and tested using canonical periodic kinematic test cases: Zalesak's disk and two- and three-dimensional deformation. The tests are conducted on the median duals of a quadrilateral and triangular primal mesh, in two-dimensions, and on the median duals of a hexahedral, wedge and tetrahedral primal mesh, in three-dimensions. Comparisons are made with the adaptation of a conventional unsplit VOF advection scheme to our collocated node-based flow solver. Depending on the choice in the nominal flux polyhedron, the NIFPA scheme presented accuracies ranging from zeroth to second order and calculation times that differed by orders of magnitude. For the nominal flux polyhedra which demonstrate second-order accuracy on all tests and meshes, the NIFPA method's cost was comparable to the traditional topologically complex second-order accurate VOF advection scheme.

A modified Dodge algorithm for the parabolized Navier-Stokes equations and compressible duct flows

NASA Technical Reports Server (NTRS)

Cooke, C. H.; Dwoyer, D. M.

1983-01-01

A revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition. Qualitative agreement with analytical predictions and experimental results was obtained for some flows with well-known solutions. Previously announced in STAR as N82-16363

A fast efficient implicit scheme for the gasdynamic equations using a matrix reduction technique

NASA Technical Reports Server (NTRS)

Barth, T. J.; Steger, J. L.

1985-01-01

An efficient implicit finite-difference algorithm for the gasdynamic equations utilizing matrix reduction techniques is presented. A significant reduction in arithmetic operations is achieved without loss of the stability characteristics generality found in the Beam and Warming approximate factorization algorithm. Steady-state solutions to the conservative Euler equations in generalized coordinates are obtained for transonic flows and used to show that the method offers computational advantages over the conventional Beam and Warming scheme. Existing Beam and Warming codes can be retrofit with minimal effort. The theoretical extension of the matrix reduction technique to the full Navier-Stokes equations in Cartesian coordinates is presented in detail. Linear stability, using a Fourier stability analysis, is demonstrated and discussed for the one-dimensional Euler equations.

Beyond the EDGE with EDAM: Prioritising British Plant Species According to Evolutionary Distinctiveness, and Accuracy and Magnitude of Decline

PubMed Central

Pearse, William D.; Chase, Mark W.; Crawley, Michael J.; Dolphin, Konrad; Fay, Michael F.; Joseph, Jeffrey A.; Powney, Gary; Preston, Chris D.; Rapacciuolo, Giovanni; Roy, David B.; Purvis, Andy

2015-01-01

Conservation biologists have only finite resources, and so must prioritise some species over others. The EDGE-listing approach ranks species according to their combined evolutionary distinctiveness and degree of threat, but ignores the uncertainty surrounding both threat and evolutionary distinctiveness. We develop a new family of measures for species, which we name EDAM, that incorporates evolutionary distinctiveness, the magnitude of decline, and the accuracy with which decline can be predicted. Further, we show how the method can be extended to explore phyogenetic uncertainty. Using the vascular plants of Britain as a case study, we find that the various EDAM measures emphasise different species and parts of Britain, and that phylogenetic uncertainty can strongly affect the prioritisation scores of some species. PMID:26018568

Thermal conductivity in one-dimensional nonlinear systems

NASA Astrophysics Data System (ADS)

Politi, Antonio; Giardinà, Cristian; Livi, Roberto; Vassalli, Massimo

2000-03-01

Thermal conducitivity of one-dimensional nonlinear systems typically diverges in the thermodynamic limit, whenever the momentum is conserved (i.e. in the absence of interactions with an external substrate). Evidence comes from detailed studies of Fermi-Pasta-Ulam and diatomic Toda chains. Here, we discuss the first example of a one-dimensional system obeying Fourier law : a chain of coupled rotators. Numerical estimates of the thermal conductivity obtained by simulating a chain in contact with two thermal baths at different temperatures are found to be consistent with those ones based on linear response theory. The dynamics of the Fourier modes provides direct evidence of energy diffusion. The finiteness of the conductivity is traced back to the occurrence of phase-jumps. Our conclusions are confirmed by the analysis of two variants of the rotator model.

Detachment and diffusive-convective transport in an evolving heterogeneous two-dimensional biofilm hybrid model.

PubMed

Luna, E; Domínguez-Zacarias, G; Ferreira, C Pio; Velasco-Hernandez, J X

2004-12-01

Under the hypothesis of correlation between biofilm survival and nutrient availability, by considering fluid drag forces and mortality due to nutrient depletion, a biofilm detachment/breaking condition is derived. The mechanisms leading to biofilm detachment/breaking are discussed. We construct and describe a hybrid model for a heterogeneous biofilm attached to walls in a channel where liquid is flowing. The model is called hybrid because it couples conservation equations with a cellular automaton. The biofilm layer is viewed as a porous medium with variable porosity, tortuosity, and permeability. The model is solved using asymptotic and finite differences methods. Results for porosity, nutrient distribution, and average surface location are presented. The model is capable of reproducing biofilm heterogeneity as well as the typical surface fingering (mushroomlike structure).

Compact Q-balls in the complex signum-Gordon model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arodz, H.; Lis, J.

2008-05-15

We discuss Q-balls in the complex signum-Gordon model in d-dimensional space for d=1, 2, 3. The Q-balls have strictly finite size. Their total energy is a powerlike function of the conserved U(1) charge with the exponent equal to (d+2)(d+3){sup -1}. In the cases d=1 and d=3 explicit analytic solutions are presented.

Development and Application of Compatible Discretizations of Maxwell's Equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

White, D; Koning, J; Rieben, R

We present the development and application of compatible finite element discretizations of electromagnetics problems derived from the time dependent, full wave Maxwell equations. We review the H(curl)-conforming finite element method, using the concepts and notations of differential forms as a theoretical framework. We chose this approach because it can handle complex geometries, it is free of spurious modes, it is numerically stable without the need for filtering or artificial diffusion, it correctly models the discontinuity of fields across material boundaries, and it can be very high order. Higher-order H(curl) and H(div) conforming basis functions are not unique and we havemore » designed an extensible C++ framework that supports a variety of specific instantiations of these such as standard interpolatory bases, spectral bases, hierarchical bases, and semi-orthogonal bases. Virtually any electromagnetics problem that can be cast in the language of differential forms can be solved using our framework. For time dependent problems a method-of-lines scheme is used where the Galerkin method reduces the PDE to a semi-discrete system of ODE's, which are then integrated in time using finite difference methods. For time integration of wave equations we employ the unconditionally stable implicit Newmark-Beta method, as well as the high order energy conserving explicit Maxwell Symplectic method; for diffusion equations, we employ a generalized Crank-Nicholson method. We conclude with computational examples from resonant cavity problems, time-dependent wave propagation problems, and transient eddy current problems, all obtained using the authors massively parallel computational electromagnetics code EMSolve.« less

Application of 'steady' state finite element and transient finite difference theory to sound propagation in a variable duct - A comparison with experiment

NASA Technical Reports Server (NTRS)

Baumeister, K. J.; Eversman, W.; Astley, R. J.; White, J. W.

1981-01-01

Experimental data are presented for sound propagation in a simulated infinite hard wall duct with a large change in duct cross sectional area. The data are conveniently tabulated for further use. The 'steady' state finite element theory of Astley and Eversman (1981) and the transient finite difference theory of White (1981) are in good agreement with the data for both the axial and transverse pressure profiles and the axial phase angle. Therefore, numerical finite difference and finite element theories appear to be ideally suited for handling duct propagation problems which encounter large axial gradients in acoustic parameters. The measured energy reflection coefficient agrees with the values from the Astley-Eversman modal coupling model.

Recent Developments in Computational Techniques for Applied Hydrodynamics.

DTIC Science & Technology

1979-12-07

by block number) Numerical Method Fluids Incompressible Flow Finite Difference Methods Poisson Equation Convective Equations -MABSTRACT (Continue on...weaknesses of the different approaches are analyzed. Finite - difference techniques have particularly attractive properties in this framework. Hence it will...be worthwhile to correct, at least partially, the difficulties from which Eulerian and Lagrangian finite - difference techniques suffer, discussed in

Mixed finite-difference scheme for free vibration analysis of noncircular cylinders

NASA Technical Reports Server (NTRS)

Noor, A. K.; Stephens, W. B.

1973-01-01

A mixed finite-difference scheme is presented for the free-vibration analysis of simply supported closed noncircular cylindrical shells. The problem is formulated in terms of eight first-order differential equations in the circumferential coordinate which possess a symmetric coefficient matrix and are free of the derivatives of the elastic and geometric characteristics of the shell. In the finite-difference discretization, two interlacing grids are used for the different fundamental unknowns in such a way as to avoid averaging in the difference-quotient expressions used for the first derivative. The resulting finite-difference equations are symmetric. The inverse-power method is used for obtaining the eigenvalues and eigenvectors.

Semi-implicit and fully implicit shock-capturing methods for hyperbolic conservation laws with stiff source terms

NASA Technical Reports Server (NTRS)

Yee, H. C.; Shinn, J. L.

1986-01-01

Some numerical aspects of finite-difference algorithms for nonlinear multidimensional hyperbolic conservation laws with stiff nonhomogenous (source) terms are discussed. If the stiffness is entirely dominated by the source term, a semi-implicit shock-capturing method is proposed provided that the Jacobian of the soruce terms possesses certain properties. The proposed semi-implicit method can be viewed as a variant of the Bussing and Murman point-implicit scheme with a more appropriate numerical dissipation for the computation of strong shock waves. However, if the stiffness is not solely dominated by the source terms, a fully implicit method would be a better choice. The situation is complicated by problems that are higher than one dimension, and the presence of stiff source terms further complicates the solution procedures for alternating direction implicit (ADI) methods. Several alternatives are discussed. The primary motivation for constructing these schemes was to address thermally and chemically nonequilibrium flows in the hypersonic regime. Due to the unique structure of the eigenvalues and eigenvectors for fluid flows of this type, the computation can be simplified, thus providing a more efficient solution procedure than one might have anticipated.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jibben, Zechariah Joel; Herrmann, Marcus

Here, we present a Runge-Kutta discontinuous Galerkin method for solving conservative reinitialization in the context of the conservative level set method. This represents an extension of the method recently proposed by Owkes and Desjardins [21], by solving the level set equations on the refined level set grid and projecting all spatially-dependent variables into the full basis used by the discontinuous Galerkin discretization. By doing so, we achieve the full k+1 order convergence rate in the L1 norm of the level set field predicted for RKDG methods given kth degree basis functions when the level set profile thickness is held constantmore » with grid refinement. Shape and volume errors for the 0.5-contour of the level set, on the other hand, are found to converge between first and second order. We show a variety of test results, including the method of manufactured solutions, reinitialization of a circle and sphere, Zalesak's disk, and deforming columns and spheres, all showing substantial improvements over the high-order finite difference traditional level set method studied for example by Herrmann. We also demonstrate the need for kth order accurate normal vectors, as lower order normals are found to degrade the convergence rate of the method.« less

A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov–Darwin particle-in-cell algorithm

DOE PAGES

Chen, G.; Chacón, L.

2015-08-11

For decades, the Vlasov–Darwin model has been recognized to be attractive for particle-in-cell (PIC) kinetic plasma simulations in non-radiative electromagnetic regimes, to avoid radiative noise issues and gain computational efficiency. However, the Darwin model results in an elliptic set of field equations that renders conventional explicit time integration unconditionally unstable. We explore a fully implicit PIC algorithm for the Vlasov–Darwin model in multiple dimensions, which overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. The finite-difference scheme for Darwin field equations and particle equations of motion is space–time-centered, employing particle sub-cycling and orbit-averaging. This algorithm conserves total energy, local charge,more » canonical-momentum in the ignorable direction, and preserves the Coulomb gauge exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. Finally, we demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 2D–3V.« less

Modeling of InP metalorganic chemical vapor deposition

NASA Technical Reports Server (NTRS)

Black, Linda R.; Clark, Ivan O.; Kui, J.; Jesser, William A.

1991-01-01

The growth of InP by metalorganic chemical vapor deposition (MOCVD) in a horizontal reactor is being modeled with a commercially available computational fluid dynamics modeling code. The mathematical treatment of the MOCVD process has four primary areas of concern: 1) transport phenomena, 2) chemistry, 3) boundary conditions, and 4) numerical solution methods. The transport processes involved in CVD are described by conservation of total mass, momentum, energy, and atomic species. Momentum conservation is described by a generalized form of the Navier-Stokes equation for a Newtonian fluid and laminar flow. The effect of Soret diffusion on the transport of particular chemical species and on the predicted deposition rate is examined. Both gas-phase and surface chemical reactions are employed in the model. Boundary conditions are specified at the inlet and walls of the reactor for temperature, fluid flow and chemical species. The coupled set of equations described above is solved by a finite difference method over a nonuniform rectilinear grid in both two and three dimensions. The results of the 2-D computational model is presented for gravity levels of zero- and one-g. The predicted growth rates at one-g are compared to measured growth rates on fused silica substrates.

A Reduced-Order Model for Efficient Simulation of Synthetic Jet Actuators

NASA Technical Reports Server (NTRS)

Yamaleev, Nail K.; Carpenter, Mark H.

2003-01-01

A new reduced-order model of multidimensional synthetic jet actuators that combines the accuracy and conservation properties of full numerical simulation methods with the efficiency of simplified zero-order models is proposed. The multidimensional actuator is simulated by solving the time-dependent compressible quasi-1-D Euler equations, while the diaphragm is modeled as a moving boundary. The governing equations are approximated with a fourth-order finite difference scheme on a moving mesh such that one of the mesh boundaries coincides with the diaphragm. The reduced-order model of the actuator has several advantages. In contrast to the 3-D models, this approach provides conservation of mass, momentum, and energy. Furthermore, the new method is computationally much more efficient than the multidimensional Navier-Stokes simulation of the actuator cavity flow, while providing practically the same accuracy in the exterior flowfield. The most distinctive feature of the present model is its ability to predict the resonance characteristics of synthetic jet actuators; this is not practical when using the 3-D models because of the computational cost involved. Numerical results demonstrating the accuracy of the new reduced-order model and its limitations are presented.

A finite element code for modelling tracer transport in a non-isothermal two-phase flow system for CO2 geological storage characterization

NASA Astrophysics Data System (ADS)

Tong, F.; Niemi, A. P.; Yang, Z.; Fagerlund, F.; Licha, T.; Sauter, M.

2011-12-01

This paper presents a new finite element method (FEM) code for modeling tracer transport in a non-isothermal two-phase flow system. The main intended application is simulation of the movement of so-called novel tracers for the purpose of characterization of geologically stored CO2 and its phase partitioning and migration in deep saline formations. The governing equations are based on the conservation of mass and energy. Among the phenomena accounted for are liquid-phase flow, gas flow, heat transport and the movement of the novel tracers. The movement of tracers includes diffusion and the advection associated with the gas and liquid flow. The temperature, gas pressure, suction, concentration of tracer in liquid phase and concentration of tracer in gas phase are chosen as the five primary variables. Parameters such as the density, viscosity, thermal expansion coefficient are expressed in terms of the primary variables. The governing equations are discretized in space using the Galerkin finite element formulation, and are discretized in time by one-dimensional finite difference scheme. This leads to an ill-conditioned FEM equation that has many small entries along the diagonal of the non-symmetric coefficient matrix. In order to deal with the problem of non-symmetric ill-conditioned matrix equation, special techniques are introduced . Firstly, only nonzero elements of the matrix need to be stored. Secondly, it is avoided to directly solve the whole large matrix. Thirdly, a strategy has been used to keep the diversity of solution methods in the calculation process. Additionally, an efficient adaptive mesh technique is included in the code in order to track the wetting front. The code has been validated against several classical analytical solutions, and will be applied for simulating the CO2 injection experiment to be carried out at the Heletz site, Israel, as part of the EU FP7 project MUSTANG.

Meshless Method for Simulation of Compressible Flow

NASA Astrophysics Data System (ADS)

Nabizadeh Shahrebabak, Ebrahim

In the present age, rapid development in computing technology and high speed supercomputers has made numerical analysis and computational simulation more practical than ever before for large and complex cases. Numerical simulations have also become an essential means for analyzing the engineering problems and the cases that experimental analysis is not practical. There are so many sophisticated and accurate numerical schemes, which do these simulations. The finite difference method (FDM) has been used to solve differential equation systems for decades. Additional numerical methods based on finite volume and finite element techniques are widely used in solving problems with complex geometry. All of these methods are mesh-based techniques. Mesh generation is an essential preprocessing part to discretize the computation domain for these conventional methods. However, when dealing with mesh-based complex geometries these conventional mesh-based techniques can become troublesome, difficult to implement, and prone to inaccuracies. In this study, a more robust, yet simple numerical approach is used to simulate problems in an easier manner for even complex problem. The meshless, or meshfree, method is one such development that is becoming the focus of much research in the recent years. The biggest advantage of meshfree methods is to circumvent mesh generation. Many algorithms have now been developed to help make this method more popular and understandable for everyone. These algorithms have been employed over a wide range of problems in computational analysis with various levels of success. Since there is no connectivity between the nodes in this method, the challenge was considerable. The most fundamental issue is lack of conservation, which can be a source of unpredictable errors in the solution process. This problem is particularly evident in the presence of steep gradient regions and discontinuities, such as shocks that frequently occur in high speed compressible flow problems. To solve this discontinuity problem, this research study deals with the implementation of a conservative meshless method and its applications in computational fluid dynamics (CFD). One of the most common types of collocating meshless method the RBF-DQ, is used to approximate the spatial derivatives. The issue with meshless methods when dealing with highly convective cases is that they cannot distinguish the influence of fluid flow from upstream or downstream and some methodology is needed to make the scheme stable. Therefore, an upwinding scheme similar to one used in the finite volume method is added to capture steep gradient or shocks. This scheme creates a flexible algorithm within which a wide range of numerical flux schemes, such as those commonly used in the finite volume method, can be employed. In addition, a blended RBF is used to decrease the dissipation ensuing from the use of a low shape parameter. All of these steps are formulated for the Euler equation and a series of test problems used to confirm convergence of the algorithm. The present scheme was first employed on several incompressible benchmarks to validate the framework. The application of this algorithm is illustrated by solving a set of incompressible Navier-Stokes problems. Results from the compressible problem are compared with the exact solution for the flow over a ramp and compared with solutions of finite volume discretization and the discontinuous Galerkin method, both requiring a mesh. The applicability of the algorithm and its robustness are shown to be applied to complex problems.

The impact of groundwater velocity fields on streamlines in an aquifer system with a discontinuous aquitard (Inner Mongolia, China)

NASA Astrophysics Data System (ADS)

Wu, Qiang; Zhao, Yingwang; Xu, Hua

2018-04-01

Many numerical methods that simulate groundwater flow, particularly the continuous Galerkin finite element method, do not produce velocity information directly. Many algorithms have been proposed to improve the accuracy of velocity fields computed from hydraulic potentials. The differences in the streamlines generated from velocity fields obtained using different algorithms are presented in this report. The superconvergence method employed by FEFLOW, a popular commercial code, and some dual-mesh methods proposed in recent years are selected for comparison. The applications to depict hydrogeologic conditions using streamlines are used, and errors in streamlines are shown to lead to notable errors in boundary conditions, the locations of material interfaces, fluxes and conductivities. Furthermore, the effects of the procedures used in these two types of methods, including velocity integration and local conservation, are analyzed. The method of interpolating velocities across edges using fluxes is shown to be able to eliminate errors associated with refraction points that are not located along material interfaces and streamline ends at no-flow boundaries. Local conservation is shown to be a crucial property of velocity fields and can result in more accurate streamline densities. A case study involving both three-dimensional and two-dimensional cross-sectional models of a coal mine in Inner Mongolia, China, are used to support the conclusions presented.

An optimization-based approach for high-order accurate discretization of conservation laws with discontinuous solutions

NASA Astrophysics Data System (ADS)

Zahr, M. J.; Persson, P.-O.

2018-07-01

This work introduces a novel discontinuity-tracking framework for resolving discontinuous solutions of conservation laws with high-order numerical discretizations that support inter-element solution discontinuities, such as discontinuous Galerkin or finite volume methods. The proposed method aims to align inter-element boundaries with discontinuities in the solution by deforming the computational mesh. A discontinuity-aligned mesh ensures the discontinuity is represented through inter-element jumps while smooth basis functions interior to elements are only used to approximate smooth regions of the solution, thereby avoiding Gibbs' phenomena that create well-known stability issues. Therefore, very coarse high-order discretizations accurately resolve the piecewise smooth solution throughout the domain, provided the discontinuity is tracked. Central to the proposed discontinuity-tracking framework is a discrete PDE-constrained optimization formulation that simultaneously aligns the computational mesh with discontinuities in the solution and solves the discretized conservation law on this mesh. The optimization objective is taken as a combination of the deviation of the finite-dimensional solution from its element-wise average and a mesh distortion metric to simultaneously penalize Gibbs' phenomena and distorted meshes. It will be shown that our objective function satisfies two critical properties that are required for this discontinuity-tracking framework to be practical: (1) possesses a local minima at a discontinuity-aligned mesh and (2) decreases monotonically to this minimum in a neighborhood of radius approximately h / 2, whereas other popular discontinuity indicators fail to satisfy the latter. Another important contribution of this work is the observation that traditional reduced space PDE-constrained optimization solvers that repeatedly solve the conservation law at various mesh configurations are not viable in this context since severe overshoot and undershoot in the solution, i.e., Gibbs' phenomena, may make it impossible to solve the discrete conservation law on non-aligned meshes. Therefore, we advocate a gradient-based, full space solver where the mesh and conservation law solution converge to their optimal values simultaneously and therefore never require the solution of the discrete conservation law on a non-aligned mesh. The merit of the proposed method is demonstrated on a number of one- and two-dimensional model problems including the L2 projection of discontinuous functions, Burgers' equation with a discontinuous source term, transonic flow through a nozzle, and supersonic flow around a bluff body. We demonstrate optimal O (h p + 1) convergence rates in the L1 norm for up to polynomial order p = 6 and show that accurate solutions can be obtained on extremely coarse meshes.

Finite difference and Runge-Kutta methods for solving vibration problems

NASA Astrophysics Data System (ADS)

Lintang Renganis Radityani, Scolastika; Mungkasi, Sudi

2017-11-01

The vibration of a storey building can be modelled into a system of second order ordinary differential equations. If the number of floors of a building is large, then the result is a large scale system of second order ordinary differential equations. The large scale system is difficult to solve, and if it can be solved, the solution may not be accurate. Therefore, in this paper, we seek for accurate methods for solving vibration problems. We compare the performance of numerical finite difference and Runge-Kutta methods for solving large scale systems of second order ordinary differential equations. The finite difference methods include the forward and central differences. The Runge-Kutta methods include the Euler and Heun methods. Our research results show that the central finite difference and the Heun methods produce more accurate solutions than the forward finite difference and the Euler methods do.

On the numerical dispersion of electromagnetic particle-in-cell code: Finite grid instability

NASA Astrophysics Data System (ADS)

Meyers, M. D.; Huang, C.-K.; Zeng, Y.; Yi, S. A.; Albright, B. J.

2015-09-01

The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the Electromagnetic PIC model. We rigorously derive the faithful 3-D numerical dispersion relation of the PIC model, for a simple, direct current deposition scheme, which does not conserve electric charge exactly. We then specialize to the Yee FDTD scheme. In particular, we clarify the presence of alias modes in an eigenmode analysis of the PIC model, which combines both discrete and continuous variables. The manner in which the PIC model updates and samples the fields and distribution function, together with the temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme, is explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1-D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical modes admitted in the system and their aliases. The most significant interaction is due critically to the correct representation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction, which is then verified by simulation. We demonstrate that our analysis is readily extendable to charge conserving models.

On the numerical dispersion of electromagnetic particle-in-cell code: Finite grid instability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Meyers, M.D., E-mail: mdmeyers@physics.ucla.edu; Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, CA 90095; Huang, C.-K., E-mail: huangck@lanl.gov

The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the Electromagnetic PIC model. We rigorously derive the faithful 3-D numerical dispersion relation of the PIC model, for a simple, direct current deposition scheme, which does not conserve electric charge exactly. We then specialize to the Yee FDTDmore » scheme. In particular, we clarify the presence of alias modes in an eigenmode analysis of the PIC model, which combines both discrete and continuous variables. The manner in which the PIC model updates and samples the fields and distribution function, together with the temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme, is explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1-D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical modes admitted in the system and their aliases. The most significant interaction is due critically to the correct representation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction, which is then verified by simulation. We demonstrate that our analysis is readily extendable to charge conserving models.« less

Deformation of two-phase aggregates using standard numerical methods

NASA Astrophysics Data System (ADS)

Duretz, Thibault; Yamato, Philippe; Schmalholz, Stefan M.

2013-04-01

Geodynamic problems often involve the large deformation of material encompassing material boundaries. In geophysical fluids, such boundaries often coincide with a discontinuity in the viscosity (or effective viscosity) field and subsequently in the pressure field. Here, we employ popular implementations of the finite difference and finite element methods for solving viscous flow problems. On one hand, we implemented finite difference method coupled with a Lagrangian marker-in-cell technique to represent the deforming fluid. Thanks to it Eulerian nature, this method has a limited geometric flexibility but is characterized by a light and stable discretization. On the other hand, we employ the Lagrangian finite element method which offers full geometric flexibility at the cost of relatively heavier discretization. In order to test the accuracy of the finite difference scheme, we ran large strain simple shear deformation of aggregates containing either weak of strong circular inclusion (1e6 viscosity ratio). The results, obtained for different grid resolutions, are compared to Lagrangian finite element results which are considered as reference solution. The comparison is then used to establish up to which strain can finite difference simulations be run given the nature of the inclusions (dimensions, viscosity) and the resolution of the Eulerian mesh.

Finite-key security analyses on passive decoy-state QKD protocols with different unstable sources.

PubMed

Song, Ting-Ting; Qin, Su-Juan; Wen, Qiao-Yan; Wang, Yu-Kun; Jia, Heng-Yue

2015-10-16

In quantum communication, passive decoy-state QKD protocols can eliminate many side channels, but the protocols without any finite-key analyses are not suitable for in practice. The finite-key securities of passive decoy-state (PDS) QKD protocols with two different unstable sources, type-II parametric down-convention (PDC) and phase randomized weak coherent pulses (WCPs), are analyzed in our paper. According to the PDS QKD protocols, we establish an optimizing programming respectively and obtain the lower bounds of finite-key rates. Under some reasonable values of quantum setup parameters, the lower bounds of finite-key rates are simulated. The simulation results show that at different transmission distances, the affections of different fluctuations on key rates are different. Moreover, the PDS QKD protocol with an unstable PDC source can resist more intensity fluctuations and more statistical fluctuation.

Localization in finite vibroimpact chains: Discrete breathers and multibreathers.

PubMed

Grinberg, Itay; Gendelman, Oleg V

2016-09-01

We explore the dynamics of strongly localized periodic solutions (discrete solitons or discrete breathers) in a finite one-dimensional chain of oscillators. Localization patterns with both single and multiple localization sites (breathers and multibreathers) are considered. The model involves parabolic on-site potential with rigid constraints (the displacement domain of each particle is finite) and a linear nearest-neighbor coupling. When the particle approaches the constraint, it undergoes an inelastic impact according to Newton's impact model. The rigid nonideal impact constraints are the only source of nonlinearity and damping in the system. We demonstrate that this vibro-impact model allows derivation of exact analytic solutions for the breathers and multibreathers with an arbitrary set of localization sites, both in conservative and in forced-damped settings. Periodic boundary conditions are considered; exact solutions for other types of boundary conditions are also available. Local character of the nonlinearity permits explicit derivation of a monodromy matrix for the breather solutions. Consequently, the stability of the derived breather and multibreather solutions can be efficiently studied in the framework of simple methods of linear algebra, and with rather moderate computational efforts. One reveals that that the finiteness of the chain fragment and possible proximity of the localization sites strongly affect both the existence and the stability patterns of these localized solutions.

GPU and APU computations of Finite Time Lyapunov Exponent fields

NASA Astrophysics Data System (ADS)

Conti, Christian; Rossinelli, Diego; Koumoutsakos, Petros

2012-03-01

We present GPU and APU accelerated computations of Finite-Time Lyapunov Exponent (FTLE) fields. The calculation of FTLEs is a computationally intensive process, as in order to obtain the sharp ridges associated with the Lagrangian Coherent Structures an extensive resampling of the flow field is required. The computational performance of this resampling is limited by the memory bandwidth of the underlying computer architecture. The present technique harnesses data-parallel execution of many-core architectures and relies on fast and accurate evaluations of moment conserving functions for the mesh to particle interpolations. We demonstrate how the computation of FTLEs can be efficiently performed on a GPU and on an APU through OpenCL and we report over one order of magnitude improvements over multi-threaded executions in FTLE computations of bluff body flows.

Unified Nusselt- and Sherwood-number correlations in axisymmetric finite-gap stagnation and rotating-disk flows

DOE PAGES

Coltrin, Michael E.; Kee, Robert J.

2016-06-18

This paper develops a unified analysis of stagnation flow heat and mass transport, considering both semi-infinite domains and finite gaps, with and without rotation of the stagnation surface. An important objective is to derive Nusselt- and Sherwood-number correlations that represent heat and mass transport at the stagnation surface. The approach is based on computationally solving the governing conservation equations in similarity form as a boundary-value problem. The formulation considers ideal gases and incompressible fluids. The correlated results depend on fluid properties in terms of Prandtl, Schmidt, and Damkohler numbers. Heterogeneous chemistry at the stagnation surface is represented as a singlemore » first-order reaction. A composite Reynolds number represents the combination of stagnation flows with and without stagnation-surface rotation.« less

A globally well-posed finite element algorithm for aerodynamics applications

NASA Technical Reports Server (NTRS)

Iannelli, G. S.; Baker, A. J.

1991-01-01

A finite element CFD algorithm is developed for Euler and Navier-Stokes aerodynamic applications. For the linear basis, the resultant approximation is at least second-order-accurate in time and space for synergistic use of three procedures: (1) a Taylor weak statement, which provides for derivation of companion conservation law systems with embedded dispersion-error control mechanisms; (2) a stiffly stable second-order-accurate implicit Rosenbrock-Runge-Kutta temporal algorithm; and (3) a matrix tensor product factorization that permits efficient numerical linear algebra handling of the terminal large-matrix statement. Thorough analyses are presented regarding well-posed boundary conditions for inviscid and viscous flow specifications. Numerical solutions are generated and compared for critical evaluation of quasi-one- and two-dimensional Euler and Navier-Stokes benchmark test problems.

Numerical simulation and experimental investigation about internal and external flows†

NASA Astrophysics Data System (ADS)

Wang, Tao; Yang, Guowei; Huang, Guojun; Zhou, Liandi

2006-06-01

In this paper, TASCflow3D is used to solve inner and outer 3D viscous incompressible turbulent flow (Re=5.6×106) around axisymmetric body with duct. The governing equation is a RANS equation with standard k ɛ turbulence model. The discrete method used is a finite volume method based on the finite element approach. In this method, the description of geometry is very flexible and at the same time important conservative properties are retained. The multi-block and algebraic multi-grid techniques are used for the convergence acceleration. Agreement between experimental results and calculation is good. It indicates that this novel approach can be used to simulate complex flow such as the interaction between rotor and stator or propulsion systems containing tip clearance and cavitation.

Lattice QCD at finite temperature and density from Taylor expansion

NASA Astrophysics Data System (ADS)

Steinbrecher, Patrick

2017-01-01

In the first part, I present an overview of recent Lattice QCD simulations at finite temperature and density. In particular, we discuss fluctuations of conserved charges: baryon number, electric charge and strangeness. These can be obtained from Taylor expanding the QCD pressure as a function of corresponding chemical potentials. Our simulations were performed using quark masses corresponding to physical pion mass of about 140 MeV and allow a direct comparison to experimental data from ultra-relativistic heavy ion beams at hadron colliders such as the Relativistic Heavy Ion Collider at Brookhaven National Laboratory and the Large Hadron Collider at CERN. In the second part, we discuss computational challenges for current and future exascale Lattice simulations with a focus on new silicon developments from Intel and NVIDIA.

Agent-based simulation of a financial market

NASA Astrophysics Data System (ADS)

Raberto, Marco; Cincotti, Silvano; Focardi, Sergio M.; Marchesi, Michele

2001-10-01

This paper introduces an agent-based artificial financial market in which heterogeneous agents trade one single asset through a realistic trading mechanism for price formation. Agents are initially endowed with a finite amount of cash and a given finite portfolio of assets. There is no money-creation process; the total available cash is conserved in time. In each period, agents make random buy and sell decisions that are constrained by available resources, subject to clustering, and dependent on the volatility of previous periods. The model proposed herein is able to reproduce the leptokurtic shape of the probability density of log price returns and the clustering of volatility. Implemented using extreme programming and object-oriented technology, the simulator is a flexible computational experimental facility that can find applications in both academic and industrial research projects.

New Finite Difference Methods Based on IIM for Inextensible Interfaces in Incompressible Flows

PubMed Central

Li, Zhilin; Lai, Ming-Chih

2012-01-01

In this paper, new finite difference methods based on the augmented immersed interface method (IIM) are proposed for simulating an inextensible moving interface in an incompressible two-dimensional flow. The mathematical models arise from studying the deformation of red blood cells in mathematical biology. The governing equations are incompressible Stokes or Navier-Stokes equations with an unknown surface tension, which should be determined in such a way that the surface divergence of the velocity is zero along the interface. Thus, the area enclosed by the interface and the total length of the interface should be conserved during the evolution process. Because of the nonlinear and coupling nature of the problem, direct discretization by applying the immersed boundary or immersed interface method yields complex nonlinear systems to be solved. In our new methods, we treat the unknown surface tension as an augmented variable so that the augmented IIM can be applied. Since finding the unknown surface tension is essentially an inverse problem that is sensitive to perturbations, our regularization strategy is to introduce a controlled tangential force along the interface, which leads to a least squares problem. For Stokes equations, the forward solver at one time level involves solving three Poisson equations with an interface. For Navier-Stokes equations, we propose a modified projection method that can enforce the pressure jump condition corresponding directly to the unknown surface tension. Several numerical experiments show good agreement with other results in the literature and reveal some interesting phenomena. PMID:23795308

Wavelet-based adaptation methodology combined with finite difference WENO to solve ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Do, Seongju; Li, Haojun; Kang, Myungjoo

2017-06-01

In this paper, we present an accurate and efficient wavelet-based adaptive weighted essentially non-oscillatory (WENO) scheme for hydrodynamics and ideal magnetohydrodynamics (MHD) equations arising from the hyperbolic conservation systems. The proposed method works with the finite difference weighted essentially non-oscillatory (FD-WENO) method in space and the third order total variation diminishing (TVD) Runge-Kutta (RK) method in time. The philosophy of this work is to use the lifted interpolating wavelets as not only detector for singularities but also interpolator. Especially, flexible interpolations can be performed by an inverse wavelet transformation. When the divergence cleaning method introducing auxiliary scalar field ψ is applied to the base numerical schemes for imposing divergence-free condition to the magnetic field in a MHD equation, the approximations to derivatives of ψ require the neighboring points. Moreover, the fifth order WENO interpolation requires large stencil to reconstruct high order polynomial. In such cases, an efficient interpolation method is necessary. The adaptive spatial differentiation method is considered as well as the adaptation of grid resolutions. In order to avoid the heavy computation of FD-WENO, in the smooth regions fixed stencil approximation without computing the non-linear WENO weights is used, and the characteristic decomposition method is replaced by a component-wise approach. Numerical results demonstrate that with the adaptive method we are able to resolve the solutions that agree well with the solution of the corresponding fine grid.

A compressible Navier-Stokes solver with two-equation and Reynolds stress turbulence closure models

NASA Technical Reports Server (NTRS)

Morrison, Joseph H.

1992-01-01

This report outlines the development of a general purpose aerodynamic solver for compressible turbulent flows. Turbulent closure is achieved using either two equation or Reynolds stress transportation equations. The applicable equation set consists of Favre-averaged conservation equations for the mass, momentum and total energy, and transport equations for the turbulent stresses and turbulent dissipation rate. In order to develop a scheme with good shock capturing capabilities, good accuracy and general geometric capabilities, a multi-block cell centered finite volume approach is used. Viscous fluxes are discretized using a finite volume representation of a central difference operator and the source terms are treated as an integral over the control volume. The methodology is validated by testing the algorithm on both two and three dimensional flows. Both the two equation and Reynolds stress models are used on a two dimensional 10 degree compression ramp at Mach 3, and the two equation model is used on the three dimensional flow over a cone at angle of attack at Mach 3.5. With the development of this algorithm, it is now possible to compute complex, compressible high speed flow fields using both two equation and Reynolds stress turbulent closure models, with the capability of eventually evaluating their predictive performance.

Full Coupling Between the Atmosphere, Surface, and Subsurface for Integrated Hydrologic Simulation

NASA Astrophysics Data System (ADS)

Davison, Jason Hamilton; Hwang, Hyoun-Tae; Sudicky, Edward A.; Mallia, Derek V.; Lin, John C.

2018-01-01

An ever increasing community of earth system modelers is incorporating new physical processes into numerical models. This trend is facilitated by advancements in computational resources, improvements in simulation skill, and the desire to build numerical simulators that represent the water cycle with greater fidelity. In this quest to develop a state-of-the-art water cycle model, we coupled HydroGeoSphere (HGS), a 3-D control-volume finite element surface and variably saturated subsurface flow model that includes evapotranspiration processes, to the Weather Research and Forecasting (WRF) Model, a 3-D finite difference nonhydrostatic mesoscale atmospheric model. The two-way coupled model, referred to as HGS-WRF, exchanges the actual evapotranspiration fluxes and soil saturations calculated by HGS to WRF; conversely, the potential evapotranspiration and precipitation fluxes from WRF are passed to HGS. The flexible HGS-WRF coupling method allows for unique meshes used by each model, while maintaining mass and energy conservation between the domains. Furthermore, the HGS-WRF coupling implements a subtime stepping algorithm to minimize computational expense. As a demonstration of HGS-WRF's capabilities, we applied it to the California Basin and found a strong connection between the depth to the groundwater table and the latent heat fluxes across the land surface.

Integral projection models for finite populations in a stochastic environment.

PubMed

Vindenes, Yngvild; Engen, Steinar; Saether, Bernt-Erik

2011-05-01

Continuous types of population structure occur when continuous variables such as body size or habitat quality affect the vital parameters of individuals. These structures can give rise to complex population dynamics and interact with environmental conditions. Here we present a model for continuously structured populations with finite size, including both demographic and environmental stochasticity in the dynamics. Using recent methods developed for discrete age-structured models we derive the demographic and environmental variance of the population growth as functions of a continuous state variable. These two parameters, together with the expected population growth rate, are used to define a one-dimensional diffusion approximation of the population dynamics. Thus, a substantial reduction in complexity is achieved as the dynamics of the complex structured model can be described by only three population parameters. We provide methods for numerical calculation of the model parameters and demonstrate the accuracy of the diffusion approximation by computer simulation of specific examples. The general modeling framework makes it possible to analyze and predict future dynamics and extinction risk of populations with various types of structure, and to explore consequences of changes in demography caused by, e.g., climate change or different management decisions. Our results are especially relevant for small populations that are often of conservation concern.

Technical Feasibility of Centrifugal Techniques for Evaluating Hazardous Waste Migration

DTIC Science & Technology

1987-12-01

direct evaluation of the -influence of acceleration on soil moisture movement. A fully implicit finite difference solution scheme was used. The...using the finite difference scheme mentioned earlier. 2. The soil test apparatus for the centrifuge tests was designed and constructed. 110 3...npcr3 f~nJPX 115 S.. 0i U 4 I3 u cc/ U) C~j tC LL~~*- Lý u ’ uiu ’ 4-’ Uju x~j~r3np~~r~tj~jpU W3= 116 Finite Difference Model The finite difference

A 3-D Finite-Volume Non-hydrostatic Icosahedral Model (NIM)

NASA Astrophysics Data System (ADS)

Lee, Jin

2014-05-01

The Nonhydrostatic Icosahedral Model (NIM) formulates the latest numerical innovation of the three-dimensional finite-volume control volume on the quasi-uniform icosahedral grid suitable for ultra-high resolution simulations. NIM's modeling goal is to improve numerical accuracy for weather and climate simulations as well as to utilize the state-of-art computing architecture such as massive parallel CPUs and GPUs to deliver routine high-resolution forecasts in timely manner. NIM dynamic corel innovations include: * A local coordinate system remapped spherical surface to plane for numerical accuracy (Lee and MacDonald, 2009), * Grid points in a table-driven horizontal loop that allow any horizontal point sequence (A.E. MacDonald, et al., 2010), * Flux-Corrected Transport formulated on finite-volume operators to maintain conservative positive definite transport (J.-L, Lee, ET. Al., 2010), *Icosahedral grid optimization (Wang and Lee, 2011), * All differentials evaluated as three-dimensional finite-volume integrals around the control volume. The three-dimensional finite-volume solver in NIM is designed to improve pressure gradient calculation and orographic precipitation over complex terrain. NIM dynamical core has been successfully verified with various non-hydrostatic benchmark test cases such as internal gravity wave, and mountain waves in Dynamical Cores Model Inter-comparisons Projects (DCMIP). Physical parameterizations suitable for NWP are incorporated into NIM dynamical core and successfully tested with multimonth aqua-planet simulations. Recently, NIM has started real data simulations using GFS initial conditions. Results from the idealized tests as well as real-data simulations will be shown in the conference.

Practical Aspects of Stabilized FEM Discretizations of Nonlinear Conservation Law Systems with Convex Extension

NASA Technical Reports Server (NTRS)

Barth, Timothy; Saini, Subhash (Technical Monitor)

1999-01-01

This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the Galerkin least-squares (GLS) and the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the POE system. Central to the development of the simplified GLS and DG methods is the Degenerative Scaling Theorem which characterizes right symmetrizes of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobean matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler, Navier-Stokes, and magnetohydrodynamic (MHD) equations. Linear and nonlinear energy stability is proven for the simplified GLS and DG methods. Spatial convergence properties of the simplified GLS and DO methods are numerical evaluated via the computation of Ringleb flow on a sequence of successively refined triangulations. Finally, we consider a posteriori error estimates for the GLS and DG demoralization assuming error functionals related to the integrated lift and drag of a body. Sample calculations in 20 are shown to validate the theory and implementation.

Mean-field behavior as a result of noisy local dynamics in self-organized criticality: Neuroscience implications

NASA Astrophysics Data System (ADS)

Moosavi, S. Amin; Montakhab, Afshin

2014-05-01

Motivated by recent experiments in neuroscience which indicate that neuronal avalanches exhibit scale invariant behavior similar to self-organized critical systems, we study the role of noisy (nonconservative) local dynamics on the critical behavior of a sandpile model which can be taken to mimic the dynamics of neuronal avalanches. We find that despite the fact that noise breaks the strict local conservation required to attain criticality, our system exhibits true criticality for a wide range of noise in various dimensions, given that conservation is respected on the average. Although the system remains critical, exhibiting finite-size scaling, the value of critical exponents change depending on the intensity of local noise. Interestingly, for a sufficiently strong noise level, the critical exponents approach and saturate at their mean-field values, consistent with empirical measurements of neuronal avalanches. This is confirmed for both two and three dimensional models. However, the addition of noise does not affect the exponents at the upper critical dimension (D =4). In addition to an extensive finite-size scaling analysis of our systems, we also employ a useful time-series analysis method to establish true criticality of noisy systems. Finally, we discuss the implications of our work in neuroscience as well as some implications for the general phenomena of criticality in nonequilibrium systems.

Design of an essentially non-oscillatory reconstruction procedure in finite-element type meshes

NASA Technical Reports Server (NTRS)

Abgrall, Remi

1992-01-01

An essentially non oscillatory reconstruction for functions defined on finite element type meshes is designed. Two related problems are studied: the interpolation of possibly unsmooth multivariate functions on arbitary meshes and the reconstruction of a function from its averages in the control volumes surrounding the nodes of the mesh. Concerning the first problem, the behavior of the highest coefficients of two polynomial interpolations of a function that may admit discontinuities of locally regular curves is studied: the Lagrange interpolation and an approximation such that the mean of the polynomial on any control volume is equal to that of the function to be approximated. This enables the best stencil for the approximation to be chosen. The choice of the smallest possible number of stencils is addressed. Concerning the reconstruction problem, two methods were studied: one based on an adaptation of the so called reconstruction via deconvolution method to irregular meshes and one that lies on the approximation on the mean as defined above. The first method is conservative up to a quadrature formula and the second one is exactly conservative. The two methods have the expected order of accuracy, but the second one is much less expensive than the first one. Some numerical examples are given which demonstrate the efficiency of the reconstruction.

Energy/dissipation-preserving Birkhoffian multi-symplectic methods for Maxwell's equations with dissipation terms

DOE PAGES

Su, Hongling; Li, Shengtai

2016-02-03

In this study, we propose two new energy/dissipation-preserving Birkhoffian multi-symplectic methods (Birkhoffian and Birkhoffian box) for Maxwell's equations with dissipation terms. After investigating the non-autonomous and autonomous Birkhoffian formalism for Maxwell's equations with dissipation terms, we first apply a novel generating functional theory to the non-autonomous Birkhoffian formalism to propose our Birkhoffian scheme, and then implement a central box method to the autonomous Birkhoffian formalism to derive the Birkhoffian box scheme. We have obtained four formal local conservation laws and three formal energy global conservation laws. We have also proved that both of our derived schemes preserve the discrete versionmore » of the global/local conservation laws. Furthermore, the stability, dissipation and dispersion relations are also investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, dissipation-preserving for Maxwell's equations in a perfectly matched layer (PML) medium and have second order accuracy in both time and space. Numerical experiments for problems with exact theoretical results are given to demonstrate that the Birkhoffian multi-symplectic schemes are much more accurate in preserving energy than both the exponential finite-difference time-domain (FDTD) method and traditional Hamiltonian scheme. Finally, we also solve the electromagnetic pulse (EMP) propagation problem and the numerical results show that the Birkhoffian scheme recovers the magnitude of the current source and reaction history very well even after long time propagation.« less

Energy/dissipation-preserving Birkhoffian multi-symplectic methods for Maxwell's equations with dissipation terms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Su, Hongling; Li, Shengtai

In this study, we propose two new energy/dissipation-preserving Birkhoffian multi-symplectic methods (Birkhoffian and Birkhoffian box) for Maxwell's equations with dissipation terms. After investigating the non-autonomous and autonomous Birkhoffian formalism for Maxwell's equations with dissipation terms, we first apply a novel generating functional theory to the non-autonomous Birkhoffian formalism to propose our Birkhoffian scheme, and then implement a central box method to the autonomous Birkhoffian formalism to derive the Birkhoffian box scheme. We have obtained four formal local conservation laws and three formal energy global conservation laws. We have also proved that both of our derived schemes preserve the discrete versionmore » of the global/local conservation laws. Furthermore, the stability, dissipation and dispersion relations are also investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, dissipation-preserving for Maxwell's equations in a perfectly matched layer (PML) medium and have second order accuracy in both time and space. Numerical experiments for problems with exact theoretical results are given to demonstrate that the Birkhoffian multi-symplectic schemes are much more accurate in preserving energy than both the exponential finite-difference time-domain (FDTD) method and traditional Hamiltonian scheme. Finally, we also solve the electromagnetic pulse (EMP) propagation problem and the numerical results show that the Birkhoffian scheme recovers the magnitude of the current source and reaction history very well even after long time propagation.« less

A study of the response of nonlinear springs

NASA Technical Reports Server (NTRS)

Hyer, M. W.; Knott, T. W.; Johnson, E. R.

1991-01-01

The various phases to developing a methodology for studying the response of a spring-reinforced arch subjected to a point load are discussed. The arch is simply supported at its ends with both the spring and the point load assumed to be at midspan. The spring is present to off-set the typical snap through behavior normally associated with arches, and to provide a structure that responds with constant resistance over a finite displacement. The various phases discussed consist of the following: (1) development of the closed-form solution for the shallow arch case; (2) development of a finite difference analysis to study (shallow) arches; and (3) development of a finite element analysis for studying more general shallow and nonshallow arches. The two numerical analyses rely on a continuation scheme to move the solution past limit points, and to move onto bifurcated paths, both characteristics being common to the arch problem. An eigenvalue method is used for a continuation scheme. The finite difference analysis is based on a mixed formulation (force and displacement variables) of the governing equations. The governing equations for the mixed formulation are in first order form, making the finite difference implementation convenient. However, the mixed formulation is not well-suited for the eigenvalue continuation scheme. This provided the motivation for the displacement based finite element analysis. Both the finite difference and the finite element analyses are compared with the closed form shallow arch solution. Agreement is excellent, except for the potential problems with the finite difference analysis and the continuation scheme. Agreement between the finite element analysis and another investigator's numerical analysis for deep arches is also good.

Optimization of finite difference forward modeling for elastic waves based on optimum combined window functions

NASA Astrophysics Data System (ADS)

Jian, Wang; Xiaohong, Meng; Hong, Liu; Wanqiu, Zheng; Yaning, Liu; Sheng, Gui; Zhiyang, Wang

2017-03-01

Full waveform inversion and reverse time migration are active research areas for seismic exploration. Forward modeling in the time domain determines the precision of the results, and numerical solutions of finite difference have been widely adopted as an important mathematical tool for forward modeling. In this article, the optimum combined of window functions was designed based on the finite difference operator using a truncated approximation of the spatial convolution series in pseudo-spectrum space, to normalize the outcomes of existing window functions for different orders. The proposed combined window functions not only inherit the characteristics of the various window functions, to provide better truncation results, but also control the truncation error of the finite difference operator manually and visually by adjusting the combinations and analyzing the characteristics of the main and side lobes of the amplitude response. Error level and elastic forward modeling under the proposed combined system were compared with outcomes from conventional window functions and modified binomial windows. Numerical dispersion is significantly suppressed, which is compared with modified binomial window function finite-difference and conventional finite-difference. Numerical simulation verifies the reliability of the proposed method.

Full Wave Analysis of Passive Microwave Monolithic Integrated Circuit Devices Using a Generalized Finite Difference Time Domain (GFDTD) Algorithm

NASA Technical Reports Server (NTRS)

Lansing, Faiza S.; Rascoe, Daniel L.

1993-01-01

This paper presents a modified Finite-Difference Time-Domain (FDTD) technique using a generalized conformed orthogonal grid. The use of the Conformed Orthogonal Grid, Finite Difference Time Domain (GFDTD) enables the designer to match all the circuit dimensions, hence eliminating a major source o error in the analysis.

Domain-adaptive finite difference methods for collapsing annular liquid jets

NASA Astrophysics Data System (ADS)

Ramos, J. I.

1993-01-01

A domain-adaptive technique which maps a time-dependent, curvilinear geometry into a unit square is used to determine the steady state mass absorption rate and the collapse of annular liquid jets. A method of lines is used to solve the one-dimensional fluid dynamics equations written in weak conservation-law form, and upwind differences are employed to evaluate the axial convective fluxes. The unknown, time-dependent, axial location of the downstream boundary is determined from the solution of an ordinary differential equation which is nonlinearly coupled to the fluid dynamics and gas concentration equations. The equation for the gas concentration in the annular liquid jet is written in strong conservation-law form and solved by means of a method of lines at high Peclet numbers and a line Gauss-Seidel method at low Peclet numbers. The effects of the number of grid points along and across the annular jet, time step, and discretization of the radial convective fluxes on both the steady state mass absorption rate and the jet's collapse rate have been analyzed on staggered and non-staggered grids. The steady state mass absorption rate and the collapse of annular liquid jets are determined as a function of the Froude, Peclet and Weber numbers, annular jet's thickness-to-radius ratio at the nozzle exit, initial pressure difference across the annular jet, nozzle exit angle, temperature of the gas enclosed by the annular jet, pressure of the gas surrounding the jet, solubilities at the inner and outer interfaces of the annular jet, and gas concentration at the nozzle exit. It is shown that the steady state mass absorption rate is proportional to the inverse square root of the Peclet number except for low values of this parameter, and that the possible mathematical incompatibilities in the concentration field at the nozzle exit exert a great influence on the steady state mass absorption rate and on the jet collapse. It is also shown that the steady state mass absorption rate increases as the Weber number, nozzle exit angle, gas concentration at the nozzle exit, and temperature of the gases enclosed by the annular liquid jet are increased, but it decreases as the Froude and Peclet numbers, and annular liquid jet's thickness-to-radius ratio at the nozzle exit are increased. It is also shown that the annular liquid jet's collapse rate increases as the Weber number, nozzle exit angle, temperature of the gases enclosed by the annular liquid jet, and pressure of the gases which surround the jet are increased, but decreases as the Froude and Peclet numbers, and annular liquid jet's thickness-toradius ratio at the nozzle exit are increased. It is also shown that both the ratio of the initial pressure of the gas enclosed by the jet to the pressure of the gas surrounding the jet and the ratio of solubilities at the annular liquid jet's inner and outer interfaces play an important role on both the steady state mass absorption rate and the jet collapse. If the product of these ratios is greater or less than one, both the pressure and the mass of the gas enclosed by the annular liquid jet decrease or increase, respectively, with time. It is also shown that the numerical results obtained with the conservative, domain-adaptive method of lines technique presented in this paper are in excellent agreement with those of a domain-adaptive, iterative, non-conservative, block-bidiagonal, finite difference method which uncouples the solution of the fluid dynamics equations from that of the convergence length.

Flowfield computation of entry vehicles

NASA Technical Reports Server (NTRS)

Prabhu, Dinesh K.

1990-01-01

The equations governing the multidimensional flow of a reacting mixture of thermally perfect gasses were derived. The modeling procedures for the various terms of the conservation laws are discussed. A numerical algorithm, based on the finite-volume approach, to solve these conservation equations was developed. The advantages and disadvantages of the present numerical scheme are discussed from the point of view of accuracy, computer time, and memory requirements. A simple one-dimensional model problem was solved to prove the feasibility and accuracy of the algorithm. A computer code implementing the above algorithm was developed and is presently being applied to simple geometries and conditions. Once the code is completely debugged and validated, it will be used to compute the complete unsteady flow field around the Aeroassist Flight Experiment (AFE) body.

A Taylor weak-statement algorithm for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Baker, A. J.; Kim, J. W.

1987-01-01

Finite element analysis, applied to computational fluid dynamics (CFD) problem classes, presents a formal procedure for establishing the ingredients of a discrete approximation numerical solution algorithm. A classical Galerkin weak-statement formulation, formed on a Taylor series extension of the conservation law system, is developed herein that embeds a set of parameters eligible for constraint according to specification of suitable norms. The derived family of Taylor weak statements is shown to contain, as special cases, over one dozen independently derived CFD algorithms published over the past several decades for the high speed flow problem class. A theoretical analysis is completed that facilitates direct qualitative comparisons. Numerical results for definitive linear and nonlinear test problems permit direct quantitative performance comparisons.

Numerical study of supersonic combustors by multi-block grids with mismatched interfaces

NASA Technical Reports Server (NTRS)

Moon, Young J.

1990-01-01

A three dimensional, finite rate chemistry, Navier-Stokes code was extended to a multi-block code with mismatched interface for practical calculations of supersonic combustors. To ensure global conservation, a conservative algorithm was used for the treatment of mismatched interfaces. The extended code was checked against one test case, i.e., a generic supersonic combustor with transverse fuel injection, examining solution accuracy, convergence, and local mass flux error. After testing, the code was used to simulate the chemically reacting flow fields in a scramjet combustor with parallel fuel injectors (unswept and swept ramps). Computational results were compared with experimental shadowgraph and pressure measurements. Fuel-air mixing characteristics of the unswept and swept ramps were compared and investigated.

A Finite Element Method for Simulation of Compressible Cavitating Flows

NASA Astrophysics Data System (ADS)

Shams, Ehsan; Yang, Fan; Zhang, Yu; Sahni, Onkar; Shephard, Mark; Oberai, Assad

2016-11-01

This work focuses on a novel approach for finite element simulations of multi-phase flows which involve evolving interface with phase change. Modeling problems, such as cavitation, requires addressing multiple challenges, including compressibility of the vapor phase, interface physics caused by mass, momentum and energy fluxes. We have developed a mathematically consistent and robust computational approach to address these problems. We use stabilized finite element methods on unstructured meshes to solve for the compressible Navier-Stokes equations. Arbitrary Lagrangian-Eulerian formulation is used to handle the interface motions. Our method uses a mesh adaptation strategy to preserve the quality of the volumetric mesh, while the interface mesh moves along with the interface. The interface jump conditions are accurately represented using a discontinuous Galerkin method on the conservation laws. Condensation and evaporation rates at the interface are thermodynamically modeled to determine the interface velocity. We will present initial results on bubble cavitation the behavior of an attached cavitation zone in a separated boundary layer. We acknowledge the support from Army Research Office (ARO) under ARO Grant W911NF-14-1-0301.

Nonlinear analysis for the response and failure of compression-loaded angle-ply laminates with a hole

NASA Technical Reports Server (NTRS)

Mathison, Steven R.; Herakovich, Carl T.; Pindera, Marek-Jerzy; Shuart, Mark J.

1987-01-01

The objective was to determine the effect of nonlinear material behavior on the response and failure of unnotched and notched angle-ply laminates under uniaxial compressive loading. The endochronic theory was chosen as the constitutive theory to model the AS4/3502 graphite-epoxy material system. Three-dimensional finite element analysis incorporating the endochronic theory was used to determine the stresses and strains in the laminates. An incremental/iterative initial strain algorithm was used in the finite element program. To increase computational efficiency, a 180 deg rotational symmetry relationship was utilized and the finite element program was vectorized to run on a supercomputer. Laminate response was compared to experimentation revealing excellent agreement for both the unnotched and notched angle-ply laminates. Predicted stresses in the region of the hole were examined and are presented, comparing linear elastic analysis to the inelastic endochronic theory analysis. A failure analysis of the unnotched and notched laminates was performed using the quadratic tensor polynomial. Predicted fracture loads compared well with experimentation for the unnotched laminates, but were very conservative in comparison with experiments for the notched laminates.

Diffusion with finite-helicity field tensor: A mechanism of generating heterogeneity

NASA Astrophysics Data System (ADS)

Sato, N.; Yoshida, Z.

2018-02-01

Topological constraints on a dynamical system often manifest themselves as breaking of the Hamiltonian structure; well-known examples are nonholonomic constraints on Lagrangian mechanics. The statistical mechanics under such topological constraints is the subject of this study. Conventional arguments based on phase spaces, Jacobi identity, invariant measure, or the H theorem are no longer applicable since all these notions stem from the symplectic geometry underlying canonical Hamiltonian systems. Remembering that Hamiltonian systems are endowed with field tensors (canonical 2-forms) that have zero helicity, our mission is to extend the scope toward the class of systems governed by finite-helicity field tensors. Here, we introduce a class of field tensors that are characterized by Beltrami vectors. We prove an H theorem for this Beltrami class. The most general class of energy-conserving systems are non-Beltrami, for which we identify the "field charge" that prevents the entropy to maximize, resulting in creation of heterogeneous distributions. The essence of the theory can be delineated by classifying three-dimensional dynamics. We then generalize to arbitrary (finite) dimensions.

Combination of the discontinuous Galerkin method with finite differences for simulation of seismic wave propagation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lisitsa, Vadim, E-mail: lisitsavv@ipgg.sbras.ru; Novosibirsk State University, Novosibirsk; Tcheverda, Vladimir

We present an algorithm for the numerical simulation of seismic wave propagation in models with a complex near surface part and free surface topography. The approach is based on the combination of finite differences with the discontinuous Galerkin method. The discontinuous Galerkin method can be used on polyhedral meshes; thus, it is easy to handle the complex surfaces in the models. However, this approach is computationally intense in comparison with finite differences. Finite differences are computationally efficient, but in general, they require rectangular grids, leading to the stair-step approximation of the interfaces, which causes strong diffraction of the wavefield. Inmore » this research we present a hybrid algorithm where the discontinuous Galerkin method is used in a relatively small upper part of the model and finite differences are applied to the main part of the model.« less

Finite-key security analyses on passive decoy-state QKD protocols with different unstable sources

PubMed Central

Song, Ting-Ting; Qin, Su-Juan; Wen, Qiao-Yan; Wang, Yu-Kun; Jia, Heng-Yue

2015-01-01

In quantum communication, passive decoy-state QKD protocols can eliminate many side channels, but the protocols without any finite-key analyses are not suitable for in practice. The finite-key securities of passive decoy-state (PDS) QKD protocols with two different unstable sources, type-II parametric down-convention (PDC) and phase randomized weak coherent pulses (WCPs), are analyzed in our paper. According to the PDS QKD protocols, we establish an optimizing programming respectively and obtain the lower bounds of finite-key rates. Under some reasonable values of quantum setup parameters, the lower bounds of finite-key rates are simulated. The simulation results show that at different transmission distances, the affections of different fluctuations on key rates are different. Moreover, the PDS QKD protocol with an unstable PDC source can resist more intensity fluctuations and more statistical fluctuation. PMID:26471947

Development of an object-oriented finite element program: application to metal-forming and impact simulations

NASA Astrophysics Data System (ADS)

Pantale, O.; Caperaa, S.; Rakotomalala, R.

2004-07-01

During the last 50 years, the development of better numerical methods and more powerful computers has been a major enterprise for the scientific community. In the same time, the finite element method has become a widely used tool for researchers and engineers. Recent advances in computational software have made possible to solve more physical and complex problems such as coupled problems, nonlinearities, high strain and high-strain rate problems. In this field, an accurate analysis of large deformation inelastic problems occurring in metal-forming or impact simulations is extremely important as a consequence of high amount of plastic flow. In this presentation, the object-oriented implementation, using the C++ language, of an explicit finite element code called DynELA is presented. The object-oriented programming (OOP) leads to better-structured codes for the finite element method and facilitates the development, the maintainability and the expandability of such codes. The most significant advantage of OOP is in the modeling of complex physical systems such as deformation processing where the overall complex problem is partitioned in individual sub-problems based on physical, mathematical or geometric reasoning. We first focus on the advantages of OOP for the development of scientific programs. Specific aspects of OOP, such as the inheritance mechanism, the operators overload procedure or the use of template classes are detailed. Then we present the approach used for the development of our finite element code through the presentation of the kinematics, conservative and constitutive laws and their respective implementation in C++. Finally, the efficiency and accuracy of our finite element program are investigated using a number of benchmark tests relative to metal forming and impact simulations.

A finite-volume module for all-scale Earth-system modelling at ECMWF

NASA Astrophysics Data System (ADS)

Kühnlein, Christian; Malardel, Sylvie; Smolarkiewicz, Piotr

2017-04-01

We highlight recent advancements in the development of the finite-volume module (FVM) (Smolarkiewicz et al., 2016) for the IFS at ECMWF. FVM represents an alternative dynamical core that complements the operational spectral dynamical core of the IFS with new capabilities. Most notably, these include a compact-stencil finite-volume discretisation, flexible meshes, conservative non-oscillatory transport and all-scale governing equations. As a default, FVM solves the compressible Euler equations in a geospherical framework (Szmelter and Smolarkiewicz, 2010). The formulation incorporates a generalised terrain-following vertical coordinate. A hybrid computational mesh, fully unstructured in the horizontal and structured in the vertical, enables efficient global atmospheric modelling. Moreover, a centred two-time-level semi-implicit integration scheme is employed with 3D implicit treatment of acoustic, buoyant, and rotational modes. The associated 3D elliptic Helmholtz problem is solved using a preconditioned Generalised Conjugate Residual approach. The solution procedure employs the non-oscillatory finite-volume MPDATA advection scheme that is bespoke for the compressible dynamics on the hybrid mesh (Kühnlein and Smolarkiewicz, 2017). The recent progress of FVM is illustrated with results of benchmark simulations of intermediate complexity, and comparison to the operational spectral dynamical core of the IFS. C. Kühnlein, P.K. Smolarkiewicz: An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics, J. Comput. Phys. (2017), in press. P.K. Smolarkiewicz, W. Deconinck, M. Hamrud, C. Kühnlein, G. Mozdzynski, J. Szmelter, N.P. Wedi: A finite-volume module for simulating global all-scale atmospheric flows, J. Comput. Phys. 314 (2016) 287-304. J. Szmelter, P.K. Smolarkiewicz: An edge-based unstructured mesh discretisation in geospherical framework, J. Comput. Phys. 229 (2010) 4980-4995.

Algebraic dynamic multilevel method for compositional flow in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Cusini, Matteo; Fryer, Barnaby; van Kruijsdijk, Cor; Hajibeygi, Hadi

2018-02-01

This paper presents the algebraic dynamic multilevel method (ADM) for compositional flow in three dimensional heterogeneous porous media in presence of capillary and gravitational effects. As a significant advancement compared to the ADM for immiscible flows (Cusini et al., 2016) [33], here, mass conservation equations are solved along with k-value based thermodynamic equilibrium equations using a fully-implicit (FIM) coupling strategy. Two different fine-scale compositional formulations are considered: (1) the natural variables and (2) the overall-compositions formulation. At each Newton's iteration the fine-scale FIM Jacobian system is mapped to a dynamically defined (in space and time) multilevel nested grid. The appropriate grid resolution is chosen based on the contrast of user-defined fluid properties and on the presence of specific features (e.g., well source terms). Consistent mapping between different resolutions is performed by the means of sequences of restriction and prolongation operators. While finite-volume restriction operators are employed to ensure mass conservation at all resolutions, various prolongation operators are considered. In particular, different interpolation strategies can be used for the different primary variables, and multiscale basis functions are chosen as pressure interpolators so that fine scale heterogeneities are accurately accounted for across different resolutions. Several numerical experiments are conducted to analyse the accuracy, efficiency and robustness of the method for both 2D and 3D domains. Results show that ADM provides accurate solutions by employing only a fraction of the number of grid-cells employed in fine-scale simulations. As such, it presents a promising approach for large-scale simulations of multiphase flow in heterogeneous reservoirs with complex non-linear fluid physics.

Discontinuous Galerkin (DG) Method for solving time dependent convection-diffusion type temperature equation : Demonstration and Comparison with Other Methods in the Mantle Convection Code ASPECT

NASA Astrophysics Data System (ADS)

He, Y.; Puckett, E. G.; Billen, M. I.; Kellogg, L. H.

2016-12-01

For a convection-dominated system, like convection in the Earth's mantle, accurate modeling of the temperature field in terms of the interaction between convective and diffusive processes is one of the most common numerical challenges. In the geodynamics community using Finite Element Method (FEM) with artificial entropy viscosity is a popular approach to resolve this difficulty, but introduce numerical diffusion. The extra artificial viscosity added into the temperature system will not only oversmooth the temperature field where the convective process dominates, but also change the physical properties by increasing the local material conductivity, which will eventually change the local conservation of energy. Accurate modeling of temperature is especially important in the mantle, where material properties are strongly dependent on temperature. In subduction zones, for example, the rheology of the cold sinking slab depends nonlinearly on the temperature, and physical processes such as slab detachment, rollback, and melting all are sensitively dependent on temperature and rheology. Therefore methods that overly smooth the temperature may inaccurately represent the physical processes governing subduction, lithospheric instabilities, plume generation and other aspects of mantle convection. Here we present a method for modeling the temperature field in mantle dynamics simulations using a new solver implemented in the ASPECT software. The new solver for the temperature equation uses a Discontinuous Galerkin (DG) approach, which combines features of both finite element and finite volume methods, and is particularly suitable for problems satisfying the conservation law, and the solution has a large variation locally. Furthermore, we have applied a post-processing technique to insure that the solution satisfies a local discrete maximum principle in order to eliminate the overshoots and undershoots in the temperature locally. To demonstrate the capabilities of this new method we present benchmark results (e.g., falling sphere), and a simple subduction models with kinematic surface boundary condition. To evaluate the trade-offs in computational speed and solution accuracy we present results for the same benchmarks using the Finite Element entropy viscosity method available in ASPECT.

Energy balance and mass conservation in reduced order models of fluid flows

NASA Astrophysics Data System (ADS)

Mohebujjaman, Muhammad; Rebholz, Leo G.; Xie, Xuping; Iliescu, Traian

2017-10-01

In this paper, we investigate theoretically and computationally the conservation properties of reduced order models (ROMs) for fluid flows. Specifically, we investigate whether the ROMs satisfy the same (or similar) energy balance and mass conservation as those satisfied by the Navier-Stokes equations. All of our theoretical findings are illustrated and tested in numerical simulations of a 2D flow past a circular cylinder at a Reynolds number Re = 100. First, we investigate the ROM energy balance. We show that using the snapshot average for the centering trajectory (which is a popular treatment of nonhomogeneous boundary conditions in ROMs) yields an incorrect energy balance. Then, we propose a new approach, in which we replace the snapshot average with the Stokes extension. Theoretically, the Stokes extension produces an accurate energy balance. Numerically, the Stokes extension yields more accurate results than the standard snapshot average, especially for longer time intervals. Our second contribution centers around ROM mass conservation. We consider ROMs created using two types of finite elements: the standard Taylor-Hood (TH) element, which satisfies the mass conservation weakly, and the Scott-Vogelius (SV) element, which satisfies the mass conservation pointwise. Theoretically, the error estimates for the SV-ROM are sharper than those for the TH-ROM. Numerically, the SV-ROM yields significantly more accurate results, especially for coarser meshes and longer time intervals.

Finite-difference computations of rotor loads

NASA Technical Reports Server (NTRS)

Caradonna, F. X.; Tung, C.

1985-01-01

This paper demonstrates the current and future potential of finite-difference methods for solving real rotor problems which now rely largely on empiricism. The demonstration consists of a simple means of combining existing finite-difference, integral, and comprehensive loads codes to predict real transonic rotor flows. These computations are performed for hover and high-advance-ratio flight. Comparisons are made with experimental pressure data.

Finite-difference computations of rotor loads

NASA Technical Reports Server (NTRS)

Caradonna, F. X.; Tung, C.

1985-01-01

The current and future potential of finite difference methods for solving real rotor problems which now rely largely on empiricism are demonstrated. The demonstration consists of a simple means of combining existing finite-difference, integral, and comprehensive loads codes to predict real transonic rotor flows. These computations are performed for hover and high-advanced-ratio flight. Comparisons are made with experimental pressure data.

A mass-energy preserving Galerkin FEM for the coupled nonlinear fractional Schrödinger equations

NASA Astrophysics Data System (ADS)

Zhang, Guoyu; Huang, Chengming; Li, Meng

2018-04-01

We consider the numerical simulation of the coupled nonlinear space fractional Schrödinger equations. Based on the Galerkin finite element method in space and the Crank-Nicolson (CN) difference method in time, a fully discrete scheme is constructed. Firstly, we focus on a rigorous analysis of conservation laws for the discrete system. The definitions of discrete mass and energy here correspond with the original ones in physics. Then, we prove that the fully discrete system is uniquely solvable. Moreover, we consider the unconditionally convergent properties (that is to say, we complete the error estimates without any mesh ratio restriction). We derive L2-norm error estimates for the nonlinear equations and L^{∞}-norm error estimates for the linear equations. Finally, some numerical experiments are included showing results in agreement with the theoretical predictions.

Vafa-Witten theorem and Lee-Yang singularities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aguado, M.; Asorey, M.

2009-12-15

We prove the analyticity of the finite volume QCD partition function for complex values of the {theta}-vacuum parameter. The absence of singularities different from Lee-Yang zeros only permits and cusp singularities in the vacuum energy density and never or cusps. This fact together with the Vafa-Witten diamagnetic inequality implies the vanishing of the density of Lee-Yang zeros at {theta}=0 and has an important consequence: the absence of a first order phase transition at {theta}=0. The result provides a key missing link in the Vafa-Witten proof of parity symmetry conservation in vectorlike gauge theories and follows from renormalizability, unitarity, positivity, andmore » existence of Bogomol'nyi-Prasad-Sommerfield bounds. Generalizations of this theorem to other physical systems are also discussed, with particular interest focused on the nonlinear CP{sup N} sigma model.« less

MULTISHOCKED,THREE-DIMENSIONAL SUPERSONIC FLOWFIELDS WITH REAL GAS EFFECTS

NASA Technical Reports Server (NTRS)

Kutler, P.

1994-01-01

This program determines the supersonic flowfield surrounding three-dimensional wing-body configurations of a delta wing. It was designed to provide the numerical computation of three dimensional inviscid, flowfields of either perfect or real gases about supersonic or hypersonic airplanes. The governing equations in conservation law form are solved by a finite difference method using a second order noncentered algorithm between the body and the outermost shock wave, which is treated as a sharp discontinuity. Secondary shocks which form between these boundaries are captured automatically. The flowfield between the body and outermost shock is treated in a shock capturing fashion and therefore allows for the correct formation of secondary internal shocks . The program operates in batch mode, is in CDC update format, has been implemented on the CDC 7600, and requires more than 140K (octal) word locations.

Exponential Boundary Observers for Pressurized Water Pipe

NASA Astrophysics Data System (ADS)

Hermine Som, Idellette Judith; Cocquempot, Vincent; Aitouche, Abdel

2015-11-01

This paper deals with state estimation on a pressurized water pipe modeled by nonlinear coupled distributed hyperbolic equations for non-conservative laws with three known boundary measures. Our objective is to estimate the fourth boundary variable, which will be useful for leakage detection. Two approaches are studied. Firstly, the distributed hyperbolic equations are discretized through a finite-difference scheme. By using the Lipschitz property of the nonlinear term and a Lyapunov function, the exponential stability of the estimation error is proven by solving Linear Matrix Inequalities (LMIs). Secondly, the distributed hyperbolic system is preserved for state estimation. After state transformations, a Luenberger-like PDE boundary observer based on backstepping mathematical tools is proposed. An exponential Lyapunov function is used to prove the stability of the resulted estimation error. The performance of the two observers are shown on a water pipe prototype simulated example.

Vacuum energy in Einstein-Gauss-Bonnet anti-de Sitter gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kofinas, Georgios; Olea, Rodrigo

2006-10-15

A finite action principle for Einstein-Gauss-Bonnet anti-de Sitter gravity is achieved by supplementing the bulk Lagrangian by a suitable boundary term, whose form substantially differs in odd and even dimensions. For even dimensions, this term is given by the boundary contribution in the Euler theorem with a coupling constant fixed, demanding the spacetime to have constant (negative) curvature in the asymptotic region. For odd dimensions, the action is stationary under a boundary condition on the variation of the extrinsic curvature. A well-posed variational principle leads to an appropriate definition of energy and other conserved quantities using the Noether theorem, andmore » to a correct description of black hole thermodynamics. In particular, this procedure assigns a nonzero energy to anti-de Sitter spacetime in all odd dimensions.« less

Assessment of chemistry models for compressible reacting flows

NASA Astrophysics Data System (ADS)

Lapointe, Simon; Blanquart, Guillaume

2014-11-01

Recent technological advances in propulsion and power devices and renewed interest in the development of next generation supersonic and hypersonic vehicles have increased the need for detailed understanding of turbulence-combustion interactions in compressible reacting flows. In numerical simulations of such flows, accurate modeling of the fuel chemistry is a critical component of capturing the relevant physics. Various chemical models are currently being used in reacting flow simulations. However, the differences between these models and their impacts on the fluid dynamics in the context of compressible flows are not well understood. In the present work, a numerical code is developed to solve the fully coupled compressible conservation equations for reacting flows. The finite volume code is based on the theoretical and numerical framework developed by Oefelein (Prog. Aero. Sci. 42 (2006) 2-37) and employs an all-Mach-number formulation with dual time-stepping and preconditioning. The numerical approach is tested on turbulent premixed flames at high Karlovitz numbers. Different chemical models of varying complexity and computational cost are used and their effects are compared.

Faraday Shields within a Solenoidal Coil to Reduce Sample Heating: Numerical Comparison of Designs and Experimental Verification

PubMed Central

Park, BuSik; Neuberger, Thomas; Webb, Andrew G.; Bigler, Don C.; Collins, Christopher M.

2009-01-01

A comparison of methods to decrease RF power dissipation and related heating in conductive samples using passive conductors surrounding a sample in a solenoid coil is presented. Full-Maxwell finite difference time domain numerical calculations were performed to evaluate the effect of the passive conductors by calculating conservative and magnetically-induced electric field and magnetic field distributions. To validate the simulation method, experimental measurements of temperature increase were conducted using a solenoidal coil (diameter 3 mm), a saline sample (10 mM NaCl) and passive copper shielding wires (50 μm diameter). The temperature increase was 58% lower with the copper wires present for several different input powers to the coil. This was in good agreement with simulation for the same geometry, which indicated 57% lower power dissipated in the sample with conductors present. Simulations indicate that some designs should be capable of reducing temperature increase by more than 85%. PMID:19879784

Comparative study of numerical schemes of TVD3, UNO3-ACM and optimized compact scheme

NASA Technical Reports Server (NTRS)

Lee, Duck-Joo; Hwang, Chang-Jeon; Ko, Duck-Kon; Kim, Jae-Wook

1995-01-01

Three different schemes are employed to solve the benchmark problem. The first one is a conventional TVD-MUSCL (Monotone Upwind Schemes for Conservation Laws) scheme. The second scheme is a UNO3-ACM (Uniformly Non-Oscillatory Artificial Compression Method) scheme. The third scheme is an optimized compact finite difference scheme modified by us: the 4th order Runge Kutta time stepping, the 4th order pentadiagonal compact spatial discretization with the maximum resolution characteristics. The problems of category 1 are solved by using the second (UNO3-ACM) and third (Optimized Compact) schemes. The problems of category 2 are solved by using the first (TVD3) and second (UNO3-ACM) schemes. The problem of category 5 is solved by using the first (TVD3) scheme. It can be concluded from the present calculations that the Optimized Compact scheme and the UN03-ACM show good resolutions for category 1 and category 2 respectively.

High-intensity discharge lamp and Duffing oscillator—Similarities and differences

NASA Astrophysics Data System (ADS)

Baumann, Bernd; Schwieger, Joerg; Stein, Ulrich; Hallerberg, Sarah; Wolff, Marcus

2017-12-01

The processes inside the arc tube of high-intensity discharge lamps are investigated using finite element simulations. The behavior of the gas mixture inside the arc tube is governed by differential equations describing mass, energy, and charge conservation, as well as the Helmholtz equation for the acoustic pressure and the Reynolds equations for the flow driven by buoyancy and Reynolds stresses. The model is highly nonlinear and requires a recursion procedure to account for the impact of acoustic streaming on the temperature and other fields. The investigations reveal the presence of a hysteresis and the corresponding jump phenomenon, quite similar to a Duffing oscillator. The similarities and, in particular, the differences of the nonlinear behavior of the high-intensity discharge lamp to that of a Duffing oscillator are discussed. For large amplitudes, the high-intensity discharge lamp exhibits a stiffening effect in contrast to the Duffing oscillator. It is speculated on how the stiffening might affect hysteresis suppression.

Effectiveness of braces designed using computer-aided design and manufacturing (CAD/CAM) and finite element simulation compared to CAD/CAM only for the conservative treatment of adolescent idiopathic scoliosis: a prospective randomized controlled trial.

PubMed

Cobetto, N; Aubin, C E; Parent, S; Clin, J; Barchi, S; Turgeon, I; Labelle, Hubert

2016-10-01

Clinical assessment of immediate in-brace effect of braces designed using CAD/CAM and FEM vs. only CAD/CAM for conservative treatment of AIS, using a randomized blinded and controlled study design. Forty AIS patients were prospectively recruited and randomized into two groups. For 19 patients (control group), the brace was designed using a scan of patient's torso and a conventional CAD/CAM approach (CtrlBrace). For the 21 other patients (test group), the brace was additionally designed using finite element modeling (FEM) and 3D reconstructions of spine, rib cage and pelvis (NewBrace). The NewBrace design was simulated and iteratively optimized to maximize the correction and minimize the contact surface and material. Both groups had comparable age, sex, weight, height, curve type and severity. Scoliosis Research Society standardized criteria for bracing were followed. Average Cobb angle prior to bracing was 27° and 28° for main thoracic (MT) and lumbar (L) curves, respectively, for the control group, while it was 33° and 28° for the test group. CtrlBraces reduced MT and L curves by 8° (29 %) and 10° (40 %), respectively, compared to 14° (43 %) and 13° (46 %) for NewBraces, which were simulated with a difference inferior to 5°. NewBraces were 50 % thinner and had 20 % less covering surface than CtrlBraces. Braces designed with CAD/CAM and 3D FEM simulation were more efficient and lighter than standard CAD/CAM TLSO's at first immediate in-brace evaluation. These results suggest that long-term effect of bracing in AIS may be improved using this new platform for brace fabrication. NCT02285621.

Computer-Oriented Calculus Courses Using Finite Differences.

ERIC Educational Resources Information Center

Gordon, Sheldon P.

The so-called discrete approach in calculus instruction involves introducing topics from the calculus of finite differences and finite sums, both for motivation and as useful tools for applications of the calculus. In particular, it provides an ideal setting in which to incorporate computers into calculus courses. This approach has been…

An Astronomical Test of CCD Photometric Precision

NASA Technical Reports Server (NTRS)

Koch, David; Dunham, Edward; Borucki, William; Jenkins, Jon; DeVingenzi, D. (Technical Monitor)

1998-01-01

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques. we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

Optimized norm-conserving Hartree-Fock pseudopotentials for plane-wave calculations

NASA Astrophysics Data System (ADS)

Al-Saidi, W. A.; Walter, E. J.; Rappe, A. M.

2008-02-01

We report Hartree-Fock (HF)-based pseudopotentials suitable for plane-wave calculations. Unlike typical effective core potentials, the present pseudopotentials are finite at the origin and exhibit rapid convergence in a plane-wave basis; the optimized pseudopotential method [A. M. Rappe , Phys. Rev. B 41, 1227 (1990)] improves plane-wave convergence. Norm-conserving HF pseudopotentials are found to develop long-range non-Coulombic behavior which does not decay faster than 1/r , and is nonlocal. This behavior, which stems from the nonlocality of the exchange potential, is remedied using a recently developed self-consistent procedure [J. R. Trail and R. J. Needs, J. Chem. Phys. 122, 014112 (2005)]. The resulting pseudopotentials slightly violate the norm conservation of the core charge. We calculated several atomic properties using these pseudopotentials, and the results are in good agreement with all-electron HF values. The dissociation energies, equilibrium bond lengths, and frequencies of vibration of several dimers obtained with these HF pseudopotentials and plane waves are also in good agreement with all-electron results.

On recontamination and directional-bias problems in Monte Carlo simulation of PDF turbulence models. [probability density function

NASA Technical Reports Server (NTRS)

Hsu, Andrew T.

1992-01-01

Turbulent combustion can not be simulated adequately by conventional moment closure turbulent models. The probability density function (PDF) method offers an attractive alternative: in a PDF model, the chemical source terms are closed and do not require additional models. Because the number of computational operations grows only linearly in the Monte Carlo scheme, it is chosen over finite differencing schemes. A grid dependent Monte Carlo scheme following J.Y. Chen and W. Kollmann has been studied in the present work. It was found that in order to conserve the mass fractions absolutely, one needs to add further restrictions to the scheme, namely alpha(sub j) + gamma(sub j) = alpha(sub j - 1) + gamma(sub j + 1). A new algorithm was devised that satisfied this restriction in the case of pure diffusion or uniform flow problems. Using examples, it is shown that absolute conservation can be achieved. Although for non-uniform flows absolute conservation seems impossible, the present scheme has reduced the error considerably.

Scattering theory of nonlinear thermoelectricity in quantum coherent conductors.

PubMed

Meair, Jonathan; Jacquod, Philippe

2013-02-27

We construct a scattering theory of weakly nonlinear thermoelectric transport through sub-micron scale conductors. The theory incorporates the leading nonlinear contributions in temperature and voltage biases to the charge and heat currents. Because of the finite capacitances of sub-micron scale conducting circuits, fundamental conservation laws such as gauge invariance and current conservation require special care to be preserved. We do this by extending the approach of Christen and Büttiker (1996 Europhys. Lett. 35 523) to coupled charge and heat transport. In this way we write relations connecting nonlinear transport coefficients in a manner similar to Mott's relation between the linear thermopower and the linear conductance. We derive sum rules that nonlinear transport coefficients must satisfy to preserve gauge invariance and current conservation. We illustrate our theory by calculating the efficiency of heat engines and the coefficient of performance of thermoelectric refrigerators based on quantum point contacts and resonant tunneling barriers. We identify, in particular, rectification effects that increase device performance.

Inference for finite-sample trajectories in dynamic multi-state site-occupancy models using hidden Markov model smoothing

USGS Publications Warehouse

Fiske, Ian J.; Royle, J. Andrew; Gross, Kevin

2014-01-01

Ecologists and wildlife biologists increasingly use latent variable models to study patterns of species occurrence when detection is imperfect. These models have recently been generalized to accommodate both a more expansive description of state than simple presence or absence, and Markovian dynamics in the latent state over successive sampling seasons. In this paper, we write these multi-season, multi-state models as hidden Markov models to find both maximum likelihood estimates of model parameters and finite-sample estimators of the trajectory of the latent state over time. These estimators are especially useful for characterizing population trends in species of conservation concern. We also develop parametric bootstrap procedures that allow formal inference about latent trend. We examine model behavior through simulation, and we apply the model to data from the North American Amphibian Monitoring Program.

Hyperbolic reformulation of a 1D viscoelastic blood flow model and ADER finite volume schemes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Montecinos, Gino I.; Müller, Lucas O.; Toro, Eleuterio F.

2014-06-01

The applicability of ADER finite volume methods to solve hyperbolic balance laws with stiff source terms in the context of well-balanced and non-conservative schemes is extended to solve a one-dimensional blood flow model for viscoelastic vessels, reformulated as a hyperbolic system, via a relaxation time. A criterion for selecting relaxation times is found and an empirical convergence rate assessment is carried out to support this result. The proposed methodology is validated by applying it to a network of viscoelastic vessels for which experimental and numerical results are available. The agreement between the results obtained in the present paper and thosemore » available in the literature is satisfactory. Key features of the present formulation and numerical methodologies, such as accuracy, efficiency and robustness, are fully discussed in the paper.« less

A second-order cell-centered Lagrangian ADER-MOOD finite volume scheme on multidimensional unstructured meshes for hydrodynamics

NASA Astrophysics Data System (ADS)

Boscheri, Walter; Dumbser, Michael; Loubère, Raphaël; Maire, Pierre-Henri

2018-04-01

In this paper we develop a conservative cell-centered Lagrangian finite volume scheme for the solution of the hydrodynamics equations on unstructured multidimensional grids. The method is derived from the Eucclhyd scheme discussed in [47,43,45]. It is second-order accurate in space and is combined with the a posteriori Multidimensional Optimal Order Detection (MOOD) limiting strategy to ensure robustness and stability at shock waves. Second-order of accuracy in time is achieved via the ADER (Arbitrary high order schemes using DERivatives) approach. A large set of numerical test cases is proposed to assess the ability of the method to achieve effective second order of accuracy on smooth flows, maintaining an essentially non-oscillatory behavior on discontinuous profiles, general robustness ensuring physical admissibility of the numerical solution, and precision where appropriate.

Navier-Stokes Solutions for Spin-Up from Rest in a Cylindrical Container

DTIC Science & Technology

1979-09-01

CONDITIONS The calculations employ a finite - difference analog of the unsteady axisyimetric Navier-Stokes equations formulated in cylindrical coordinates...derivatives are approximated by second- order accurate one-sided difference formulae involving three time levels. * The following finite - difference ...equation are identical in form to Equations (13). The finite - difference representations for the ?-equation are: "(i)[aJ~lk " /i’,J-l2k] T (14a) •g I

An Exponential Finite Difference Technique for Solving Partial Differential Equations. M.S. Thesis - Toledo Univ., Ohio

NASA Technical Reports Server (NTRS)

Handschuh, Robert F.

1987-01-01

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that were more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.

exponential finite difference technique for solving partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Handschuh, R.F.

1987-01-01

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that weremore » more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.« less

3D Gaussian Beam Modeling

DTIC Science & Technology

2011-09-01

optimized building blocks such as a parallelized tri-diagonal linear solver (used in the “implicit finite differences ” and split-step Pade PE models...and Ding Lee. “A finite - difference treatment of interface conditions for the parabolic wave equation: The horizontal interface.” The Journal of the...Acoustical Society of America, 71(4):855, 1982. 3. Ding Lee and Suzanne T. McDaniel. “A finite - difference treatment of interface conditions for

SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES

PubMed Central

Wan, Xiaohai; Li, Zhilin

2012-01-01

Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size. PMID:22701346

SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES.

PubMed

Wan, Xiaohai; Li, Zhilin

2012-06-01

Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size.

A Finite Difference Numerical Model for the Propagation of Finite Amplitude Acoustical Blast Waves Outdoors Over Hard and Porous Surfaces

DTIC Science & Technology

1991-09-01

Difference Numerical Model for the Propagation of Finite Amplitude Acoustical Blast Waves Outdoors Over Hard and Porous Surfaces by Victor W. Sparrow...The nonlinear acoustic propagation effects require a numerical solution in the time domain. To model a porous ground surface, which in the frequency...incident on the hard and porous surfaces were produced. The model predicted that near grazing finite amplitude acoustic blast waves decay with distance

A progress report on estuary modeling by the finite-element method

USGS Publications Warehouse

Gray, William G.

1978-01-01

Various schemes are investigated for finite-element modeling of two-dimensional surface-water flows. The first schemes investigated combine finite-element spatial discretization with split-step time stepping schemes that have been found useful in finite-difference computations. Because of the large number of numerical integrations performed in space and the large sparse matrices solved, these finite-element schemes were found to be economically uncompetitive with finite-difference schemes. A very promising leapfrog scheme is proposed which, when combined with a novel very fast spatial integration procedure, eliminates the need to solve any matrices at all. Additional problems attacked included proper propagation of waves and proper specification of the normal flow-boundary condition. This report indicates work in progress and does not come to a definitive conclusion as to the best approach for finite-element modeling of surface-water problems. The results presented represent findings obtained between September 1973 and July 1976. (Woodard-USGS)

Fluctuations of conserved charges in relativistic heavy ion collisions: An introduction

NASA Astrophysics Data System (ADS)

Asakawa, Masayuki; Kitazawa, Masakiyo

2016-09-01

Bulk fluctuations of conserved charges measured by event-by-event analysis in relativistic heavy ion collisions are observables which are believed to carry significant amount of information on the hot medium created by the collisions. Active studies have been done recently experimentally, theoretically, and on the lattice. In particular, non-Gaussianity of the fluctuations has acquired much attention recently. In this review, we give a pedagogical introduction to these issues, and survey recent developments in this field of research. Starting from the definition of cumulants, basic concepts in fluctuation physics, such as thermal fluctuations in statistical mechanics and time evolution of fluctuations in diffusive systems, are described. Phenomena which are expected to occur in finite temperature and/or density QCD matter and their measurement by event-by-event analyses are also elucidated.