Modeling ultrasonic transient scattering from biological tissues including their dispersive properties directly in the time domain.

PubMed

Norton, G V; Novarini, J C

2007-06-01

Ultrasonic imaging in medical applications involves propagation and scattering of acoustic waves within and by biological tissues that are intrinsically dispersive. Analytical approaches for modeling propagation and scattering in inhomogeneous media are difficult and often require extremely simplifying approximations in order to achieve a solution. To avoid such approximations, the direct numerical solution of the wave equation via the method of finite differences offers the most direct tool, which takes into account diffraction and refraction. It also allows for detailed modeling of the real anatomic structure and combination/layering of tissues. In all cases the correct inclusion of the dispersive properties of the tissues can make the difference in the interpretation of the results. However, the inclusion of dispersion directly in the time domain proved until recently to be an elusive problem. In order to model the transient signal a convolution operator that takes into account the dispersive characteristics of the medium is introduced to the linear wave equation. To test the ability of this operator to handle scattering from localized scatterers, in this work, two-dimensional numerical modeling of scattering from an infinite cylinder with physical properties associated with biological tissue is calculated. The numerical solutions are compared with the exact solution synthesized from the frequency domain for a variety of tissues having distinct dispersive properties. It is shown that in all cases, the use of the convolutional propagation operator leads to the correct solution for the scattered field.

Magnetic Field in a Screw Flow with Fluctuations

NASA Astrophysics Data System (ADS)

Titov, V. V.; Stepanov, R. A.; Sokoloff, D. D.

2018-04-01

We consider the influence of fluctuations in a screw flow of a conducting liquid on the effect of magnetic field self-excitation; the solution of this problem is important for experimental realization of a turbulent dynamo. We propose a theoretical approach based on the solution of averaged equations obtained in the limit of a short correlation time. The applicability of this approach is confirmed by direct numerical simulation of the initial equations. We demonstrate the influence of the correlation of fluctuations on the dynamo effect threshold. It is shown that the solution of the mean-field equations differs from the solution based on direct numerical simulation for a finite correlation time. The advantages and disadvantages of the two approaches are estimates, as well as the importance of the discovered difference in the context of problems of magnetic field self-excitation. The influence of helicity and intermittency on the type of the solution is considered.

Tensor-product preconditioners for a space-time discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Diosady, Laslo T.; Murman, Scott M.

2014-10-01

A space-time discontinuous Galerkin spectral element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equations. An efficient solution technique based on a matrix-free Newton-Krylov method is presented. A diagonalized alternating direction implicit preconditioner is extended to a space-time formulation using entropy variables. The effectiveness of this technique is demonstrated for the direct numerical simulation of turbulent flow in a channel.

A direct numerical method for predicting concentration profiles in a turbulent boundary layer over a flat plate. M.S. Thesis

NASA Technical Reports Server (NTRS)

Dow, J. W.

1972-01-01

A numerical solution of the turbulent mass transport equation utilizing the concept of eddy diffusivity is presented as an efficient method of investigating turbulent mass transport in boundary layer type flows. A FORTRAN computer program is used to study the two-dimensional diffusion of ammonia, from a line source on the surface, into a turbulent boundary layer over a flat plate. The results of the numerical solution are compared with experimental data to verify the results of the solution. Several other solutions to diffusion problems are presented to illustrate the versatility of the computer program and to provide some insight into the problem of mass diffusion as a whole.

Direct numerical simulations of three-dimensional electrokinetic flows

NASA Astrophysics Data System (ADS)

Chiam, Keng-Hwee

2006-11-01

We discuss direct numerical simulations of three-dimensional electrokinetic flows in microfluidic devices. In particular, we focus on the study of the electrokinetic instability that develops when two solutions with different electrical conductivities are coupled to an external electric field. We characterize this ``mixing'' instability as a function of the parameters of the model, namely the Reynolds number of the flow, the electric Peclet number of the electrolyte solution, and the ratio of the electroosmotic to the electroviscous time scales. Finally, we describe how this model breaks down when the length scale of the device approaches the nanoscale, where the width of the electric Debye layer is comparable to the width of the channel, and discuss solutions to overcome this.

Numerical Modeling of Ablation Heat Transfer

NASA Technical Reports Server (NTRS)

Ewing, Mark E.; Laker, Travis S.; Walker, David T.

2013-01-01

A unique numerical method has been developed for solving one-dimensional ablation heat transfer problems. This paper provides a comprehensive description of the method, along with detailed derivations of the governing equations. This methodology supports solutions for traditional ablation modeling including such effects as heat transfer, material decomposition, pyrolysis gas permeation and heat exchange, and thermochemical surface erosion. The numerical scheme utilizes a control-volume approach with a variable grid to account for surface movement. This method directly supports implementation of nontraditional models such as material swelling and mechanical erosion, extending capabilities for modeling complex ablation phenomena. Verifications of the numerical implementation are provided using analytical solutions, code comparisons, and the method of manufactured solutions. These verifications are used to demonstrate solution accuracy and proper error convergence rates. A simple demonstration of a mechanical erosion (spallation) model is also provided to illustrate the unique capabilities of the method.

Numerical solution of the exterior oblique derivative BVP using the direct BEM formulation

NASA Astrophysics Data System (ADS)

Čunderlík, Róbert; Špir, Róbert; Mikula, Karol

2016-04-01

The fixed gravimetric boundary value problem (FGBVP) represents an exterior oblique derivative problem for the Laplace equation. A direct formulation of the boundary element method (BEM) for the Laplace equation leads to a boundary integral equation (BIE) where a harmonic function is represented as a superposition of the single-layer and double-layer potential. Such a potential representation is applied to obtain a numerical solution of FGBVP. The oblique derivative problem is treated by a decomposition of the gradient of the unknown disturbing potential into its normal and tangential components. Our numerical scheme uses the collocation with linear basis functions. It involves a triangulated discretization of the Earth's surface as our computational domain considering its complicated topography. To achieve high-resolution numerical solutions, parallel implementations using the MPI subroutines as well as an iterative elimination of far zones' contributions are performed. Numerical experiments present a reconstruction of a harmonic function above the Earth's topography given by the spherical harmonic approach, namely by the EGM2008 geopotential model up to degree 2160. The SRTM30 global topography model is used to approximate the Earth's surface by the triangulated discretization. The obtained BEM solution with the resolution 0.05 deg (12,960,002 nodes) is compared with EGM2008. The standard deviation of residuals 5.6 cm indicates a good agreement. The largest residuals are obviously in high mountainous regions. They are negative reaching up to -0.7 m in Himalayas and about -0.3 m in Andes and Rocky Mountains. A local refinement in the area of Slovakia confirms an improvement of the numerical solution in this mountainous region despite of the fact that the Earth's topography is here considered in more details.

Third order maximum-principle-satisfying direct discontinuous Galerkin methods for time dependent convection diffusion equations on unstructured triangular meshes

DOE PAGES

Chen, Zheng; Huang, Hongying; Yan, Jue

2015-12-21

We develop 3rd order maximum-principle-satisfying direct discontinuous Galerkin methods [8], [9], [19] and [21] for convection diffusion equations on unstructured triangular mesh. We carefully calculate the normal derivative numerical flux across element edges and prove that, with proper choice of parameter pair (β 0,β 1) in the numerical flux formula, the quadratic polynomial solution satisfies strict maximum principle. The polynomial solution is bounded within the given range and third order accuracy is maintained. There is no geometric restriction on the meshes and obtuse triangles are allowed in the partition. As a result, a sequence of numerical examples are carried outmore » to demonstrate the accuracy and capability of the maximum-principle-satisfying limiter.« less

Exact solutions of the Navier-Stokes equations generalized for flow in porous media

NASA Astrophysics Data System (ADS)

Daly, Edoardo; Basser, Hossein; Rudman, Murray

2018-05-01

Flow of Newtonian fluids in porous media is often modelled using a generalized version of the full non-linear Navier-Stokes equations that include additional terms describing the resistance to flow due to the porous matrix. Because this formulation is becoming increasingly popular in numerical models, exact solutions are required as a benchmark of numerical codes. The contribution of this study is to provide a number of non-trivial exact solutions of the generalized form of the Navier-Stokes equations for parallel flow in porous media. Steady-state solutions are derived in the case of flows in a medium with constant permeability along the main direction of flow and a constant cross-stream velocity in the case of both linear and non-linear drag. Solutions are also presented for cases in which the permeability changes in the direction normal to the main flow. An unsteady solution for a flow with velocity driven by a time-periodic pressure gradient is also derived. These solutions form a basis for validating computational models across a wide range of Reynolds and Darcy numbers.

Numerical modeling of solute transport in a sand tank physical model under varying hydraulic gradient and hydrological stresses

NASA Astrophysics Data System (ADS)

Atlabachew, Abunu; Shu, Longcang; Wu, Peipeng; Zhang, Yongjie; Xu, Yang

2018-03-01

This laboratory study improves the understanding of the impacts of horizontal hydraulic gradient, artificial recharge, and groundwater pumping on solute transport through aquifers. Nine experiments and numerical simulations were carried out using a sand tank. The variable-density groundwater flow and sodium chloride transport were simulated using the three-dimensional numerical model SEAWAT. Numerical modelling results successfully reproduced heads and concentrations observed in the sand tank. A higher horizontal hydraulic gradient enhanced the migration of sodium chloride, particularly in the groundwater flow direction. The application of constant artificial recharge increased the spread of the sodium chloride plume in both the longitudinal and lateral directions. In addition, groundwater pumping accelerated spreading of the sodium chloride plume towards the pumping well. Both higher hydraulic gradient and pumping rate generated oval-shaped plumes in the horizontal plane. However, the artificial recharge process produced stretched plumes. These effects of artificial recharge and groundwater pumping were greater under higher hydraulic gradient. The concentration breakthrough curves indicated that emerging solutions never attained the concentration of the originally injected solution. This is probably because of sorption of sodium chloride onto the silica sand and/or the exchange of sodium chloride between the mobile and immobile liquid domains. The fingering and protruding plume shapes in the numerical models constitute instability zones produced by buoyancy-driven flow. Overall, the results have substantiated the influences of hydraulic gradient, boundary condition, artificial recharge, pumping rate and density differences on solute transport through a homogeneous unconfined aquifer. The implications of these findings are important for managing liquid wastes.

Dual solutions of three-dimensional flow and heat transfer over a non-linearly stretching/shrinking sheet

NASA Astrophysics Data System (ADS)

Naganthran, Kohilavani; Nazar, Roslinda; Pop, Ioan

2018-05-01

This study investigated the influence of the non-linearly stretching/shrinking sheet on the boundary layer flow and heat transfer. A proper similarity transformation simplified the system of partial differential equations into a system of ordinary differential equations. This system of similarity equations is then solved numerically by using the bvp4c function in the MATLAB software. The generated numerical results presented graphically and discussed in the relevance of the governing parameters. Dual solutions found as the sheet stretched and shrunk in the horizontal direction. Stability analysis showed that the first solution is physically realizable whereas the second solution is not practicable.

International Conference on Numerical Methods in Fluid Dynamics, 7th, Stanford University, Stanford and Moffett Field, CA, June 23-27, 1980, Proceedings

NASA Technical Reports Server (NTRS)

Reynolds, W. C. (Editor); Maccormack, R. W.

1981-01-01

Topics discussed include polygon transformations in fluid mechanics, computation of three-dimensional horseshoe vortex flow using the Navier-Stokes equations, an improved surface velocity method for transonic finite-volume solutions, transonic flow calculations with higher order finite elements, the numerical calculation of transonic axial turbomachinery flows, and the simultaneous solutions of inviscid flow and boundary layer at transonic speeds. Also considered are analytical solutions for the reflection of unsteady shock waves and relevant numerical tests, reformulation of the method of characteristics for multidimensional flows, direct numerical simulations of turbulent shear flows, the stability and separation of freely interacting boundary layers, computational models of convective motions at fluid interfaces, viscous transonic flow over airfoils, and mixed spectral/finite difference approximations for slightly viscous flows.

On the Minimal Accuracy Required for Simulating Self-gravitating Systems by Means of Direct N-body Methods

NASA Astrophysics Data System (ADS)

Portegies Zwart, Simon; Boekholt, Tjarda

2014-04-01

The conservation of energy, linear momentum, and angular momentum are important drivers of our physical understanding of the evolution of the universe. These quantities are also conserved in Newton's laws of motion under gravity. Numerical integration of the associated equations of motion is extremely challenging, in particular due to the steady growth of numerical errors (by round-off and discrete time-stepping and the exponential divergence between two nearby solutions. As a result, numerical solutions to the general N-body problem are intrinsically questionable. Using brute force integrations to arbitrary numerical precision we demonstrate empirically that ensembles of different realizations of resonant three-body interactions produce statistically indistinguishable results. Although individual solutions using common integration methods are notoriously unreliable, we conjecture that an ensemble of approximate three-body solutions accurately represents an ensemble of true solutions, so long as the energy during integration is conserved to better than 1/10. We therefore provide an independent confirmation that previous work on self-gravitating systems can actually be trusted, irrespective of the intrinsically chaotic nature of the N-body problem.

Numerical method and FORTRAN program for the solution of an axisymmetric electrostatic collector design problem

NASA Technical Reports Server (NTRS)

Reese, O. W.

1972-01-01

The numerical calculation is described of the steady-state flow of electrons in an axisymmetric, spherical, electrostatic collector for a range of boundary conditions. The trajectory equations of motion are solved alternately with Poisson's equation for the potential field until convergence is achieved. A direct (noniterative) numerical technique is used to obtain the solution to Poisson's equation. Space charge effects are included for initial current densities as large as 100 A/sq cm. Ways of dealing successfully with the difficulties associated with these high densities are discussed. A description of the mathematical model, a discussion of numerical techniques, results from two typical runs, and the FORTRAN computer program are included.

Numerical method for predicting flow characteristics and performance of nonaxisymmetric nozzles, theory

NASA Technical Reports Server (NTRS)

Thomas, P. D.

1979-01-01

The theoretical foundation and formulation of a numerical method for predicting the viscous flowfield in and about isolated three dimensional nozzles of geometrically complex configuration are presented. High Reynolds number turbulent flows are of primary interest for any combination of subsonic, transonic, and supersonic flow conditions inside or outside the nozzle. An alternating-direction implicit (ADI) numerical technique is employed to integrate the unsteady Navier-Stokes equations until an asymptotic steady-state solution is reached. Boundary conditions are computed with an implicit technique compatible with the ADI technique employed at interior points of the flow region. The equations are formulated and solved in a boundary-conforming curvilinear coordinate system. The curvilinear coordinate system and computational grid is generated numerically as the solution to an elliptic boundary value problem. A method is developed that automatically adjusts the elliptic system so that the interior grid spacing is controlled directly by the a priori selection of the grid spacing on the boundaries of the flow region.

System Simulation by Recursive Feedback: Coupling A Set of Stand-Alone Subsystem Simulations

NASA Technical Reports Server (NTRS)

Nixon, Douglas D.; Hanson, John M. (Technical Monitor)

2002-01-01

Recursive feedback is defined and discussed as a framework for development of specific algorithms and procedures that propagate the time-domain solution for a dynamical system simulation consisting of multiple numerically coupled self-contained stand-alone subsystem simulations. A satellite motion example containing three subsystems (other dynamics, attitude dynamics, and aerodynamics) has been defined and constructed using this approach. Conventional solution methods are used in the subsystem simulations. Centralized and distributed versions of coupling structure have been addressed. Numerical results are evaluated by direct comparison with a standard total-system simultaneous-solution approach.

System Simulation by Recursive Feedback: Coupling a Set of Stand-Alone Subsystem Simulations

NASA Technical Reports Server (NTRS)

Nixon, D. D.

2001-01-01

Conventional construction of digital dynamic system simulations often involves collecting differential equations that model each subsystem, arran g them to a standard form, and obtaining their numerical gin solution as a single coupled, total-system simultaneous set. Simulation by numerical coupling of independent stand-alone subsimulations is a fundamentally different approach that is attractive because, among other things, the architecture naturally facilitates high fidelity, broad scope, and discipline independence. Recursive feedback is defined and discussed as a candidate approach to multidiscipline dynamic system simulation by numerical coupling of self-contained, single-discipline subsystem simulations. A satellite motion example containing three subsystems (orbit dynamics, attitude dynamics, and aerodynamics) has been defined and constructed using this approach. Conventional solution methods are used in the subsystem simulations. Distributed and centralized implementations of coupling have been considered. Numerical results are evaluated by direct comparison with a standard total-system, simultaneous-solution approach.

A mathematical solution for the parameters of three interfering resonances

NASA Astrophysics Data System (ADS)

Han, X.; Shen, C. P.

2018-04-01

The multiple-solution problem in determining the parameters of three interfering resonances from a fit to an experimentally measured distribution is considered from a mathematical viewpoint. It is shown that there are four numerical solutions for a fit with three coherent Breit-Wigner functions. Although explicit analytical formulae cannot be derived in this case, we provide some constraint equations between the four solutions. For the cases of nonrelativistic and relativistic Breit-Wigner forms of amplitude functions, a numerical method is provided to derive the other solutions from that already obtained, based on the obtained constraint equations. In real experimental measurements with more complicated amplitude forms similar to Breit-Wigner functions, the same method can be deduced and performed to get numerical solutions. The good agreement between the solutions found using this mathematical method and those directly from the fit verifies the correctness of the constraint equations and mathematical methodology used. Supported by National Natural Science Foundation of China (NSFC) (11575017, 11761141009), the Ministry of Science and Technology of China (2015CB856701) and the CAS Center for Excellence in Particle Physics (CCEPP)

Limit Theorems and Their Relation to Solute Transport in Simulated Fractured Media

NASA Astrophysics Data System (ADS)

Reeves, D. M.; Benson, D. A.; Meerschaert, M. M.

2003-12-01

Solute particles that travel through fracture networks are subject to wide velocity variations along a restricted set of directions. This may result in super-Fickian dispersion along a few primary scaling directions. The fractional advection-dispersion equation (FADE), a modification of the original advection-dispersion equation in which a fractional derivative replaces the integer-order dispersion term, has the ability to model rapid, non-Gaussian solute transport. The FADE assumes that solute particle motions converge to either α -stable or operator stable densities, which are modeled by spatial fractional derivatives. In multiple dimensions, the multi-fractional dispersion derivative dictates the order and weight of differentiation in all directions, which correspond to the statistics of large particle motions in all directions. This study numerically investigates the presence of super- Fickian solute transport through simulated two-dimensional fracture networks. An ensemble of networks is gen

Numerical study of radiometric forces via the direct solution of the Boltzmann kinetic equation

NASA Astrophysics Data System (ADS)

Anikin, Yu. A.

2011-07-01

The two-dimensional rarefied gas motion in a Crookes radiometer and the resulting radiometric forces are studied by numerically solving the Boltzmann kinetic equation. The collision integral is directly evaluated using a projection method, and second-order accurate TVD schemes are used to solve the advection equation. The radiometric forces are found as functions of the Knudsen number and the temperatures, and their spatial distribution is analyzed.

Fast sweeping method for the factored eikonal equation

NASA Astrophysics Data System (ADS)

Fomel, Sergey; Luo, Songting; Zhao, Hongkai

2009-09-01

We develop a fast sweeping method for the factored eikonal equation. By decomposing the solution of a general eikonal equation as the product of two factors: the first factor is the solution to a simple eikonal equation (such as distance) or a previously computed solution to an approximate eikonal equation. The second factor is a necessary modification/correction. Appropriate discretization and a fast sweeping strategy are designed for the equation of the correction part. The key idea is to enforce the causality of the original eikonal equation during the Gauss-Seidel iterations. Using extensive numerical examples we demonstrate that (1) the convergence behavior of the fast sweeping method for the factored eikonal equation is the same as for the original eikonal equation, i.e., the number of iterations for the Gauss-Seidel iterations is independent of the mesh size, (2) the numerical solution from the factored eikonal equation is more accurate than the numerical solution directly computed from the original eikonal equation, especially for point sources.

Toward a Nonlinear Acoustic Analogy: Turbulence as a Source of Sound and Nonlinear Propagation

NASA Technical Reports Server (NTRS)

Miller, Steven A. E.

2015-01-01

An acoustic analogy is proposed that directly includes nonlinear propagation effects. We examine the Lighthill acoustic analogy and replace the Green's function of the wave equation with numerical solutions of the generalized Burgers' equation. This is justified mathematically by using similar arguments that are the basis of the solution of the Lighthill acoustic analogy. This approach is superior to alternatives because propagation is accounted for directly from the source to the far-field observer instead of from an arbitrary intermediate point. Validation of a numerical solver for the generalized Burgers' equation is performed by comparing solutions with the Blackstock bridging function and measurement data. Most importantly, the mathematical relationship between the Navier- Stokes equations, the acoustic analogy that describes the source, and canonical nonlinear propagation equations is shown. Example predictions are presented for nonlinear propagation of jet mixing noise at the sideline angle

Toward a Nonlinear Acoustic Analogy: Turbulence as a Source of Sound and Nonlinear Propagation

NASA Technical Reports Server (NTRS)

Miller, Steven A. E.

2015-01-01

An acoustic analogy is proposed that directly includes nonlinear propagation effects. We examine the Lighthill acoustic analogy and replace the Green's function of the wave equation with numerical solutions of the generalized Burgers' equation. This is justified mathematically by using similar arguments that are the basis of the solution of the Lighthill acoustic analogy. This approach is superior to alternatives because propagation is accounted for directly from the source to the far-field observer instead of from an arbitrary intermediate point. Validation of a numerical solver for the generalized Burgers' equation is performed by comparing solutions with the Blackstock bridging function and measurement data. Most importantly, the mathematical relationship between the Navier-Stokes equations, the acoustic analogy that describes the source, and canonical nonlinear propagation equations is shown. Example predictions are presented for nonlinear propagation of jet mixing noise at the sideline angle.

The origin of spurious solutions in computational electromagnetics

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Wu, Jie; Povinelli, L. A.

1995-01-01

The origin of spurious solutions in computational electromagnetics, which violate the divergence equations, is deeply rooted in a misconception about the first-order Maxwell's equations and in an incorrect derivation and use of the curl-curl equations. The divergence equations must be always included in the first-order Maxwell's equations to maintain the ellipticity of the system in the space domain and to guarantee the uniqueness of the solution and/or the accuracy of the numerical solutions. The div-curl method and the least-squares method provide rigorous derivation of the equivalent second-order Maxwell's equations and their boundary conditions. The node-based least-squares finite element method (LSFEM) is recommended for solving the first-order full Maxwell equations directly. Examples of the numerical solutions by LSFEM for time-harmonic problems are given to demonstrate that the LSFEM is free of spurious solutions.

A Novel Quantum-Behaved Bat Algorithm with Mean Best Position Directed for Numerical Optimization

PubMed Central

Zhu, Wenyong; Liu, Zijuan; Duan, Qingyan; Cao, Long

2016-01-01

This paper proposes a novel quantum-behaved bat algorithm with the direction of mean best position (QMBA). In QMBA, the position of each bat is mainly updated by the current optimal solution in the early stage of searching and in the late search it also depends on the mean best position which can enhance the convergence speed of the algorithm. During the process of searching, quantum behavior of bats is introduced which is beneficial to jump out of local optimal solution and make the quantum-behaved bats not easily fall into local optimal solution, and it has better ability to adapt complex environment. Meanwhile, QMBA makes good use of statistical information of best position which bats had experienced to generate better quality solutions. This approach not only inherits the characteristic of quick convergence, simplicity, and easy implementation of original bat algorithm, but also increases the diversity of population and improves the accuracy of solution. Twenty-four benchmark test functions are tested and compared with other variant bat algorithms for numerical optimization the simulation results show that this approach is simple and efficient and can achieve a more accurate solution. PMID:27293424

Transitions of stationary to pulsating solutions in the complex cubic-quintic Ginzburg-Landau equation under the influence of nonlinear gain and higher-order effects

NASA Astrophysics Data System (ADS)

Uzunov, Ivan M.; Georgiev, Zhivko D.; Arabadzhiev, Todor N.

2018-05-01

In this paper we study the transitions of stationary to pulsating solutions in the complex cubic-quintic Ginzburg-Landau equation (CCQGLE) under the influence of nonlinear gain, its saturation, and higher-order effects: self-steepening, third-order of dispersion, and intrapulse Raman scattering in the anomalous dispersion region. The variation method and the method of moments are applied in order to obtain the dynamic models with finite degrees of freedom for the description of stationary and pulsating solutions. Having applied the first model and its bifurcation analysis we have discovered the existence of families of subcritical Poincaré-Andronov-Hopf bifurcations due to the intrapulse Raman scattering, as well as some small nonlinear gain and the saturation of the nonlinear gain. A phenomenon of nonlinear stability has been studied and it has been shown that long living pulsating solutions with relatively small fluctuations of amplitude and frequencies exist at the bifurcation point. The numerical analysis of the second model has revealed the existence of Poincaré-Andronov-Hopf bifurcations of Raman dissipative soliton under the influence of the self-steepening effect and large nonlinear gain. All our theoretical predictions have been confirmed by the direct numerical solution of the full perturbed CCQGLE. The detailed comparison between the results obtained by both dynamic models and the direct numerical solution of the perturbed CCQGLE has proved the applicability of the proposed models in the investigation of the solutions of the perturbed CCQGLE.

Intercomparison of 3D pore-scale flow and solute transport simulation methods

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

Yang, Xiaofan; Mehmani, Yashar; Perkins, William A.

2016-09-01

Multiple numerical approaches have been developed to simulate porous media fluid flow and solute transport at the pore scale. These include methods that 1) explicitly model the three-dimensional geometry of pore spaces and 2) those that conceptualize the pore space as a topologically consistent set of stylized pore bodies and pore throats. In previous work we validated a model of class 1, based on direct numerical simulation using computational fluid dynamics (CFD) codes, against magnetic resonance velocimetry (MRV) measurements of pore-scale velocities. Here we expand that validation to include additional models of class 1 based on the immersed-boundary method (IMB),more » lattice Boltzmann method (LBM), smoothed particle hydrodynamics (SPH), as well as a model of class 2 (a pore-network model or PNM). The PNM approach used in the current study was recently improved and demonstrated to accurately simulate solute transport in a two-dimensional experiment. While the PNM approach is computationally much less demanding than direct numerical simulation methods, the effect of conceptualizing complex three-dimensional pore geometries on solute transport in the manner of PNMs has not been fully determined. We apply all four approaches (CFD, LBM, SPH and PNM) to simulate pore-scale velocity distributions and nonreactive solute transport, and intercompare the model results with previously reported experimental observations. Experimental observations are limited to measured pore-scale velocities, so solute transport comparisons are made only among the various models. Comparisons are drawn both in terms of macroscopic variables (e.g., permeability, solute breakthrough curves) and microscopic variables (e.g., local velocities and concentrations).« less

ON THE MINIMAL ACCURACY REQUIRED FOR SIMULATING SELF-GRAVITATING SYSTEMS BY MEANS OF DIRECT N-BODY METHODS

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

Portegies Zwart, Simon; Boekholt, Tjarda

2014-04-10

The conservation of energy, linear momentum, and angular momentum are important drivers of our physical understanding of the evolution of the universe. These quantities are also conserved in Newton's laws of motion under gravity. Numerical integration of the associated equations of motion is extremely challenging, in particular due to the steady growth of numerical errors (by round-off and discrete time-stepping and the exponential divergence between two nearby solutions. As a result, numerical solutions to the general N-body problem are intrinsically questionable. Using brute force integrations to arbitrary numerical precision we demonstrate empirically that ensembles of different realizations of resonant three-bodymore » interactions produce statistically indistinguishable results. Although individual solutions using common integration methods are notoriously unreliable, we conjecture that an ensemble of approximate three-body solutions accurately represents an ensemble of true solutions, so long as the energy during integration is conserved to better than 1/10. We therefore provide an independent confirmation that previous work on self-gravitating systems can actually be trusted, irrespective of the intrinsically chaotic nature of the N-body problem.« less

On the Unreasonable Effectiveness of post-Newtonian Theory in Gravitational-Wave Physics

ScienceCinema

Will, Clifford M.

2017-12-22

The first indirect detection of gravitational waves involved a binary system of neutron stars.  In the future, the first direct detection may also involve binary systems -- inspiralling and merging binary neutron stars or black holes. This means that it is essential to understand in full detail the two-body system in general relativity, a notoriously difficult problem with a long history. Post-Newtonian approximation methods are thought to work only under slow motion and weak field conditions, while numerical solutions of Einstein's equations are thought to be limited to the final merger phase.  Recent results have shown that post-Newtonian approximations seem to remain unreasonably valid well into the relativistic regime, while advances in numerical relativity now permit solutions for numerous orbits before merger.  It is now possible to envision linking post-Newtonian theory and numerical relativity to obtain a complete "solution" of the general relativistic two-body problem.  These solutions will play a central role in detecting and understanding gravitational wave signals received by interferometric observatories on Earth and in space.

Numerical method for the solution of large systems of differential equations of the boundary layer type

NASA Technical Reports Server (NTRS)

Green, M. J.; Nachtsheim, P. R.

1972-01-01

A numerical method for the solution of large systems of nonlinear differential equations of the boundary-layer type is described. The method is a modification of the technique for satisfying asymptotic boundary conditions. The present method employs inverse interpolation instead of the Newton method to adjust the initial conditions of the related initial-value problem. This eliminates the so-called perturbation equations. The elimination of the perturbation equations not only reduces the user's preliminary work in the application of the method, but also reduces the number of time-consuming initial-value problems to be numerically solved at each iteration. For further ease of application, the solution of the overdetermined system for the unknown initial conditions is obtained automatically by applying Golub's linear least-squares algorithm. The relative ease of application of the proposed numerical method increases directly as the order of the differential-equation system increases. Hence, the method is especially attractive for the solution of large-order systems. After the method is described, it is applied to a fifth-order problem from boundary-layer theory.

Spectral-based propagation schemes for time-dependent quantum systems with application to carbon nanotubes

NASA Astrophysics Data System (ADS)

Chen, Zuojing; Polizzi, Eric

2010-11-01

Effective modeling and numerical spectral-based propagation schemes are proposed for addressing the challenges in time-dependent quantum simulations of systems ranging from atoms, molecules, and nanostructures to emerging nanoelectronic devices. While time-dependent Hamiltonian problems can be formally solved by propagating the solutions along tiny simulation time steps, a direct numerical treatment is often considered too computationally demanding. In this paper, however, we propose to go beyond these limitations by introducing high-performance numerical propagation schemes to compute the solution of the time-ordered evolution operator. In addition to the direct Hamiltonian diagonalizations that can be efficiently performed using the new eigenvalue solver FEAST, we have designed a Gaussian propagation scheme and a basis-transformed propagation scheme (BTPS) which allow to reduce considerably the simulation times needed by time intervals. It is outlined that BTPS offers the best computational efficiency allowing new perspectives in time-dependent simulations. Finally, these numerical schemes are applied to study the ac response of a (5,5) carbon nanotube within a three-dimensional real-space mesh framework.

Direct Coupling Method for Time-Accurate Solution of Incompressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Soh, Woo Y.

1992-01-01

A noniterative finite difference numerical method is presented for the solution of the incompressible Navier-Stokes equations with second order accuracy in time and space. Explicit treatment of convection and diffusion terms and implicit treatment of the pressure gradient give a single pressure Poisson equation when the discretized momentum and continuity equations are combined. A pressure boundary condition is not needed on solid boundaries in the staggered mesh system. The solution of the pressure Poisson equation is obtained directly by Gaussian elimination. This method is tested on flow problems in a driven cavity and a curved duct.

New distributed activation energy model: numerical solution and application to pyrolysis kinetics of some types of biomass.

PubMed

Cai, Junmeng; Liu, Ronghou

2008-05-01

In the present paper, a new distributed activation energy model has been developed, considering the reaction order and the dependence of frequency factor on temperature. The proposed DAEM cannot be solved directly in a closed from, thus a method was used to obtain the numerical solution of the new DAEM equation. Two numerical examples to illustrate the proposed method were presented. The traditional DAEM and new DAEM have been used to simulate the pyrolytic process of some types of biomass. The new DAEM fitted the experimental data much better than the traditional DAEM as the dependence of the frequency factor on temperature was taken into account.

Block structured adaptive mesh and time refinement for hybrid, hyperbolic + N-body systems

NASA Astrophysics Data System (ADS)

Miniati, Francesco; Colella, Phillip

2007-11-01

We present a new numerical algorithm for the solution of coupled collisional and collisionless systems, based on the block structured adaptive mesh and time refinement strategy (AMR). We describe the issues associated with the discretization of the system equations and the synchronization of the numerical solution on the hierarchy of grid levels. We implement a code based on a higher order, conservative and directionally unsplit Godunov’s method for hydrodynamics; a symmetric, time centered modified symplectic scheme for collisionless component; and a multilevel, multigrid relaxation algorithm for the elliptic equation coupling the two components. Numerical results that illustrate the accuracy of the code and the relative merit of various implemented schemes are also presented.

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

Chen, Zheng; Huang, Hongying; Yan, Jue

We develop 3rd order maximum-principle-satisfying direct discontinuous Galerkin methods [8], [9], [19] and [21] for convection diffusion equations on unstructured triangular mesh. We carefully calculate the normal derivative numerical flux across element edges and prove that, with proper choice of parameter pair (β 0,β 1) in the numerical flux formula, the quadratic polynomial solution satisfies strict maximum principle. The polynomial solution is bounded within the given range and third order accuracy is maintained. There is no geometric restriction on the meshes and obtuse triangles are allowed in the partition. As a result, a sequence of numerical examples are carried outmore » to demonstrate the accuracy and capability of the maximum-principle-satisfying limiter.« less

Dispersive shock waves in the Kadomtsev-Petviashvili and two dimensional Benjamin-Ono equations

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Demirci, Ali; Ma, Yi-Ping

2016-10-01

Dispersive shock waves (DSWs) in the Kadomtsev-Petviashvili (KP) equation and two dimensional Benjamin-Ono (2DBO) equation are considered using step like initial data along a parabolic front. Employing a parabolic similarity reduction exactly reduces the study of such DSWs in two space one time (2 + 1) dimensions to finding DSW solutions of (1 + 1) dimensional equations. With this ansatz, the KP and 2DBO equations can be exactly reduced to the cylindrical Korteweg-de Vries (cKdV) and cylindrical Benjamin-Ono (cBO) equations, respectively. Whitham modulation equations which describe DSW evolution in the cKdV and cBO equations are derived and Riemann type variables are introduced. DSWs obtained from the numerical solutions of the corresponding Whitham systems and direct numerical simulations of the cKdV and cBO equations are compared with very good agreement obtained. In turn, DSWs obtained from direct numerical simulations of the KP and 2DBO equations are compared with the cKdV and cBO equations, again with good agreement. It is concluded that the (2 + 1) DSW behavior along self similar parabolic fronts can be effectively described by the DSW solutions of the reduced (1 + 1) dimensional equations.

The impact of the form of the Euler equations for radial flow in cylindrical and spherical coordinates on numerical conservation and accuracy

NASA Astrophysics Data System (ADS)

Crittenden, P. E.; Balachandar, S.

2018-07-01

The radial one-dimensional Euler equations are often rewritten in what is known as the geometric source form. The differential operator is identical to the Cartesian case, but source terms result. Since the theory and numerical methods for the Cartesian case are well-developed, they are often applied without modification to cylindrical and spherical geometries. However, numerical conservation is lost. In this article, AUSM^+-up is applied to a numerically conservative (discrete) form of the Euler equations labeled the geometric form, a nearly conservative variation termed the geometric flux form, and the geometric source form. The resulting numerical methods are compared analytically and numerically through three types of test problems: subsonic, smooth, steady-state solutions, Sedov's similarity solution for point or line-source explosions, and shock tube problems. Numerical conservation is analyzed for all three forms in both spherical and cylindrical coordinates. All three forms result in constant enthalpy for steady flows. The spatial truncation errors have essentially the same order of convergence, but the rate constants are superior for the geometric and geometric flux forms for the steady-state solutions. Only the geometric form produces the correct shock location for Sedov's solution, and a direct connection between the errors in the shock locations and energy conservation is found. The shock tube problems are evaluated with respect to feature location using an approximation with a very fine discretization as the benchmark. Extensions to second order appropriate for cylindrical and spherical coordinates are also presented and analyzed numerically. Conclusions are drawn, and recommendations are made. A derivation of the steady-state solution is given in the Appendix.

The impact of the form of the Euler equations for radial flow in cylindrical and spherical coordinates on numerical conservation and accuracy

NASA Astrophysics Data System (ADS)

Crittenden, P. E.; Balachandar, S.

2018-03-01

The radial one-dimensional Euler equations are often rewritten in what is known as the geometric source form. The differential operator is identical to the Cartesian case, but source terms result. Since the theory and numerical methods for the Cartesian case are well-developed, they are often applied without modification to cylindrical and spherical geometries. However, numerical conservation is lost. In this article, AUSM^+ -up is applied to a numerically conservative (discrete) form of the Euler equations labeled the geometric form, a nearly conservative variation termed the geometric flux form, and the geometric source form. The resulting numerical methods are compared analytically and numerically through three types of test problems: subsonic, smooth, steady-state solutions, Sedov's similarity solution for point or line-source explosions, and shock tube problems. Numerical conservation is analyzed for all three forms in both spherical and cylindrical coordinates. All three forms result in constant enthalpy for steady flows. The spatial truncation errors have essentially the same order of convergence, but the rate constants are superior for the geometric and geometric flux forms for the steady-state solutions. Only the geometric form produces the correct shock location for Sedov's solution, and a direct connection between the errors in the shock locations and energy conservation is found. The shock tube problems are evaluated with respect to feature location using an approximation with a very fine discretization as the benchmark. Extensions to second order appropriate for cylindrical and spherical coordinates are also presented and analyzed numerically. Conclusions are drawn, and recommendations are made. A derivation of the steady-state solution is given in the Appendix.

Computer simulation of concentrated solid solution strengthening

NASA Technical Reports Server (NTRS)

Kuo, C. T. K.; Arsenault, R. J.

1976-01-01

The interaction forces between a straight edge dislocation moving through a three-dimensional block containing a random array of solute atoms were determined. The yield stress at 0 K was obtained by determining the average maximum solute-dislocation interaction force that is encountered by edge dislocation, and an expression relating the yield stress to the length of the dislocation and the solute concentration is provided. The magnitude of the solid solution strengthening due to solute atoms can be determined directly from the numerical results, provided the dislocation line length that moves as a unit is specified.

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.

Plane Poiseuille flow of a rarefied gas in the presence of strong gravitation.

PubMed

Doi, Toshiyuki

2011-02-01

Plane Poiseuille flow of a rarefied gas, which flows horizontally in the presence of strong gravitation, is studied based on the Boltzmann equation. Applying the asymptotic analysis for a small variation in the flow direction [Y. Sone, Molecular Gas Dynamics (Birkhäuser, 2007)], the two-dimensional problem is reduced to a one-dimensional problem, as in the case of a Poiseuille flow in the absence of gravitation, and the solution is obtained in a semianalytical form. The reduced one-dimensional problem is solved numerically for a hard sphere molecular gas over a wide range of the gas-rarefaction degree and the gravitational strength. The presence of gravitation reduces the mass flow rate, and the effect of gravitation is significant for large Knudsen numbers. To verify the validity of the asymptotic solution, a two-dimensional problem of a flow through a long channel is directly solved numerically, and the validity of the asymptotic solution is confirmed. ©2011 American Physical Society

Application of matched asymptotic expansions to lunar and interplanetary trajectories. Volume 1: Technical discussion

NASA Technical Reports Server (NTRS)

Lancaster, J. E.

1973-01-01

Previously published asymptotic solutions for lunar and interplanetary trajectories have been modified and combined to formulate a general analytical solution to the problem on N-bodies. The earlier first-order solutions, derived by the method of matched asymptotic expansions, have been extended to second order for the purpose of obtaining increased accuracy. The derivation of the second-order solution is summarized by showing the essential steps, some in functional form. The general asymptotic solution has been used as a basis for formulating a number of analytical two-point boundary value solutions. These include earth-to-moon, one- and two-impulse moon-to-earth, and interplanetary solutions. The results show that the accuracies of the asymptotic solutions range from an order of magnitude better than conic approximations to that of numerical integration itself. Also, since no iterations are required, the asymptotic boundary value solutions are obtained in a fraction of the time required for comparable numerically integrated solutions. The subject of minimizing the second-order error is discussed, and recommendations made for further work directed toward achieving a uniform accuracy in all applications.

Numerical solution methods for viscoelastic orthotropic materials

NASA Technical Reports Server (NTRS)

Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.

1988-01-01

Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral, Zienkiewicz's linear Prony series method, and a new method called Nonlinear Differential Equation Method (NDEM) which uses a nonlinear Prony series. The criteria used for comparison of the various methods include the stability of the solution technique, time step size stability, computer solution time length, and computer memory storage. The Volterra Integral allowed the implementation of higher order solution techniques but had difficulties solving singular and weakly singular compliance function. The Zienkiewicz solution technique, which requires the viscoelastic response to be modeled by a Prony series, works well for linear viscoelastic isotropic materials and small time steps. The new method, NDEM, uses a modified Prony series which allows nonlinear stress effects to be included and can be used with orthotropic nonlinear viscoelastic materials. The NDEM technique is shown to be accurate and stable for both linear and nonlinear conditions with minimal computer time.

CSR Fields: Direct Numerical Solution of the Maxwell___s Equation

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

Novokhatski, A.; /SLAC

2011-06-22

We discuss the properties of the coherent electromagnetic fields of a very short, ultra-relativistic bunch in a rectangular vacuum chamber inside a bending magnet. The analysis is based on the results of a direct numerical solution of Maxwell's equations together with Newton's equations. We use a new dispersion-free time-domain algorithm which employs a more efficient use of finite element mesh techniques and hence produces self-consistent and stable solutions for very short bunches. We investigate the fine structure of the CSR fields including coherent edge radiation. This approach should be useful in the study of existing and future concepts of particlemore » accelerators and ultrafast coherent light sources. The coherent synchrotron radiation (CSR) fields have a strong action on the beam dynamics of very short bunches, which are moving in the bends of all kinds of magnetic elements. They are responsible for additional energy loss and energy spread; micro bunching and beam emittance growth. These fields may bound the efficiency of damping rings, electron-positron colliders and ultrafast coherent light sources, where high peak currents and very short bunches are envisioned. This is relevant to most high-brightness beam applications. On the other hand these fields together with transition radiation fields can be used for beam diagnostics or even as a powerful resource of THz radiation. A history of the study of CSR and a good collection of references can be found in [1]. Electromagnetic theory suggests several methods on how to calculate CSR fields. The most popular method is to use Lienard-Wiechert potentials. Other approach is to solve numerically the approximate equations, which are a Schrodinger type equation. These numerical methods are described in [2]. We suggest that a direct solution of Maxwell's equations together with Newton's equations can describe the detailed structure of the CSR fields [3].« less

Apparent dispersion in transient groundwater flow

USGS Publications Warehouse

Goode, Daniel J.; Konikow, Leonard F.

1990-01-01

This paper investigates the effects of large-scale temporal velocity fluctuations, particularly changes in the direction of flow, on solute spreading in a two-dimensional aquifer. Relations for apparent longitudinal and transverse dispersivity are developed through an analytical solution for dispersion in a fluctuating, quasi-steady uniform flow field, in which storativity is zero. For transient flow, spatial moments are evaluated from numerical solutions. Ignored or unknown transients in the direction of flow primarily act to increase the apparent transverse dispersivity because the longitudinal dispersivity is acting in a direction that is not the assumed flow direction. This increase is a function of the angle between the transient flow vector and the assumed steady state flow direction and the ratio of transverse to longitudinal dispersivity. The maximum effect on transverse dispersivity occurs if storativity is assumed to be zero, such that the flow field responds instantly to boundary condition changes.

Salty popcorn in a homogeneous low-dimensional toy model of holographic QCD

NASA Astrophysics Data System (ADS)

Elliot-Ripley, Matthew

2017-04-01

Recently, a homogeneous ansatz has been used to study cold dense nuclear matter in the Sakai-Sugimoto model of holographic QCD. To justify this homogeneous approximation we here investigate a homogeneous ansatz within a low-dimensional toy version of Sakai-Sugimoto to study finite baryon density configurations and compare it to full numerical solutions. We find the ansatz corresponds to enforcing a dyon salt arrangement in which the soliton solutions are split into half-soliton layers. Within this ansatz we find analogues of the proposed baryonic popcorn transitions, in which solutions split into multiple layers in the holographic direction. The homogeneous results are found to qualitatively match the full numerical solutions, lending confidence to the homogeneous approximations of the full Sakai-Sugimoto model. In addition, we find exact compact solutions in the high density, flat space limit which demonstrate the existence of further popcorn transitions to three layers and beyond.

Common aero vehicle autonomous reentry trajectory optimization satisfying waypoint and no-fly zone constraints

NASA Astrophysics Data System (ADS)

Jorris, Timothy R.

2007-12-01

To support the Air Force's Global Reach concept, a Common Aero Vehicle is being designed to support the Global Strike mission. "Waypoints" are specified for reconnaissance or multiple payload deployments and "no-fly zones" are specified for geopolitical restrictions or threat avoidance. Due to time critical targets and multiple scenario analysis, an autonomous solution is preferred over a time-intensive, manually iterative one. Thus, a real-time or near real-time autonomous trajectory optimization technique is presented to minimize the flight time, satisfy terminal and intermediate constraints, and remain within the specified vehicle heating and control limitations. This research uses the Hypersonic Cruise Vehicle (HCV) as a simplified two-dimensional platform to compare multiple solution techniques. The solution techniques include a unique geometric approach developed herein, a derived analytical dynamic optimization technique, and a rapidly emerging collocation numerical approach. This up-and-coming numerical technique is a direct solution method involving discretization then dualization, with pseudospectral methods and nonlinear programming used to converge to the optimal solution. This numerical approach is applied to the Common Aero Vehicle (CAV) as the test platform for the full three-dimensional reentry trajectory optimization problem. The culmination of this research is the verification of the optimality of this proposed numerical technique, as shown for both the two-dimensional and three-dimensional models. Additionally, user implementation strategies are presented to improve accuracy and enhance solution convergence. Thus, the contributions of this research are the geometric approach, the user implementation strategies, and the determination and verification of a numerical solution technique for the optimal reentry trajectory problem that minimizes time to target while satisfying vehicle dynamics and control limitation, and heating, waypoint, and no-fly zone constraints.

Direct Linearization and Adjoint Approaches to Evaluation of Atmospheric Weighting Functions and Surface Partial Derivatives: General Principles, Synergy and Areas of Application

NASA Technical Reports Server (NTRS)

Ustino, Eugene A.

2006-01-01

This slide presentation reviews the observable radiances as functions of atmospheric parameters and of surface parameters; the mathematics of atmospheric weighting functions (WFs) and surface partial derivatives (PDs) are presented; and the equation of the forward radiative transfer (RT) problem is presented. For non-scattering atmospheres this can be done analytically, and all WFs and PDs can be computed analytically using the direct linearization approach. For scattering atmospheres, in general case, the solution of the forward RT problem can be obtained only numerically, but we need only two numerical solutions: one of the forward RT problem and one of the adjoint RT problem to compute all WFs and PDs we can think of. In this presentation we discuss applications of both the linearization and adjoint approaches

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

Sidler, Rolf, E-mail: rsidler@gmail.com; Carcione, José M.; Holliger, Klaus

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in themore » radial direction and a Fourier expansion in the azimuthal direction and a Runge–Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid–solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently benchmarked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.« less

Development and application of a three dimensional numerical model for predicting pollutant and sediment transport using an Eulerian-Lagrangian marker particle technique

NASA Technical Reports Server (NTRS)

Pavish, D. L.; Spaulding, M. L.

1977-01-01

A computer coded Lagrangian marker particle in Eulerian finite difference cell solution to the three dimensional incompressible mass transport equation, Water Advective Particle in Cell Technique, WAPIC, was developed, verified against analytic solutions, and subsequently applied in the prediction of long term transport of a suspended sediment cloud resulting from an instantaneous dredge spoil release. Numerical results from WAPIC were verified against analytic solutions to the three dimensional incompressible mass transport equation for turbulent diffusion and advection of Gaussian dye releases in unbounded uniform and uniformly sheared uni-directional flow, and for steady-uniform plug channel flow. WAPIC was utilized to simulate an analytic solution for non-equilibrium sediment dropout from an initially vertically uniform particle distribution in one dimensional turbulent channel flow.

A computing method for sound propagation through a nonuniform jet stream

NASA Technical Reports Server (NTRS)

Padula, S. L.; Liu, C. H.

1974-01-01

The classical formulation of sound propagation through a jet flow was found to be inadequate for computer solutions. Previous investigations selected the phase and amplitude of the acoustic pressure as dependent variables requiring the solution of a system of nonlinear algebraic equations. The nonlinearities complicated both the analysis and the computation. A reformulation of the convective wave equation in terms of a new set of dependent variables is developed with a special emphasis on its suitability for numerical solutions on fast computers. The technique is very attractive because the resulting equations are linear in nonwaving variables. The computer solution to such a linear system of algebraic equations may be obtained by well-defined and direct means which are conservative of computer time and storage space. Typical examples are illustrated and computational results are compared with available numerical and experimental data.

Chemical Transport in a Fissured Rock: Verification of a Numerical Model

NASA Astrophysics Data System (ADS)

Rasmuson, A.; Narasimhan, T. N.; Neretnieks, I.

1982-10-01

Numerical models for simulating chemical transport in fissured rocks constitute powerful tools for evaluating the acceptability of geological nuclear waste repositories. Due to the very long-term, high toxicity of some nuclear waste products, the models are required to predict, in certain cases, the spatial and temporal distribution of chemical concentration less than 0.001% of the concentration released from the repository. Whether numerical models can provide such accuracies is a major question addressed in the present work. To this end we have verified a numerical model, TRUMP, which solves the advective diffusion equation in general three dimensions, with or without decay and source terms. The method is based on an integrated finite difference approach. The model was verified against known analytic solution of the one-dimensional advection-diffusion problem, as well as the problem of advection-diffusion in a system of parallel fractures separated by spherical particles. The studies show that as long as the magnitude of advectance is equal to or less than that of conductance for the closed surface bounding any volume element in the region (that is, numerical Peclet number <2), the numerical method can indeed match the analytic solution within errors of ±10-3% or less. The realistic input parameters used in the sample calculations suggest that such a range of Peclet numbers is indeed likely to characterize deep groundwater systems in granitic and ancient argillaceous systems. Thus TRUMP in its present form does provide a viable tool for use in nuclear waste evaluation studies. A sensitivity analysis based on the analytic solution suggests that the errors in prediction introduced due to uncertainties in input parameters are likely to be larger than the computational inaccuracies introduced by the numerical model. Currently, a disadvantage in the TRUMP model is that the iterative method of solving the set of simultaneous equations is rather slow when time constants vary widely over the flow region. Although the iterative solution may be very desirable for large three-dimensional problems in order to minimize computer storage, it seems desirable to use a direct solver technique in conjunction with the mixed explicit-implicit approach whenever possible. Work in this direction is in progress.

On the Solution of the Three-Dimensional Flowfield About a Flow-Through Nacelle. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Compton, William Bernard

1985-01-01

The solution of the three dimensional flow field for a flow through nacelle was studied. Both inviscid and viscous inviscid interacting solutions were examined. Inviscid solutions were obtained with two different computational procedures for solving the three dimensional Euler equations. The first procedure employs an alternating direction implicit numerical algorithm, and required the development of a complete computational model for the nacelle problem. The second computational technique employs a fourth order Runge-Kutta numerical algorithm which was modified to fit the nacelle problem. Viscous effects on the flow field were evaluated with a viscous inviscid interacting computational model. This model was constructed by coupling the explicit Euler solution procedure with a flag entrainment boundary layer solution procedure in a global iteration scheme. The computational techniques were used to compute the flow field for a long duct turbofan engine nacelle at free stream Mach numbers of 0.80 and 0.94 and angles of attack of 0 and 4 deg.

Direction dependence of displacement time for two-fluid electroosmotic flow.

PubMed

Lim, Chun Yee; Lam, Yee Cheong

2012-03-01

Electroosmotic flow that involves one fluid displacing another fluid is commonly encountered in various microfludic applications and experiments, for example, current monitoring technique to determine zeta potential of microchannel. There is experimentally observed anomaly in such flow, namely, the displacement time is flow direction dependent, i.e., it depends if it is a high concentration fluid displacing a low concentration fluid, or vice versa. Thus, this investigation focuses on the displacement flow of two fluids with various concentration differences. The displacement time was determined experimentally with current monitoring method. It is concluded that the time required for a high concentration solution to displace a low concentration solution is smaller than the time required for a low concentration solution to displace a high concentration solution. The percentage displacement time difference increases with increasing concentration difference and independent of the length or width of the channel and the voltage applied. Hitherto, no theoretical analysis or numerical simulation has been conducted to explain this phenomenon. A numerical model based on finite element method was developed to explain the experimental observations. Simulations showed that the velocity profile and ion distribution deviate significantly from a single fluid electroosmotic flow. The distortion of ion distribution near the electrical double layer is responsible for the displacement time difference for the two different flow directions. The trends obtained from simulations agree with the experimental findings.

Direction dependence of displacement time for two-fluid electroosmotic flow

PubMed Central

Lim, Chun Yee; Lam, Yee Cheong

2012-01-01

Electroosmotic flow that involves one fluid displacing another fluid is commonly encountered in various microfludic applications and experiments, for example, current monitoring technique to determine zeta potential of microchannel. There is experimentally observed anomaly in such flow, namely, the displacement time is flow direction dependent, i.e., it depends if it is a high concentration fluid displacing a low concentration fluid, or vice versa. Thus, this investigation focuses on the displacement flow of two fluids with various concentration differences. The displacement time was determined experimentally with current monitoring method. It is concluded that the time required for a high concentration solution to displace a low concentration solution is smaller than the time required for a low concentration solution to displace a high concentration solution. The percentage displacement time difference increases with increasing concentration difference and independent of the length or width of the channel and the voltage applied. Hitherto, no theoretical analysis or numerical simulation has been conducted to explain this phenomenon. A numerical model based on finite element method was developed to explain the experimental observations. Simulations showed that the velocity profile and ion distribution deviate significantly from a single fluid electroosmotic flow. The distortion of ion distribution near the electrical double layer is responsible for the displacement time difference for the two different flow directions. The trends obtained from simulations agree with the experimental findings. PMID:22662083

Galois groups of Schubert problems via homotopy computation

NASA Astrophysics Data System (ADS)

Leykin, Anton; Sottile, Frank

2009-09-01

Numerical homotopy continuation of solutions to polynomial equations is the foundation for numerical algebraic geometry, whose development has been driven by applications of mathematics. We use numerical homotopy continuation to investigate the problem in pure mathematics of determining Galois groups in the Schubert calculus. For example, we show by direct computation that the Galois group of the Schubert problem of 3-planes in mathbb{C}^8 meeting 15 fixed 5-planes non-trivially is the full symmetric group S_{6006} .

Analytical and numerical analysis of the slope of von Mises planar trusses

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

Kalina, M.; Frantík, P.

2016-06-08

In the present paper, there are presented post-critical stress states which will occur at loading by vertical shift of the top joint in the direction downwards. The formation of certain stress states depends on the size of the angle formed by a straight beam of the von Mises planar truss with horizontal plane. Numerical and analytical methods and their problems with finding the angle were described. The numerical solution applies the method of searching for a minimum of potential energy.

Numerical Solution of the Kzk Equation for Pulsed Finite Amplitude Sound Beams in Thermoviscous Fluids

NASA Astrophysics Data System (ADS)

Lee, Yang-Sub

A time-domain numerical algorithm for solving the KZK (Khokhlov-Zabolotskaya-Kuznetsov) nonlinear parabolic wave equation is developed for pulsed, axisymmetric, finite amplitude sound beams in thermoviscous fluids. The KZK equation accounts for the combined effects of diffraction, absorption, and nonlinearity at the same order of approximation. The accuracy of the algorithm is established via comparison with analytical solutions for several limiting cases, and with numerical results obtained from a widely used algorithm for solving the KZK equation in the frequency domain. The time domain algorithm is used to investigate waveform distortion and shock formation in directive sound beams radiated by pulsed circular piston sources. New results include predictions for the entire process of self-demodulation, and for the effect of frequency modulation on pulse envelope distortion. Numerical results are compared with measurements, and focused sources are investigated briefly.

Modeling of Electromagnetic Scattering by Discrete and Discretely Heterogeneous Random Media by Using Numerically Exact Solutions of the Maxwell Equations

NASA Technical Reports Server (NTRS)

Dlugach, Janna M.; Mishchenko, Michael I.

2017-01-01

In this paper, we discuss some aspects of numerical modeling of electromagnetic scattering by discrete random medium by using numerically exact solutions of the macroscopic Maxwell equations. Typical examples of such media are clouds of interstellar dust, clouds of interplanetary dust in the Solar system, dusty atmospheres of comets, particulate planetary rings, clouds in planetary atmospheres, aerosol particles with numerous inclusions and so on. Our study is based on the results of extensive computations of different characteristics of electromagnetic scattering obtained by using the superposition T-matrix method which represents a direct computer solver of the macroscopic Maxwell equations for an arbitrary multisphere configuration. As a result, in particular, we clarify the range of applicability of the low-density theories of radiative transfer and coherent backscattering as well as of widely used effective-medium approximations.

Aeroacoustic Simulations of a Nose Landing Gear Using FUN3D on Pointwise Unstructured Grids

NASA Technical Reports Server (NTRS)

Vatsa, Veer N.; Khorrami, Mehdi R.; Rhoads, John; Lockard, David P.

2015-01-01

Numerical simulations have been performed for a partially-dressed, cavity-closed (PDCC) nose landing gear configuration that was tested in the University of Florida's open-jet acoustic facility known as the UFAFF. The unstructured-grid flow solver FUN3D is used to compute the unsteady flow field for this configuration. Mixed-element grids generated using the Pointwise(TradeMark) grid generation software are used for these simulations. Particular care is taken to ensure quality cells and proper resolution in critical areas of interest in an effort to minimize errors introduced by numerical artifacts. A hybrid Reynolds-averaged Navier-Stokes/large eddy simulation (RANS/LES) turbulence model is used for these simulations. Solutions are also presented for a wall function model coupled to the standard turbulence model. Time-averaged and instantaneous solutions obtained on these Pointwise grids are compared with the measured data and previous numerical solutions. The resulting CFD solutions are used as input to a Ffowcs Williams-Hawkings noise propagation code to compute the farfield noise levels in the flyover and sideline directions. The computed noise levels compare well with previous CFD solutions and experimental data.

Review of some vortex relations

NASA Technical Reports Server (NTRS)

Krause, E.

1984-01-01

The evaluation of the circulation from numerical solutions of the momentum and energy equations is discussed for incompressible and compressible flows. It is shown how artificial damping directly influences the time ratio of change of the circulation.

Simulation of a Single-Element Lean-Direct Injection Combustor Using a Polyhedral Mesh Derived from Hanging-Node Elements

NASA Technical Reports Server (NTRS)

Wey, Thomas; Liu, Nan-Suey

2013-01-01

This paper summarizes the procedures of generating a polyhedral mesh derived from hanging-node elements as well as presents sample results from its application to the numerical solution of a single element lean direct injection (LDI) combustor using an open-source version of the National Combustion Code (NCC).

Finite Element Analysis of Magnetic Damping Effects on G-Jitter Induced Fluid Flow

NASA Technical Reports Server (NTRS)

Pan, Bo; Li, Ben Q.; deGroh, Henry C., III

1997-01-01

This paper reports some interim results on numerical modeling and analyses of magnetic damping of g-jitter driven fluid flow in microgravity. A finite element model is developed to represent the fluid flow, thermal and solute transport phenomena in a 2-D cavity under g-jitter conditions with and without an applied magnetic field. The numerical model is checked by comparing with analytical solutions obtained for a simple parallel plate channel flow driven by g-jitter in a transverse magnetic field. The model is then applied to study the effect of steady state g-jitter induced oscillation and on the solute redistribution in the liquid that bears direct relevance to the Bridgman-Stockbarger single crystal growth processes. A selection of computed results is presented and the results indicate that an applied magnetic field can effectively damp the velocity caused by g-jitter and help to reduce the time variation of solute redistribution.

Super-rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations.

PubMed

Slunyaev, A; Pelinovsky, E; Sergeeva, A; Chabchoub, A; Hoffmann, N; Onorato, M; Akhmediev, N

2013-07-01

The rogue wave solutions (rational multibreathers) of the nonlinear Schrödinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5 are considered. A higher accuracy of wave propagation in space is reached using the modified NLS equation, also known as the Dysthe equation. This numerical modeling allowed us to directly compare simulations with recent results of laboratory measurements in Chabchoub et al. [Phys. Rev. E 86, 056601 (2012)]. In order to achieve even higher physical accuracy, we employed fully nonlinear simulations of potential Euler equations. These simulations provided us with basic characteristics of long time evolution of rational solutions of the NLS equation in the case of near-breaking conditions. The analytic NLS solutions are found to describe the actual wave dynamics of steep waves reasonably well.

Gravitational modulation of thermosolutal convection during directional solidification

NASA Astrophysics Data System (ADS)

Murray, B. T.; Coriell, S. R.; McFadden, G. B.; Wheeler, A. A.; Saunders, B. V.

1993-03-01

During directional solidification of a binary alloy at constant velocity, thermosolutal convection may occur due to the temperature and solute gradients associated with the solidification process. For vertical growth in an ideal furnace (lacking horizontal gradients) a quiescent state is possible. The effect of a time-periodic vertical gravitational acceleration (or equivalently vibration) on the onset of thermosolutal convection is calculated based on linear stability using Floquet theory. Numerical calculations for the onset of instability have been carried out for a semiconductor alloy with Schmidt number of 10 and Prandtl number of 0.1 with primary emphasis on large modulation frequencies in a microgravity environment for which the background gravitational acceleration is negligible. The numerical results demonstrate that there is a significant difference in stability depending on whether a heavier or lighter solute is rejected. For large modulation frequencies, the stability behavior can be described by either the method of averaging or an asymptotic resonant mode analysis.

The exact solution of shear-lag problems in flat panels and box beams assumed rigid in the transverse direction

NASA Technical Reports Server (NTRS)

Hildebrand, Francis B

1943-01-01

A mathematical procedure is herein developed for obtaining exact solutions of shear-lag problems in flat panels and box beams: the method is based on the assumption that the amount of stretching of the sheets in the direction perpendicular to the direction of essential normal stresses is negligible. Explicit solutions, including the treatment of cut-outs, are given for several cases and numerical results are presented in graphic and tabular form. The general theory is presented in a from which further solutions can be readily obtained. The extension of the theory to cover certain cases of non-uniform cross section is indicated. Although the solutions are obtained in terms of infinite series, the present developments differ from those previously given in that, in practical cases, the series usually converge so rapidly that sufficient accuracy is afforded by a small number of terms. Comparisons are made in several cases between the present results and the corresponding solutions obtained by approximate procedures devised by Reissner and by Kuhn and Chiarito.

A three-dimensional, compressible, laminar boundary-layer method for general fuselages. Volume 1: Numerical method

NASA Technical Reports Server (NTRS)

Wie, Yong-Sun

1990-01-01

A procedure for calculating 3-D, compressible laminar boundary layer flow on general fuselage shapes is described. The boundary layer solutions can be obtained in either nonorthogonal 'body oriented' coordinates or orthogonal streamline coordinates. The numerical procedure is 'second order' accurate, efficient and independent of the cross flow velocity direction. Numerical results are presented for several test cases, including a sharp cone, an ellipsoid of revolution, and a general aircraft fuselage at angle of attack. Comparisons are made between numerical results obtained using nonorthogonal curvilinear 'body oriented' coordinates and streamline coordinates.

Electroosmotic flow hysteresis for dissimilar ionic solutions

PubMed Central

Lim, An Eng; Lam, Yee Cheong

2015-01-01

Electroosmotic flow (EOF) with two or more fluids is commonly encountered in various microfluidics applications. However, no investigation has hitherto been conducted to investigate the hysteretic or flow direction-dependent behavior during the displacement flow of solutions with dissimilar ionic species. In this investigation, electroosmotic displacement flow involving dissimilar ionic solutions was studied experimentally through a current monitoring method and numerically through finite element simulations. The flow hysteresis can be characterized by the turning and displacement times; turning time refers to the abrupt gradient change of current-time curve while displacement time is the time for one solution to completely displace the other solution. Both experimental and simulation results illustrate that the turning and displacement times for a particular solution pair can be directional-dependent, indicating that the flow conditions in the microchannel are not the same in the two different flow directions. The mechanics of EOF hysteresis was elucidated through the theoretical model which includes the ionic mobility of each species, a major governing parameter. Two distinct mechanics have been identified as the causes for the EOF hysteresis involving dissimilar ionic solutions: the widening/sharpening effect of interfacial region between the two solutions and the difference in ion concentration distributions (and thus average zeta potentials) in different flow directions. The outcome of this investigation contributes to the fundamental understanding of flow behavior in microfluidic systems involving solution pair with dissimilar ionic species. PMID:25945139

Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations

NASA Astrophysics Data System (ADS)

Kao, Chiu Yen; Osher, Stanley; Qian, Jianliang

2004-05-01

We propose a simple, fast sweeping method based on the Lax-Friedrichs monotone numerical Hamiltonian to approximate viscosity solutions of arbitrary static Hamilton-Jacobi equations in any number of spatial dimensions. By using the Lax-Friedrichs numerical Hamiltonian, we can easily obtain the solution at a specific grid point in terms of its neighbors, so that a Gauss-Seidel type nonlinear iterative method can be utilized. Furthermore, by incorporating a group-wise causality principle into the Gauss-Seidel iteration by following a finite group of characteristics, we have an easy-to-implement, sweeping-type, and fast convergent numerical method. However, unlike other methods based on the Godunov numerical Hamiltonian, some computational boundary conditions are needed in the implementation. We give a simple recipe which enforces a version of discrete min-max principle. Some convergence analysis is done for the one-dimensional eikonal equation. Extensive 2-D and 3-D numerical examples illustrate the efficiency and accuracy of the new approach. To our knowledge, this is the first fast numerical method based on discretizing the Hamilton-Jacobi equation directly without assuming convexity and/or homogeneity of the Hamiltonian.

An investigation of several numerical procedures for time-asymptotic compressible Navier-Stokes solutions

NASA Technical Reports Server (NTRS)

Rudy, D. H.; Morris, D. J.; Blanchard, D. K.; Cooke, C. H.; Rubin, S. G.

1975-01-01

The status of an investigation of four numerical techniques for the time-dependent compressible Navier-Stokes equations is presented. Results for free shear layer calculations in the Reynolds number range from 1000 to 81000 indicate that a sequential alternating-direction implicit (ADI) finite-difference procedure requires longer computing times to reach steady state than a low-storage hopscotch finite-difference procedure. A finite-element method with cubic approximating functions was found to require excessive computer storage and computation times. A fourth method, an alternating-direction cubic spline technique which is still being tested, is also described.

Nonlinear grid error effects on numerical solution of partial differential equations

NASA Technical Reports Server (NTRS)

Dey, S. K.

1980-01-01

Finite difference solutions of nonlinear partial differential equations require discretizations and consequently grid errors are generated. These errors strongly affect stability and convergence properties of difference models. Previously such errors were analyzed by linearizing the difference equations for solutions. Properties of mappings of decadence were used to analyze nonlinear instabilities. Such an analysis is directly affected by initial/boundary conditions. An algorithm was developed, applied to nonlinear Burgers equations, and verified computationally. A preliminary test shows that Navier-Stokes equations may be treated similarly.

Modification of a method-of-characteristics solute-transport model to incorporate decay and equilibrium-controlled sorption or ion exchange

USGS Publications Warehouse

Goode, D.J.; Konikow, Leonard F.

1989-01-01

The U.S. Geological Survey computer model of two-dimensional solute transport and dispersion in ground water (Konikow and Bredehoeft, 1978) has been modified to incorporate the following types of chemical reactions: (1) first-order irreversible rate-reaction, such as radioactive decay; (2) reversible equilibrium-controlled sorption with linear, Freundlich, or Langmuir isotherms; and (3) reversible equilibrium-controlled ion exchange for monovalent or divalent ions. Numerical procedures are developed to incorporate these processes in the general solution scheme that uses method-of- characteristics with particle tracking for advection and finite-difference methods for dispersion. The first type of reaction is accounted for by an exponential decay term applied directly to the particle concentration. The second and third types of reactions are incorporated through a retardation factor, which is a function of concentration for nonlinear cases. The model is evaluated and verified by comparison with analytical solutions for linear sorption and decay, and by comparison with other numerical solutions for nonlinear sorption and ion exchange.

Analytical theory of two-dimensional ring dark soliton in nonlocal nonlinear media

NASA Astrophysics Data System (ADS)

Chen, Wei; Wang, Qi; Shi, Jielong; Shen, Ming

2017-11-01

Completely stable two-dimensional ring dark soliton in nonlocal media with an arbitrary degree of nonlocality are investigated. The exact solution of the ring dark solitons is obtained with the variational method and a cylindrical nonlocal response function. The analytical results are confirmed by directly numerical simulations. We also analytically and numerically study the expansion dynamics of the gray ring dark solitons in detail.

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

Stochastic weighted particle methods for population balance equations with coagulation, fragmentation and spatial inhomogeneity

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

Lee, Kok Foong; Patterson, Robert I.A.; Wagner, Wolfgang

2015-12-15

Graphical abstract: -- Highlights: •Problems concerning multi-compartment population balance equations are studied. •A class of fragmentation weight transfer functions is presented. •Three stochastic weighted algorithms are compared against the direct simulation algorithm. •The numerical errors of the stochastic solutions are assessed as a function of fragmentation rate. •The algorithms are applied to a multi-dimensional granulation model. -- Abstract: This paper introduces stochastic weighted particle algorithms for the solution of multi-compartment population balance equations. In particular, it presents a class of fragmentation weight transfer functions which are constructed such that the number of computational particles stays constant during fragmentation events. Themore » weight transfer functions are constructed based on systems of weighted computational particles and each of it leads to a stochastic particle algorithm for the numerical treatment of population balance equations. Besides fragmentation, the algorithms also consider physical processes such as coagulation and the exchange of mass with the surroundings. The numerical properties of the algorithms are compared to the direct simulation algorithm and an existing method for the fragmentation of weighted particles. It is found that the new algorithms show better numerical performance over the two existing methods especially for systems with significant amount of large particles and high fragmentation rates.« less

3PE: A Tool for Estimating Groundwater Flow Vectors

EPA Science Inventory

Evaluation of hydraulic gradients and the associated groundwater flow rates and directions is a fundamental aspect of hydrogeologic characterization. Many methods, ranging in complexity from simple three-point solution techniques to complex numerical models of groundwater flow, ...

Direct Solve of Electrically Large Integral Equations for Problem Sizes to 1M Unknowns

NASA Technical Reports Server (NTRS)

Shaeffer, John

2008-01-01

Matrix methods for solving integral equations via direct solve LU factorization are presently limited to weeks to months of very expensive supercomputer time for problems sizes of several hundred thousand unknowns. This report presents matrix LU factor solutions for electromagnetic scattering problems for problem sizes to one million unknowns with thousands of right hand sides that run in mere days on PC level hardware. This EM solution is accomplished by utilizing the numerical low rank nature of spatially blocked unknowns using the Adaptive Cross Approximation for compressing the rank deficient blocks of the system Z matrix, the L and U factors, the right hand side forcing function and the final current solution. This compressed matrix solution is applied to a frequency domain EM solution of Maxwell's equations using standard Method of Moments approach. Compressed matrix storage and operations count leads to orders of magnitude reduction in memory and run time.

Analytical and numerical construction of vertical periodic orbits about triangular libration points based on polynomial expansion relations among directions

NASA Astrophysics Data System (ADS)

Qian, Ying-Jing; Yang, Xiao-Dong; Zhai, Guan-Qiao; Zhang, Wei

2017-08-01

Innovated by the nonlinear modes concept in the vibrational dynamics, the vertical periodic orbits around the triangular libration points are revisited for the Circular Restricted Three-body Problem. The ζ -component motion is treated as the dominant motion and the ξ and η -component motions are treated as the slave motions. The slave motions are in nature related to the dominant motion through the approximate nonlinear polynomial expansions with respect to the ζ -position and ζ -velocity during the one of the periodic orbital motions. By employing the relations among the three directions, the three-dimensional system can be transferred into one-dimensional problem. Then the approximate three-dimensional vertical periodic solution can be analytically obtained by solving the dominant motion only on ζ -direction. To demonstrate the effectiveness of the proposed method, an accuracy study was carried out to validate the polynomial expansion (PE) method. As one of the applications, the invariant nonlinear relations in polynomial expansion form are used as constraints to obtain numerical solutions by differential correction. The nonlinear relations among the directions provide an alternative point of view to explore the overall dynamics of periodic orbits around libration points with general rules.

Fast Numerical Solution of the Plasma Response Matrix for Real-time Ideal MHD Control

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

Glasser, Alexander; Kolemen, Egemen; Glasser, Alan H.

To help effectuate near real-time feedback control of ideal MHD instabilities in tokamak geometries, a parallelized version of A.H. Glasser’s DCON (Direct Criterion of Newcomb) code is developed. To motivate the numerical implementation, we first solve DCON’s δW formulation with a Hamilton-Jacobi theory, elucidating analytical and numerical features of the ideal MHD stability problem. The plasma response matrix is demonstrated to be the solution of an ideal MHD Riccati equation. We then describe our adaptation of DCON with numerical methods natural to solutions of the Riccati equation, parallelizing it to enable its operation in near real-time. We replace DCON’s serial integration of perturbed modes—which satisfy a singular Euler- Lagrange equation—with a domain-decomposed integration of state transition matrices. Output is shown to match results from DCON with high accuracy, and with computation time < 1s. Such computational speed may enable active feedback ideal MHD stability control, especially in plasmas whose ideal MHD equilibria evolve with inductive timescalemore » $$\\tau$$ ≳ 1s—as in ITER. Further potential applications of this theory are discussed.« less

Fast Numerical Solution of the Plasma Response Matrix for Real-time Ideal MHD Control

DOE PAGES

Glasser, Alexander; Kolemen, Egemen; Glasser, Alan H.

2018-03-26

To help effectuate near real-time feedback control of ideal MHD instabilities in tokamak geometries, a parallelized version of A.H. Glasser’s DCON (Direct Criterion of Newcomb) code is developed. To motivate the numerical implementation, we first solve DCON’s δW formulation with a Hamilton-Jacobi theory, elucidating analytical and numerical features of the ideal MHD stability problem. The plasma response matrix is demonstrated to be the solution of an ideal MHD Riccati equation. We then describe our adaptation of DCON with numerical methods natural to solutions of the Riccati equation, parallelizing it to enable its operation in near real-time. We replace DCON’s serial integration of perturbed modes—which satisfy a singular Euler- Lagrange equation—with a domain-decomposed integration of state transition matrices. Output is shown to match results from DCON with high accuracy, and with computation time < 1s. Such computational speed may enable active feedback ideal MHD stability control, especially in plasmas whose ideal MHD equilibria evolve with inductive timescalemore » $$\\tau$$ ≳ 1s—as in ITER. Further potential applications of this theory are discussed.« less

Numerical Studies of Boundary-Layer Receptivity

NASA Technical Reports Server (NTRS)

Reed, Helen L.

1995-01-01

Direct numerical simulations (DNS) of the acoustic receptivity process on a semi-infinite flat plate with a modified-super-elliptic (MSE) leading edge are performed. The incompressible Navier-Stokes equations are solved in stream-function/vorticity form in a general curvilinear coordinate system. The steady basic-state solution is found by solving the governing equations using an alternating direction implicit (ADI) procedure which takes advantage of the parallelism present in line-splitting techniques. Time-harmonic oscillations of the farfield velocity are applied as unsteady boundary conditions to the unsteady disturbance equations. An efficient time-harmonic scheme is used to produce the disturbance solutions. Buffer-zone techniques have been applied to eliminate wave reflection from the outflow boundary. The spatial evolution of Tollmien-Schlichting (T-S) waves is analyzed and compared with experiment and theory. The effects of nose-radius, frequency, Reynolds number, angle of attack, and amplitude of the acoustic wave are investigated. This work is being performed in conjunction with the experiments at the Arizona State University Unsteady Wind Tunnel under the direction of Professor William Saric. The simulations are of the same configuration and parameters used in the wind-tunnel experiments.

Spikes and matter inhomogeneities in massless scalar field models

NASA Astrophysics Data System (ADS)

Coley, A. A.; Lim, W. C.

2016-01-01

We shall discuss the general relativistic generation of spikes in a massless scalar field or stiff perfect fluid model. We first investigate orthogonally transitive (OT) G 2 stiff fluid spike models both heuristically and numerically, and give a new exact OT G 2 stiff fluid spike solution. We then present a new two-parameter family of non-OT G 2 stiff fluid spike solutions, obtained by the generalization of non-OT G 2 vacuum spike solutions to the stiff fluid case by applying Geroch's transformation on a Jacobs seed. The dynamics of these new stiff fluid spike solutions is qualitatively different from that of the vacuum spike solutions in that the matter (stiff fluid) feels the spike directly and the stiff fluid spike solution can end up with a permanent spike. We then derive the evolution equations of non-OT G 2 stiff fluid models, including a second perfect fluid, in full generality, and briefly discuss some of their qualitative properties and their potential numerical analysis. Finally, we discuss how a fluid, and especially a stiff fluid or massless scalar field, affects the physics of the generation of spikes.

Computation of steady and unsteady quasi-one-dimensional viscous/inviscid interacting internal flows at subsonic, transonic, and supersonic Mach numbers

NASA Technical Reports Server (NTRS)

Swafford, Timothy W.; Huddleston, David H.; Busby, Judy A.; Chesser, B. Lawrence

1992-01-01

Computations of viscous-inviscid interacting internal flowfields are presented for steady and unsteady quasi-one-dimensional (Q1D) test cases. The unsteady Q1D Euler equations are coupled with integral boundary-layer equations for unsteady, two-dimensional (planar or axisymmetric), turbulent flow over impermeable, adiabatic walls. The coupling methodology differs from that used in most techniques reported previously in that the above mentioned equation sets are written as a complete system and solved simultaneously; that is, the coupling is carried out directly through the equations as opposed to coupling the solutions of the different equation sets. Solutions to the coupled system of equations are obtained using both explicit and implicit numerical schemes for steady subsonic, steady transonic, and both steady and unsteady supersonic internal flowfields. Computed solutions are compared with measurements as well as Navier-Stokes and inverse boundary-layer methods. An analysis of the eigenvalues of the coefficient matrix associated with the quasi-linear form of the coupled system of equations indicates the presence of complex eigenvalues for certain flow conditions. It is concluded that although reasonable solutions can be obtained numerically, these complex eigenvalues contribute to the overall difficulty in obtaining numerical solutions to the coupled system of equations.

Chemical transport in a fissured rock: Verification of a numerical model

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

Rasmuson, A.; Narasimhan, T. N.; Neretnieks, I.

1982-10-01

Numerical models for simulating chemical transport in fissured rocks constitute powerful tools for evaluating the acceptability of geological nuclear waste repositories. Due to the very long-term, high toxicity of some nuclear waste products, the models are required to predict, in certain cases, the spatial and temporal distribution of chemical concentration less than 0.001% of the concentration released from the repository. Whether numerical models can provide such accuracies is a major question addressed in the present work. To this end, we have verified a numerical model, TRUMP, which solves the advective diffusion equation in general three dimensions with or without decaymore » and source terms. The method is based on an integrated finite-difference approach. The model was verified against known analytic solution of the one-dimensional advection-diffusion problem as well as the problem of advection-diffusion in a system of parallel fractures separated by spherical particles. The studies show that as long as the magnitude of advectance is equal to or less than that of conductance for the closed surface bounding any volume element in the region (that is, numerical Peclet number <2), the numerical method can indeed match the analytic solution within errors of ±10{sup -3} % or less. The realistic input parameters used in the sample calculations suggest that such a range of Peclet numbers is indeed likely to characterize deep groundwater systems in granitic and ancient argillaceous systems. Thus TRUMP in its present form does provide a viable tool for use in nuclear waste evaluation studies. A sensitivity analysis based on the analytic solution suggests that the errors in prediction introduced due to uncertainties in input parameters is likely to be larger than the computational inaccuracies introduced by the numerical model. Currently, a disadvantage in the TRUMP model is that the iterative method of solving the set of simultaneous equations is rather slow when time constants vary widely over the flow region. Although the iterative solution may be very desirable for large three-dimensional problems in order to minimize computer storage, it seems desirable to use a direct solver technique in conjunction with the mixed explicit-implicit approach whenever possible. work in this direction is in progress.« less

Stress waves in transversely isotropic media: The homogeneous problem

NASA Technical Reports Server (NTRS)

Marques, E. R. C.; Williams, J. H., Jr.

1986-01-01

The homogeneous problem of stress wave propagation in unbounded transversely isotropic media is analyzed. By adopting plane wave solutions, the conditions for the existence of the solution are established in terms of phase velocities and directions of particle displacements. Dispersion relations and group velocities are derived from the phase velocity expressions. The deviation angles (e.g., angles between the normals to the adopted plane waves and the actual directions of their propagation) are numerically determined for a specific fiber-glass epoxy composite. A graphical method is introduced for the construction of the wave surfaces using magnitudes of phase velocities and deviation angles. The results for the case of isotropic media are shown to be contained in the solutions for the transversely isotropic media.

Mathematical formulation and numerical simulation of bird flu infection process within a poultry farm

NASA Astrophysics Data System (ADS)

Putri, Arrival Rince; Nova, Tertia Delia; Watanabe, M.

2016-02-01

Bird flu infection processes within a poultry farm are formulated mathematically. A spatial effect is taken into account for the virus concentration with a diffusive term. An infection process is represented in terms of a traveling wave solutions. For a small removal rate, a singular perturbation analysis lead to existence of traveling wave solutions, that correspond to progressive infection in one direction.

Robust Multigrid Smoothers for Three Dimensional Elliptic Equations with Strong Anisotropies

NASA Technical Reports Server (NTRS)

Llorente, Ignacio M.; Melson, N. Duane

1998-01-01

We discuss the behavior of several plane relaxation methods as multigrid smoothers for the solution of a discrete anisotropic elliptic model problem on cell-centered grids. The methods compared are plane Jacobi with damping, plane Jacobi with partial damping, plane Gauss-Seidel, plane zebra Gauss-Seidel, and line Gauss-Seidel. Based on numerical experiments and local mode analysis, we compare the smoothing factor of the different methods in the presence of strong anisotropies. A four-color Gauss-Seidel method is found to have the best numerical and architectural properties of the methods considered in the present work. Although alternating direction plane relaxation schemes are simpler and more robust than other approaches, they are not currently used in industrial and production codes because they require the solution of a two-dimensional problem for each plane in each direction. We verify the theoretical predictions of Thole and Trottenberg that an exact solution of each plane is not necessary and that a single two-dimensional multigrid cycle gives the same result as an exact solution, in much less execution time. Parallelization of the two-dimensional multigrid cycles, the kernel of the three-dimensional implicit solver, is also discussed. Alternating-plane smoothers are found to be highly efficient multigrid smoothers for anisotropic elliptic problems.

On traveling waves in beams

NASA Technical Reports Server (NTRS)

Leonard, Robert W; Budiansky, Bernard

1954-01-01

The basic equations of Timoshenko for the motion of vibrating nonuniform beams, which allow for effects of transverse shear deformation and rotary inertia, are presented in several forms, including one in which the equations are written in the directions of the characteristics. The propagation of discontinuities in moment and shear, as governed by these equations, is discussed. Numerical traveling-wave solutions are obtained for some elementary problems of finite uniform beams for which the propagation velocities of bending and shear discontinuities are taken to be equal. These solutions are compared with modal solutions of Timoshenko's equations and, in some cases, with exact closed solutions. (author)

Study of viscous flow about airfoils by the integro-differential method

NASA Technical Reports Server (NTRS)

Wu, J. C.; Sampath, S.

1975-01-01

An integro-differential method was used for numerically solving unsteady incompressible viscous flow problems. A computer program was prepared to solve the problem of an impulsively started 9% thick symmetric Joukowski airfoil at an angle of attack of 15 deg and a Reynolds number of 1000. Some of the results obtained for this problem were discussed and compared with related work completed previously. Two numerical procedures were used, an Alternating Direction Implicit (ADI) method and a Successive Line Relaxation (SLR) method. Generally, the ADI solution agrees well with the SLR solution and with previous results are stations away from the trailing edge. At the trailing edge station, the ADI solution differs substantially from previous results, while the vorticity profiles obtained from the SLR method there are in good qualitative agreement with previous results.

Direct Solution of the Chemical Master Equation Using Quantized Tensor Trains

PubMed Central

Kazeev, Vladimir; Khammash, Mustafa; Nip, Michael; Schwab, Christoph

2014-01-01

The Chemical Master Equation (CME) is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks. Yet direct solutions of the CME have remained elusive. Although several approaches overcome the infinite dimensional nature of the CME through projections or other means, a common feature of proposed approaches is their susceptibility to the curse of dimensionality, i.e. the exponential growth in memory and computational requirements in the number of problem dimensions. We present a novel approach that has the potential to “lift” this curse of dimensionality. The approach is based on the use of the recently proposed Quantized Tensor Train (QTT) formatted numerical linear algebra for the low parametric, numerical representation of tensors. The QTT decomposition admits both, algorithms for basic tensor arithmetics with complexity scaling linearly in the dimension (number of species) and sub-linearly in the mode size (maximum copy number), and a numerical tensor rounding procedure which is stable and quasi-optimal. We show how the CME can be represented in QTT format, then use the exponentially-converging -discontinuous Galerkin discretization in time to reduce the CME evolution problem to a set of QTT-structured linear equations to be solved at each time step using an algorithm based on Density Matrix Renormalization Group (DMRG) methods from quantum chemistry. Our method automatically adapts the “basis” of the solution at every time step guaranteeing that it is large enough to capture the dynamics of interest but no larger than necessary, as this would increase the computational complexity. Our approach is demonstrated by applying it to three different examples from systems biology: independent birth-death process, an example of enzymatic futile cycle, and a stochastic switch model. The numerical results on these examples demonstrate that the proposed QTT method achieves dramatic speedups and several orders of magnitude storage savings over direct approaches. PMID:24626049

Multiple burn fuel-optimal orbit transfers: Numerical trajectory computation and neighboring optimal feedback guidance

NASA Technical Reports Server (NTRS)

Chuang, C.-H.; Goodson, Troy D.; Ledsinger, Laura A.

1995-01-01

This report describes current work in the numerical computation of multiple burn, fuel-optimal orbit transfers and presents an analysis of the second variation for extremal multiple burn orbital transfers as well as a discussion of a guidance scheme which may be implemented for such transfers. The discussion of numerical computation focuses on the use of multivariate interpolation to aid the computation in the numerical optimization. The second variation analysis includes the development of the conditions for the examination of both fixed and free final time transfers. Evaluations for fixed final time are presented for extremal one, two, and three burn solutions of the first variation. The free final time problem is considered for an extremal two burn solution. In addition, corresponding changes of the second variation formulation over thrust arcs and coast arcs are included. The guidance scheme discussed is an implicit scheme which implements a neighboring optimal feedback guidance strategy to calculate both thrust direction and thrust on-off times.

Effects of Space Environment on Flow and Concentration During Directional Solidification

NASA Technical Reports Server (NTRS)

Benjapiyaporn, C.; Timchenko, V.; Leonardi, E.; deVahlDavis, G.; deGroh, H. C., III

2000-01-01

A study of directional solidification of a weak binary alloy (specifically, Bi - 1 at% Sn) based on the fixed grid single domain approach is being undertaken. The enthalpy method is used to solve for the temperature field over the computational domain including both the solid and liquid phases; latent heat evolution is treated with the aid of an effective specific heat coefficient. A source term accounting for the release of solute into the liquid during solidification has been incorporated into the solute transport equation. The vorticity-stream function formulation is used to describe thermosolutal convection in the liquid region. In this paper we numerically investigate the effects of g-jitter on directional solidification. A background gravity of 1 micro-g has been assumed, and new results for the effects of periodic disturbances over a range of amplitudes and frequencies on solute field and segregation have been presented.

A NURBS-enhanced finite volume solver for steady Euler equations

NASA Astrophysics Data System (ADS)

Meng, Xucheng; Hu, Guanghui

2018-04-01

In Hu and Yi (2016) [20], a non-oscillatory k-exact reconstruction method was proposed towards the high-order finite volume methods for steady Euler equations, which successfully demonstrated the high-order behavior in the simulations. However, the degeneracy of the numerical accuracy of the approximate solutions to problems with curved boundary can be observed obviously. In this paper, the issue is resolved by introducing the Non-Uniform Rational B-splines (NURBS) method, i.e., with given discrete description of the computational domain, an approximate NURBS curve is reconstructed to provide quality quadrature information along the curved boundary. The advantages of using NURBS include i). both the numerical accuracy of the approximate solutions and convergence rate of the numerical methods are improved simultaneously, and ii). the NURBS curve generation is independent of other modules of the numerical framework, which makes its application very flexible. It is also shown in the paper that by introducing more elements along the normal direction for the reconstruction patch of the boundary element, significant improvement in the convergence to steady state can be achieved. The numerical examples confirm the above features very well.

Propagation of singularities for linearised hybrid data impedance tomography

NASA Astrophysics Data System (ADS)

Bal, Guillaume; Hoffmann, Kristoffer; Knudsen, Kim

2018-02-01

For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit propagating singularities under certain non-elliptic conditions, and the associated directions of propagation are precisely identified relative to the directions in which ellipticity is lost. The same result is found in the setting for the corresponding normal formulation of the scalar pseudo-differential equations. A numerical reconstruction procedure based of the least squares finite element method is derived, and a series of numerical experiments visualise exactly how the loss of ellipticity manifests itself as propagating singularities.

Simulation of a Single-Element Lean-Direct Injection Combustor Using Arbitrary Polyhedral Mesh

NASA Technical Reports Server (NTRS)

Wey, Thomas; Liu, Nan-Suey

2012-01-01

This paper summarizes procedures of generating the arbitrary polyhedral mesh as well as presents sample results from its application to the numerical solution of a single-element LDI combustor using a preliminary version of the new OpenNCC.

Researched applied to transonic compressors in numerical fluid mechanics of inviscid flow and viscous flow

NASA Technical Reports Server (NTRS)

Thompkins, W. T., Jr.

1985-01-01

A streamline Euler solver which combines high accuracy and good convergence rates with capabilities for inverse or direct mode solution modes and an analysis technique for finite difference models of hyperbolic partial difference equations were developed.

Structure of solar coronal streamers

NASA Astrophysics Data System (ADS)

Schultz, C. G.

The present, direct method for the solution of generalized potential problems works outward from an O-point, under an assumption of the existence of flux surfaces. At each flux surface, a Fourier filter is used for the flux surface length variable to prevent numerical error amplifications, and the value of the inverse curvature radius and the normal direction are filtered to avoid the effects of local wrinkles.

Piezoviscosity In Lubrication Of Nonconformal Contacts

NASA Technical Reports Server (NTRS)

Jeng, Yeau-Ren; Hamrock, Bernard J.; Brewe, David E.

1988-01-01

Developments in theory of lubrication. Analysis of piezoviscous-rigid regime of lubrication of two ellipsoidal contacts. Begins with Reynolds equation for point contact. Equation nondimensionalized using Roelands empirical formula and Dowson and Higginson formula. Equation solved numerically. Solutions obtained for full spectrum of conditions to find effects of dimensionless load, speed, parameters of lubricated and lubricating materials, and angle between direction of rolling and direction of entrainment of lubricant.

Analytical solution for wave propagation through a graded index interface between a right-handed and a left-handed material.

PubMed

Dalarsson, Mariana; Tassin, Philippe

2009-04-13

We have investigated the transmission and reflection properties of structures incorporating left-handed materials with graded index of refraction. We present an exact analytical solution to Helmholtz' equation for a graded index profile changing according to a hyperbolic tangent function along the propagation direction. We derive expressions for the field intensity along the graded index structure, and we show excellent agreement between the analytical solution and the corresponding results obtained by accurate numerical simulations. Our model straightforwardly allows for arbitrary spectral dispersion.

Fiber-reinforced materials: finite elements for the treatment of the inextensibility constraint

NASA Astrophysics Data System (ADS)

Auricchio, Ferdinando; Scalet, Giulia; Wriggers, Peter

2017-12-01

The present paper proposes a numerical framework for the analysis of problems involving fiber-reinforced anisotropic materials. Specifically, isotropic linear elastic solids, reinforced by a single family of inextensible fibers, are considered. The kinematic constraint equation of inextensibility in the fiber direction leads to the presence of an undetermined fiber stress in the constitutive equations. To avoid locking-phenomena in the numerical solution due to the presence of the constraint, mixed finite elements based on the Lagrange multiplier, perturbed Lagrangian, and penalty method are proposed. Several boundary-value problems under plane strain conditions are solved and numerical results are compared to analytical solutions, whenever the derivation is possible. The performed simulations allow to assess the performance of the proposed finite elements and to discuss several features of the developed formulations concerning the effective approximation for the displacement and fiber stress fields, mesh convergence, and sensitivity to penalty parameters.

Numerical simulation of fire vortex

NASA Astrophysics Data System (ADS)

Barannikova, D. D.; Borzykh, V. E.; Obukhov, A. G.

2018-05-01

The article considers the numerical simulation of the swirling flow of air around the smoothly heated vertical cylindrical domain in the conditions of gravity and Coriolis forces action. The solutions of the complete system of Navie-Stocks equations are numerically solved at constant viscosity and heat conductivity factors. Along with the proposed initial and boundary conditions, these solutions describe the complex non-stationary 3D flows of viscous compressible heat conducting gas. For various instants of time of the initial flow formation stage using the explicit finite-difference scheme the calculations of all gas dynamics parameters, that is density, temperature, pressure and three velocity components of gas particles, have been run. The current instant lines corresponding to the trajectories of the particles movement in the emerging flow have been constructed. A negative direction of the air flow swirling occurred in the vertical cylindrical domain heating has been defined.

Performance and cavitation characteristics of bi-directional hydrofoils

NASA Astrophysics Data System (ADS)

Nedyalkov, Ivaylo; Wosnik, Martin

2013-11-01

Tidal turbines extract energy from flows which reverse direction. One way to address this bi-directionality in horizontal axis turbines that avoid the use of complex and maintenance-intensive yaw or blade pitch mechanisms, is to design bi-directional blades which perform (equally) well in either flow direction. A large number of proposed hydrofoil designs were investigated using numerical simulations. Selected candidate foils were also tested (at various speeds and angles of attack) in the High-Speed Cavitation Tunnel (HICaT) at the University of New Hampshire. Lift and drag were measured using a force balance, and cavitation inception and desinence were recorded. Experimental and numerical results were compared, and the foils were compared to each other and to reference foils. Bi-directional hydrofoils may provide a feasible solution to the problem of reversing flow direction, when their performance and cavitation characteristics are comparable to those for unidirectional foils, and the penalty in decreased energy production is outweighed by the cost reduction due to lower complexity and respectively lower installation and maintenance costs.

Transonic small disturbances equation applied to the solution of two-dimensional nonsteady flows

NASA Technical Reports Server (NTRS)

Couston, M.; Angelini, J. J.; Mulak, P.

1980-01-01

Transonic nonsteady flows are of large practical interest. Aeroelastic instability prediction, control figured vehicle techniques or rotary wings in forward flight are some examples justifying the effort undertaken to improve knowledge of these problems is described. The numerical solution of these problems under the potential flow hypothesis is described. The use of an alternating direction implicit scheme allows the efficient resolution of the two dimensional transonic small perturbations equation.

Hypersonic shock structure with Burnett terms in the viscous stress and heat flux

NASA Technical Reports Server (NTRS)

Chapman, Dean R.; Fiscko, Kurt A.

1988-01-01

The continuum Navier-Stokes and Burnett equations are solved for one-dimensional shock structure in various monatomic gases. A new numerical method is employed which utilizes the complete time-dependent continuum equations and obtains the steady-state shock structure by allowing the system to relax from arbitrary initial conditions. Included is discussion of numerical difficulties encountered when solving the Burnett equations. Continuum solutions are compared to those obtained utilizing the Direct Simulation Monte Carlo method. Shock solutions are obtained for a hard sphere gas and for argon from Mach 1.3 to Mach 50. Solutions for a Maxwellian gas are obtained from Mach 1.3 to Mach 3.8. It is shown that the Burnett equations yield shock structure solutions in much closer agreement to both Monte Carlo and experimental results than do the Navier-Stokes equations. Shock density thickness, density asymmetry, and density-temperature separation are all more accurately predicted by the Burnett equations than by the Navier-Stokes equations.

Thermodynamics of Inozemtsev's elliptic spin chain

NASA Astrophysics Data System (ADS)

Klabbers, Rob

2016-06-01

We study the thermodynamic behaviour of Inozemtsev's long-range elliptic spin chain using the Bethe ansatz equations describing the spectrum of the model in the infinite-length limit. We classify all solutions of these equations in that limit and argue which of these solutions determine the spectrum in the thermodynamic limit. Interestingly, some of the solutions are not selfconjugate, which puts the model in sharp contrast to one of the model's limiting cases, the Heisenberg XXX spin chain. Invoking the string hypothesis we derive the thermodynamic Bethe ansatz equations (TBA-equations) from which we determine the Helmholtz free energy in thermodynamic equilibrium and derive the associated Y-system. We corroborate our results by comparing numerical solutions of the TBA-equations to a direct computation of the free energy for the finite-length hamiltonian. In addition we confirm numerically the interesting conjecture put forward by Finkel and González-López that the original and supersymmetric versions of Inozemtsev's elliptic spin chain are equivalent in the thermodynamic limit.

On concentrated solute sources in faulted aquifers

NASA Astrophysics Data System (ADS)

Robinson, N. I.; Werner, A. D.

2017-06-01

Finite aperture faults and fractures within aquifers (collectively called 'faults' hereafter) theoretically enable flowing water to move through them but with refractive displacement, both on entry and exit. When a 2D or 3D point source of solute concentration is located upstream of the fault, the plume emanating from the source relative to one in a fault-free aquifer is affected by the fault, both before it and after it. Previous attempts to analyze this situation using numerical methods faced challenges in overcoming computational constraints that accompany requisite fine mesh resolutions. To address these, an analytical solution of this problem is developed and interrogated using statistical evaluation of solute distributions. The method of solution is based on novel spatial integral representations of the source with axes rotated from the direction of uniform water flow and aligning with fault faces and normals. Numerical exemplification is given to the case of a 2D steady state source, using various parameter combinations. Statistical attributes of solute plumes show the relative impact of parameters, the most important being, fault rotation, aperture and conductivity ratio. New general observations of fault-affected solution plumes are offered, including: (a) the plume's mode (i.e. peak concentration) on the downstream face of the fault is less displaced than the refracted groundwater flowline, but at some distance downstream of the fault, these realign; (b) porosities have no influence in steady state calculations; (c) previous numerical modeling results of barrier faults show significant boundary effects. The current solution adds to available benchmark problems involving fractures, faults and layered aquifers, in which grid resolution effects are often barriers to accurate simulation.

Tetrahedral-Mesh Simulation of Turbulent Flows with the Space-Time Conservative Schemes

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan; Venkatachari, Balaji; Cheng, Gary C.

2015-01-01

Direct numerical simulations of turbulent flows are predominantly carried out using structured, hexahedral meshes despite decades of development in unstructured mesh methods. Tetrahedral meshes offer ease of mesh generation around complex geometries and the potential of an orientation free grid that would provide un-biased small-scale dissipation and more accurate intermediate scale solutions. However, due to the lack of consistent multi-dimensional numerical formulations in conventional schemes for triangular and tetrahedral meshes at the cell interfaces, numerical issues exist when flow discontinuities or stagnation regions are present. The space-time conservative conservation element solution element (CESE) method - due to its Riemann-solver-free shock capturing capabilities, non-dissipative baseline schemes, and flux conservation in time as well as space - has the potential to more accurately simulate turbulent flows using unstructured tetrahedral meshes. To pave the way towards accurate simulation of shock/turbulent boundary-layer interaction, a series of wave and shock interaction benchmark problems that increase in complexity, are computed in this paper with triangular/tetrahedral meshes. Preliminary computations for the normal shock/turbulence interactions are carried out with a relatively coarse mesh, by direct numerical simulations standards, in order to assess other effects such as boundary conditions and the necessity of a buffer domain. The results indicate that qualitative agreement with previous studies can be obtained for flows where, strong shocks co-exist along with unsteady waves that display a broad range of scales, with a relatively compact computational domain and less stringent requirements for grid clustering near the shock. With the space-time conservation properties, stable solutions without any spurious wave reflections can be obtained without a need for buffer domains near the outflow/farfield boundaries. Computational results for the isotropic turbulent flow decay, at a relatively high turbulent Mach number, show a nicely behaved spectral decay rate for medium to high wave numbers. The high-order CESE schemes offer very robust solutions even with the presence of strong shocks or widespread shocklets. The explicit formulation in conjunction with a close to unity theoretical upper Courant number bound has the potential to offer an efficient numerical framework for general compressible turbulent flow simulations with unstructured meshes.

Convection equation modeling: A non-iterative direct matrix solution algorithm for use with SINDA

NASA Technical Reports Server (NTRS)

Schrage, Dean S.

1993-01-01

The determination of the boundary conditions for a component-level analysis, applying discrete finite element and finite difference modeling techniques often requires an analysis of complex coupled phenomenon that cannot be described algebraically. For example, an analysis of the temperature field of a coldplate surface with an integral fluid loop requires a solution to the parabolic heat equation and also requires the boundary conditions that describe the local fluid temperature. However, the local fluid temperature is described by a convection equation that can only be solved with the knowledge of the locally-coupled coldplate temperatures. Generally speaking, it is not computationally efficient, and sometimes, not even possible to perform a direct, coupled phenomenon analysis of the component-level and boundary condition models within a single analysis code. An alternative is to perform a disjoint analysis, but transmit the necessary information between models during the simulation to provide an indirect coupling. For this approach to be effective, the component-level model retains full detail while the boundary condition model is simplified to provide a fast, first-order prediction of the phenomenon in question. Specifically for the present study, the coldplate structure is analyzed with a discrete, numerical model (SINDA) while the fluid loop convection equation is analyzed with a discrete, analytical model (direct matrix solution). This indirect coupling allows a satisfactory prediction of the boundary condition, while not subjugating the overall computational efficiency of the component-level analysis. In the present study a discussion of the complete analysis of the derivation and direct matrix solution algorithm of the convection equation is presented. Discretization is analyzed and discussed to extend of solution accuracy, stability and computation speed. Case studies considering a pulsed and harmonic inlet disturbance to the fluid loop are analyzed to assist in the discussion of numerical dissipation and accuracy. In addition, the issues of code melding or integration with standard class solvers such as SINDA are discussed to advise the user of the potential problems to be encountered.

The Pursuit of K: Reflections on the Current State-of-the-Art in Stress Intensity Factor Solutions for Practical Aerospace Applications

NASA Technical Reports Server (NTRS)

CraigMcClung, R.; Lee, Yi-Der; Cardinal, Joseph W.; Guo, Yajun

2012-01-01

The elastic stress intensity factor (SIF, commonly denoted as K) is the foundation of practical fracture mechanics (FM) analysis for aircraft structures. This single parameter describes the first-order effects of stress magnitude and distribution as well as the geometry of both structure/component and crack. Hence, the calculation of K is often the most significant step in fatigue analysis based on FM. This presentation will provide several reflections on the current state-of-the-art in SIF solution methods used for practical aerospace applications, including a brief historical perspective, descriptions of some recent and ongoing advances, and comments on some remaining challenges. Newman and Raju made significant early contributions to practical structural analysis by developing closed-form SIF equations for surface and corner cracks in simplified geometries, often based on empirical fits of finite element (FE) solutions. Those solutions (and others like them) were sometimes revised as new analyses were conducted or limitations discovered. The foundational solutions have exhibited striking longevity, despite the relatively "coarse" FE models employed many decades ago. However, in recent years, the accumulation of different generations of solutions for the same nominal geometry has led to some confusion (which solution is correct?), and steady increases in computational capabilities have facilitated the discovery of inaccuracies in some (not all!) of the legacy solutions. Some examples of problems and solutions are presented and discussed, including the challenge of maintaining consistency with legacy design applications. As computational power has increased, the prospect of calculating large numbers of SIF solutions for specific complex geometries with advanced numerical methods has grown more attractive. Fawaz and Andersson, for example, have been generating literally millions of new SIF solutions for different combinations of multiple cracks under simplified loading schemes using p-version FE methods. These data are invaluable, but questions remain about their practical use, because the tabular databases of key results needed to support practical life analysis can occupy gigabytes of storage for only a few classes of geometries. The prospect of using such advanced numerical methods to calculate in real time only those K solutions actually needed to support a specific crack growth analysis is also tempting, but the stark reality is that the computational cost is still so high that the approach is not practical except for specific, critical application problems. Some thoughts are offered about alternative paradigms. Compounding approaches are some of the earliest building blocks of SIF development for more complex geometries. These approaches are especially attractive because of their very low computational cost and their conceptual robustness; they are, in some ways, an intriguing contrast and complement to the brute-force numerical methods. In recent years, researchers at NRC-Canada have published remarkable results showing how compounding approaches can be used to generate accurate solutions for very difficult problems. Examples are provided of some successes--and some limitations--using this approach. These closed-form, tabulated numerical, and compounding approaches have typically been used for simple remote loading with simple load paths to the crack. However, many significant cracks occur in complex stress gradient fields. This is a job for weight function (WF) methods, where the arbitrary stress distribution on the crack plane in the corresponding uncracked body (typically determined using FE methods) is used to determine K. Several significant recent advances in WF methods and solutions are highlighted here. Fueled by advanced 3D numerical methods, many new solutions have been generated for classic geometries such as surface and corner cracks with wide ranges of geometrical validity. A new WF formulation has also be developed for part-through cracks considering the arbitrary stress gradients in all directions in the crack plane (so-called bivariant solutions). Basic WF methods have recently been combined with analytical expressions for crack plane stresses to develop a large family of accurate SIF solutions for corner, surface, and through cracks at internal or external notches with very wide ranges of shapes, sizes, acuities, and offsets. Finally, WF solutions are much faster than FE or boundary element solutions, but can still be much slower than simple closed-form solutions, especially for bivariant solutions that can require 2D numerical integration. Novel pre-integration and dynamic tabular methods have been developed that substantially increase the speed of these advanced WF solutions. The practical utility of advanced SIF methods, including both WF and direct numerical methods, is greatly enhanced if the FM life analysis can be directly and efficiently linked with digital models of the actual structure or component (e.g., FE models for stress analysis). Two recent advances of this type will be described. One approach directly interfaces the FM life analysis with the FE model of the uncracked component (including stress results). Through a powerful graphical user interface, simplified FM life models can be constructed (and visualized) directly on the component model, with the computer collecting the geometry and stress gradient information needed for the life calculation. An even more powerful paradigm uses expert logic to automatically build an optimum simple fracture model at any and every desired location in the component model, perform the life calculation, and even generate fatigue crack growth life contour maps, all with minimal user intervention. This paradigm has also been extended to the automatic calculation of fracture risk, considering uncertainty or variability in key input parameters such as initial crack size or location. Another new integrated approach links the engineering life analysis, the component model, and a 3D numerical fracture analysis built with the same component model to generate a table of SIF values at a specific location that can then be employed efficiently to perform the life calculation. Some attention must be given to verification and validation (V&V) issues and challenges: how good are these SIF solutions, how good is good enough, and does anyone believe the life answer? It is important to think critically about the different sources of error or uncertainty and to perform V&V in a hierarchal, building-block manner. Some accuracy issues for SIF solutions, for example, may actually involve independent material behavior issues, such as constraint loss effects for crack fronts near component surfaces, and can be a source of confusion. Recommendations are proposed for improved V&V approaches. This presentation will briefly but critically survey the range of issues and advances mentioned above, with a particular view towards assembling an integrated approach that combines different methods to create practical tools for real-world design and analysis problems. Examples will be selectively drawn from the recent literature, from recent enhancements in the NASGRO and DARWIN computer codes, and from previously unpublished research

Spurious Grain Formation at Cross-Sectional Expansion During Directional Solidification: Influence of Thermosolutal Convection

NASA Astrophysics Data System (ADS)

Ghods, M.; Lauer, M.; Upadhyay, S. R.; Grugel, R. N.; Tewari, S. N.; Poirier, D. R.

2018-04-01

Formation of spurious grains during directional solidification (DS) of Al-7 wt.% Si and Al-19 wt.% Cu alloys through an abrupt increase in cross-sectional area has been examined by experiments and by numerical simulations. Stray grains were observed in the Al-19 wt.% Cu samples and almost none in the Al-7 wt.% Si. The locations of the stray grains correlate well where numerical solutions indicate the solute-rich melt to be flowing up the thermal gradient faster than the isotherm velocity. It is proposed that the spurious grain formation occurred by fragmentation of slender tertiary dendrite arms was enhanced by thermosolutal convection. In Al-7 wt.% Si, the dendrite fragments sink in the surrounding melt and get trapped in the dendritic array growing around them, and therefore they do not grow further. In the Al-19 wt.% Cu alloy, on the other hand, the dendrite fragments float in the surrounding melt and some find conducive thermal conditions for further growth and become stray grains.

Weibel instability for a streaming electron, counterstreaming e-e, and e-p plasmas with intrinsic temperature anisotropy

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

Ghorbanalilu, M.; Physics Department, Azarbaijan Shahid Madani University, Tabriz; Sadegzadeh, S.

2014-05-15

The existence of Weibel instability for a streaming electron, counterstreaming electron-electron (e-e), and electron-positron (e-p) plasmas with intrinsic temperature anisotropy is investigated. The temperature anisotropy is included in the directions perpendicular and parallel to the streaming direction. It is shown that the beam mean speed changes the instability mode, for a streaming electron beam, from the classic Weibel to the Weibel-like mode. The analytical and numerical solutions approved that Weibel-like modes are excited for both counterstreaming e-e and e-p plasmas. The growth rates of the instabilities in e-e and e-p plasmas are compared. The growth rate is larger for e-pmore » plasmas if the thermal anisotropy is small and the opposite is true for large thermal anisotropies. The analytical and numerical solutions are in good agreement only in the small parallel temperature and wave number limits, when the instability growth rate increases linearly with normalized wave number kc∕ω{sub p}.« less

Effects of solar radiation pressure torque on the rotational motion of an artificial satellite

NASA Technical Reports Server (NTRS)

Zanardi, Maria Cecilia F. P. S.; Vilhenademoraes, Rodolpho

1992-01-01

The motion of an artificial satellite about its center of mass is studied considering torques due to the gravity gradient and direct solar radiation pressure. A model for direct solar radiation torque is derived for a circular cylindrical satellite. An analytical solution is obtained by the method of variation of the parameters. This solution shows that the angular variables have secular variation but that the modulus of the rotational angular momentum, the projection of rotational angular momentum on the z axis of the moment of inertia and inertial axis z, suffer only periodic variations. Considering a hypothetical artificial satellite, a numerical application is demonstrated.

Persistent superconductor currents in holographic lattices.

PubMed

Iizuka, Norihiro; Ishibashi, Akihiro; Maeda, Kengo

2014-07-04

We consider a persistent superconductor current along the direction with no translational symmetry in a holographic gravity model. Incorporating a lattice structure into the model, we numerically construct novel solutions of hairy charged stationary black branes with momentum or rotation along the latticed direction. The lattice structure prevents the horizon from rotating, and the total momentum is only carried by matter fields outside the black brane horizon. This is consistent with the black hole rigidity theorem, and it suggests that in dual field theory with lattices, superconductor currents are made up of "composite" fields, rather than "fractionalized" degrees of freedom. We also show that our solutions are consistent with the superfluid hydrodynamics.

A Computing Method for Sound Propagation Through a Nonuniform Jet Stream

NASA Technical Reports Server (NTRS)

Padula, S. L.; Liu, C. H.

1974-01-01

Understanding the principles of jet noise propagation is an essential ingredient of systematic noise reduction research. High speed computer methods offer a unique potential for dealing with complex real life physical systems whereas analytical solutions are restricted to sophisticated idealized models. The classical formulation of sound propagation through a jet flow was found to be inadequate for computer solutions and a more suitable approach was needed. Previous investigations selected the phase and amplitude of the acoustic pressure as dependent variables requiring the solution of a system of nonlinear algebraic equations. The nonlinearities complicated both the analysis and the computation. A reformulation of the convective wave equation in terms of a new set of dependent variables is developed with a special emphasis on its suitability for numerical solutions on fast computers. The technique is very attractive because the resulting equations are linear in nonwaving variables. The computer solution to such a linear system of algebraic equations may be obtained by well-defined and direct means which are conservative of computer time and storage space. Typical examples are illustrated and computational results are compared with available numerical and experimental data.

Towards wall functions for the prediction of solute segregation in plane front directional solidification

NASA Astrophysics Data System (ADS)

Chatelain, M.; Rhouzlane, S.; Botton, V.; Albaric, M.; Henry, D.; Millet, S.; Pelletier, D.; Garandet, J. P.

2017-10-01

The present paper focuses on solute segregation occurring in directional solidification processes with sharp solid/liquid interface, like silicon crystal growth. A major difficulty for the simulation of such processes is their inherently multi-scale nature: the impurity segregation problem is controlled at the solute boundary layer scale (micrometers) while the thermal problem is ruled at the crucible scale (meters). The thickness of the solute boundary layer is controlled by the convection regime and requires a specific refinement of the mesh of numerical models. In order to improve numerical simulations, wall functions describing solute boundary layers for convecto-diffusive regimes are derived from a scaling analysis. The aim of these wall functions is to obtain segregation profiles from purely thermo-hydrodynamic simulations, which do not require solute boundary layer refinement at the solid/liquid interface. Regarding industrial applications, various stirring techniques can be used to enhance segregation, leading to fully turbulent flows in the melt. In this context, the scaling analysis is further improved by taking into account the turbulent solute transport. The solute boundary layers predicted by the analytical model are compared to those obtained by transient segregation simulations in a canonical 2D lid driven cavity configuration for validation purposes. Convective regimes ranging from laminar to fully turbulent are considered. Growth rate and molecular diffusivity influences are also investigated. Then, a procedure to predict concentration fields in the solid phase from a hydrodynamic simulation of the solidification process is proposed. This procedure is based on the analytical wall functions and on solute mass conservation. It only uses wall shear-stress profiles at the solidification front as input data. The 2D analytical concentration fields are directly compared to the results of the complete simulation of segregation in the lid driven cavity configuration. Finally, an additional output from the analytical model is also presented. We put in light the correlation between different species convecto-diffusive behaviour; we use it to propose an estimation method for the segregation parameters of various chemical species knowing segregation parameters of one specific species.

Numerical modeling of runback water on ice protected aircraft surfaces

NASA Technical Reports Server (NTRS)

Al-Khalil, Kamel M.; Keith, Theo G., Jr.; Dewitt, Kenneth J.

1992-01-01

A numerical simulation for 'running wet' aircraft anti-icing systems is developed. The model includes breakup of the water film, which exists in regions of direct impingement, into individual rivulets. The wetness factor distribution resulting from the film breakup and the rivulet configuration on the surface are predicted in the numerical solution procedure. The solid wall is modeled as a multilayer structure and the anti-icing system used is of the thermal type utilizing hot air and/or electrical heating elements embedded with the layers. Details of the calculation procedure and the methods used are presented.

Classical problems in computational aero-acoustics

NASA Technical Reports Server (NTRS)

Hardin, Jay C.

1996-01-01

In relation to the expected problems in the development of computational aeroacoustics (CAA), the preliminary applications were to classical problems where the known analytical solutions could be used to validate the numerical results. Such comparisons were used to overcome the numerical problems inherent in these calculations. Comparisons were made between the various numerical approaches to the problems such as direct simulations, acoustic analogies and acoustic/viscous splitting techniques. The aim was to demonstrate the applicability of CAA as a tool in the same class as computational fluid dynamics. The scattering problems that occur are considered and simple sources are discussed.

Turbulent solutions of equations of fluid motion

NASA Technical Reports Server (NTRS)

Deissler, R. G.

1985-01-01

Some turbulent solutions of the unaveraged Navier-Stokes equations (equations of fluid motion) are reviewed. Those equations are solved numerically in order to study the nonlinear physics of incompressible turbulent flow. The three components of the mean-square velocity fluctuations are initially equal for the conditions chosen. The resulting solutions show characteristics of turbulence, such as the linear and nonlinear excitation of small-scale fluctuations. For the stronger fluctuations the initially nonrandom flow develops into an apparently random turbulence. The cases considered include turbulence that is statistically homogeneous or inhomogeneous and isotropic or anisotropic. A statistically steady-state turbulence is obtained by using a spatially periodic body force. Various turbulence processes, including the transfer of energy between eddy sizes and between directional components and the production, dissipation, and spatial diffusion of turbulence, are considered. It is concluded that the physical processes occurring in turbulence can be profitably studied numerically.

Asymptotic solution of the turbulent mixing layer for velocity ratio close to unity

NASA Technical Reports Server (NTRS)

Higuera, F. J.; Jimenez, J.; Linan, A.

1996-01-01

The equations describing the first two terms of an asymptotic expansion of the solution of the planar turbulent mixing layer for values of the velocity ratio close to one are obtained. The first term of this expansion is the solution of the well-known time-evolving problem and the second, which includes the effects of the increase of the turbulence scales in the stream-wise direction, obeys a linear system of equations. Numerical solutions of these equations for a two-dimensional reacting mixing layer show that the correction to the time-evolving solution may explain the asymmetry of the entrainment and the differences in product generation observed in flip experiments.

Engine dynamic analysis with general nonlinear finite element codes. II - Bearing element implementation, overall numerical characteristics and benchmarking

NASA Technical Reports Server (NTRS)

Padovan, J.; Adams, M.; Lam, P.; Fertis, D.; Zeid, I.

1982-01-01

Second-year efforts within a three-year study to develop and extend finite element (FE) methodology to efficiently handle the transient/steady state response of rotor-bearing-stator structure associated with gas turbine engines are outlined. The two main areas aim at (1) implanting the squeeze film damper element into a general purpose FE code for testing and evaluation; and (2) determining the numerical characteristics of the FE-generated rotor-bearing-stator simulation scheme. The governing FE field equations are set out and the solution methodology is presented. The choice of ADINA as the general-purpose FE code is explained, and the numerical operational characteristics of the direct integration approach of FE-generated rotor-bearing-stator simulations is determined, including benchmarking, comparison of explicit vs. implicit methodologies of direct integration, and demonstration problems.

Numerical Technology for Large-Scale Computational Electromagnetics

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

Sharpe, R; Champagne, N; White, D

The key bottleneck of implicit computational electromagnetics tools for large complex geometries is the solution of the resulting linear system of equations. The goal of this effort was to research and develop critical numerical technology that alleviates this bottleneck for large-scale computational electromagnetics (CEM). The mathematical operators and numerical formulations used in this arena of CEM yield linear equations that are complex valued, unstructured, and indefinite. Also, simultaneously applying multiple mathematical modeling formulations to different portions of a complex problem (hybrid formulations) results in a mixed structure linear system, further increasing the computational difficulty. Typically, these hybrid linear systems aremore » solved using a direct solution method, which was acceptable for Cray-class machines but does not scale adequately for ASCI-class machines. Additionally, LLNL's previously existing linear solvers were not well suited for the linear systems that are created by hybrid implicit CEM codes. Hence, a new approach was required to make effective use of ASCI-class computing platforms and to enable the next generation design capabilities. Multiple approaches were investigated, including the latest sparse-direct methods developed by our ASCI collaborators. In addition, approaches that combine domain decomposition (or matrix partitioning) with general-purpose iterative methods and special purpose pre-conditioners were investigated. Special-purpose pre-conditioners that take advantage of the structure of the matrix were adapted and developed based on intimate knowledge of the matrix properties. Finally, new operator formulations were developed that radically improve the conditioning of the resulting linear systems thus greatly reducing solution time. The goal was to enable the solution of CEM problems that are 10 to 100 times larger than our previous capability.« less

Direct Retrieval of Exterior Orientation Parameters Using A 2-D Projective Transformation

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

Seedahmed, Gamal H.

2006-09-01

Direct solutions are very attractive because they obviate the need for initial approximations associated with non-linear solutions. The Direct Linear Transformation (DLT) establishes itself as a method of choice for direct solutions in photogrammetry and other fields. The use of the DLT with coplanar object space points leads to a rank deficient model. This rank deficient model leaves the DLT defined up to a 2-D projective transformation, which makes the direct retrieval of the exterior orientation parameters (EOPs) a non-trivial task. This paper presents a novel direct algorithm to retrieve the EOPs from the 2-D projective transformation. It is basedmore » on a direct relationship between the 2-D projective transformation and the collinearity model using homogeneous coordinates representation. This representation offers a direct matrix correspondence between the 2-D projective transformation parameters and the collinearity model parameters. This correspondence lends itself to a direct matrix factorization to retrieve the EOPs. An important step in the proposed algorithm is a normalization process that provides the actual link between the 2-D projective transformation and the collinearity model. This paper explains the theoretical basis of the proposed algorithm as well as the necessary steps for its practical implementation. In addition, numerical examples are provided to demonstrate its validity.« less

Couette flow through a porous medium with heat and mass transfer in the presence of tranverse magnetic field

NASA Astrophysics Data System (ADS)

Lawanya, T.; Vidhya, M.; Govindarajan, A.

2018-04-01

This present paper deals with the investigation of couette flow of a viscous electrically conducting incompressible fluid three dimensionally through a porous medium in presence of transverse magnetic field. Approximate Solution of equations of motion and energy equations are derived using series solution method. Hartmann number, Schmidt number and Grashoff number (or) modified Grashoff number for mass transfer on the velocity and temperature distribution are numerically discussed and shown graphically. The Nusselt number and skin friction coefficients atthe plate are derived and their numerical values are shown graphically. It is seen that in the main flow direction the velocity profiles decreases due to either an increase in Schmidt number (Or) Hartmann number.

Application of CFD to aerothermal heating problems

NASA Technical Reports Server (NTRS)

Macaraeg, M. G.

1986-01-01

Numerical solutions of the compressible Navier-Stokes equations by an alternating direction implicit scheme, applied to two experimental investigations are presented. The first is cooling by injection of a gas jet through the nose of an ogive-cone, and the second is the aerothermal environment in the gap formed by the wing and elevon section of a test model of the space shuttle. The simulations demonstrate that accurate pressure calculations are easily obtained on a coarse grid, while convergence is obtained after the residual reduces by four orders of magnitude. Accurate heating rates, however, require a fine grid solution, with convergence requiring at least a reduction of six orders of magnitude in the residual. The effect of artificial dissipation on numerical results is also assessed.

Iterative discrete ordinates solution of the equation for surface-reflected radiance

NASA Astrophysics Data System (ADS)

Radkevich, Alexander

2017-11-01

This paper presents a new method of numerical solution of the integral equation for the radiance reflected from an anisotropic surface. The equation relates the radiance at the surface level with BRDF and solutions of the standard radiative transfer problems for a slab with no reflection on its surfaces. It is also shown that the kernel of the equation satisfies the condition of the existence of a unique solution and the convergence of the successive approximations to that solution. The developed method features two basic steps: discretization on a 2D quadrature, and solving the resulting system of algebraic equations with successive over-relaxation method based on the Gauss-Seidel iterative process. Presented numerical examples show good coincidence between the surface-reflected radiance obtained with DISORT and the proposed method. Analysis of contributions of the direct and diffuse (but not yet reflected) parts of the downward radiance to the total solution is performed. Together, they represent a very good initial guess for the iterative process. This fact ensures fast convergence. The numerical evidence is given that the fastest convergence occurs with the relaxation parameter of 1 (no relaxation). An integral equation for BRDF is derived as inversion of the original equation. The potential of this new equation for BRDF retrievals is analyzed. The approach is found not viable as the BRDF equation appears to be an ill-posed problem, and it requires knowledge the surface-reflected radiance on the entire domain of both Sun and viewing zenith angles.

Convection and macrosegregation in Al-19Cu alloy directionally solidified through an abrupt contraction in cross-section: A comparison with Al-7Si

NASA Astrophysics Data System (ADS)

Ghods, M.; Lauer, M.; Grugel, R. N.; Tewari, S. N.; Poirier, D. R.

2017-02-01

Hypoeutectic Al-19 wt. % Cu alloys were directionally solidified in cylindrical molds that featured an abrupt cross-section decrease 9.5 to 3.2 mm in diameter). Thermo-solutal convection and cross-section-change-induced shrinkage flow effects on macrosegregation were investigated. Dendrite clustering and extensive radial macrosegregation was seen, particularly in the larger cross-section before contraction. This alloy shows positive longitudinal macrosegregation near the contraction followed by negative macrosegregation right after it; the extent of macrosegregation, however, decreases with increasing growth speed. The degree of thermo-solutal convection was compared to another study investigating directional solidification of Al-7 wt. % Si [1] in order to study the effect of solutal expansion coefficient on macrosegregation. An interesting change of the radial macrosegregation profile, attributable to the area-change-induced-shrinkage flow, was observed very close to the contraction. A two-dimensional model accounting for both shrinkage and thermo-solutal convection was used to simulate solidification, the resulting steepling as well as axial and radial macrosegregation. The experimentally observed macrosegregation associated with the contraction during directional solidification was well predicted by the numerical simulations.

Multi-hump bright solitons in a Schrödinger-mKdV system

NASA Astrophysics Data System (ADS)

Cisneros-Ake, Luis A.; Parra Prado, Hugo; López Villatoro, Diego Joselito; Carretero-González, R.

2018-03-01

We consider the problem of energy transport in a Davydov model along an anharmonic crystal medium obeying quartic longitudinal interactions corresponding to rigid interacting particles. The Zabusky and Kruskal unidirectional continuum limit of the original discrete equations reduces, in the long wave approximation, to a coupled system between the linear Schrödinger (LS) equation and the modified Korteweg-de Vries (mKdV) equation. Single- and two-hump bright soliton solutions for this LS-mKdV system are predicted to exist by variational means and numerically confirmed. The one-hump bright solitons are found to be the anharmonic supersonic analogue of the Davydov's solitons while the two-hump (in both components) bright solitons are found to be a novel type of soliton consisting of a two-soliton solution of mKdV trapped by the wave function associated to the LS equation. This two-hump soliton solution, as a two component solution, represents a new class of polaron solution to be contrasted with the two-soliton interaction phenomena from soliton theory, as revealed by a variational approach and direct numerical results for the two-soliton solution.

Revealing Numerical Solutions of a Differential Equation

ERIC Educational Resources Information Center

Glaister, P.

2006-01-01

In this article, the author considers a student exercise that involves determining the exact and numerical solutions of a particular differential equation. He shows how a typical student solution is at variance with a numerical solution, suggesting that the numerical solution is incorrect. However, further investigation shows that this numerical…

Iterative methods for 3D implicit finite-difference migration using the complex Padé approximation

NASA Astrophysics Data System (ADS)

Costa, Carlos A. N.; Campos, Itamara S.; Costa, Jessé C.; Neto, Francisco A.; Schleicher, Jörg; Novais, Amélia

2013-08-01

Conventional implementations of 3D finite-difference (FD) migration use splitting techniques to accelerate performance and save computational cost. However, such techniques are plagued with numerical anisotropy that jeopardises the correct positioning of dipping reflectors in the directions not used for the operator splitting. We implement 3D downward continuation FD migration without splitting using a complex Padé approximation. In this way, the numerical anisotropy is eliminated at the expense of a computationally more intensive solution of a large-band linear system. We compare the performance of the iterative stabilized biconjugate gradient (BICGSTAB) and that of the multifrontal massively parallel direct solver (MUMPS). It turns out that the use of the complex Padé approximation not only stabilizes the solution, but also acts as an effective preconditioner for the BICGSTAB algorithm, reducing the number of iterations as compared to the implementation using the real Padé expansion. As a consequence, the iterative BICGSTAB method is more efficient than the direct MUMPS method when solving a single term in the Padé expansion. The results of both algorithms, here evaluated by computing the migration impulse response in the SEG/EAGE salt model, are of comparable quality.

Nonlocal electron transport: direct and Greens function solution and comparison of our model with the SNB model

NASA Astrophysics Data System (ADS)

Colombant, Denis; Manheimer, Wallace; Schmitt, Andrew J.

2013-10-01

At least two models, ours and SNB (Schurtz-Nicolai-Busquet), and two methods of solution, direct numerical solution (DS) and Greens function (GF) are being used in multi-dimensional radiation hydrodynamics codes. We present results of a laser target implosion using both methods of solution. Although our model and SNB differ in some physical content, direct comparisons have been non-existent up to now. However a paper by Marocchino et al. has recently presented the results of two nanosecond-time-scale test problems, showing that the preheat calculated by the two models are different by about three orders of magnitude. We have rerun these problems and we find much less difference between the two than they do. One can show analytically that the results should be quite similar and are about an order of magnitude less than the maximum, and two orders of magnitude more than the minimum preheating in. We have been able to trace the somewhat different results back to the different physical assumptions made in each model. Work supported by DoE-NNSA and ONR.

Surface electrical properties experiment. Part 2: Theory of radio-frequency interferometry in geophysical subsurface probing

NASA Technical Reports Server (NTRS)

Kong, J. A.; Tsang, L.

1974-01-01

The radiation fields due to a horizontal electric dipole laid on the surface of a stratified medium were calculated using a geometrical optics approximation, a modal approach, and direct numerical integration. The solutions were obtained from the reflection coefficient formulation and written in integral forms. The calculated interference patterns are compared in terms of the usefulness of the methods used to obtain them. Scattering effects are also discussed and all numerical results for anisotropic and isotropic cases are presented.

Numerical Modeling of Solidification in Space With MEPHISTO-4. Part 2

NASA Technical Reports Server (NTRS)

Simpson, James E.; Yoa, Minwu; deGroh, Henry C., III; Garimella, V. Suresh

1998-01-01

A pre-flight analysis of the directional solidification of BiSn with MEPHISTO-4 is presented. Simplified Bridgman growth under microgravity conditions is simulated using a two dimensional finite element model. This numerical model is a single domain, pseudo-steady state model, and includes the effects of both thermal and solutal convection. The results show that for all orientations of the applied steady state gravity vector, of magnitude 1 micro-g, the directional solidification process remains diffusion controlled. The maximum convective velocity was found to be 4.424 x 10(exp -5) cm/s for the horizontal Bridgman growth configuration. This value is an order of magnitude lower than the growth velocity. The maximum and minimum values or solute concentration in the liquid at the crystal-melt interface were 13.867 at.% and 13.722 at.%, respectively. This gives a radial segregation value of xi = 1.046% at the interface. A secondary objective of this work was to compare the results obtained to those that consider thermal convection only (no solutal convection). It was found that the convective flow patterns in simulations which included solutal convection were significantly different from those which ignored solutal convection. The level of radial segregation predicted by the current simulations is an order of magnitude lower than that found in simulations which ignore solutal convection. The final aim was to investigate the effect of g-jitter on the crystal growth process. A simulation was performed to calculate the system response to a 1 second, 100 micro-g gravity impulse acting normal to the direction of growth. This pulse is consistent with that induced by Orbiter thruster firings. The results obtained indicate that such a gravity pulse causes an increase in the level of radial solute segregation at the interface from the steady state values. The maximum value of solute concentration in the liquid was found to be 13.888 at.%, the minimum value calculated was 13.706 at.%, yielding a radial segregation value of xi = 1.31% at the interface. These values occurred 126 seconds after the pulse terminated. Thus it is anticipated that the process will remain diffusion controlled even when subjected to such g-jitter.

Thermosolutal convection during directional solidification. II - Flow transitions

NASA Technical Reports Server (NTRS)

Mcfadden, G. B.; Coriell, S. R.

1987-01-01

The influence of thermosolutal convection on solute segregation in crystals grown by vertical directional solidification of binary metallic alloys or semiconductors is studied. Finite differences are used in a two-dimensional time-dependent model which assumes a planar crystal-melt interface to obtain numerical results. It is assumed that the configuration is periodic in the horizontal direction. Consideration is given to the possibility of multiple flow states sharing the same period. The results are represented in bifurcation diagrams of the nonlinear states associated with the critical points of linear theory. Variations of the solutal Rayleigh number can lead to the occurrence of multiple steady states, time-periodic states, and quasi-periodic states. This case is compared to that of thermosolutal convection with linear vertical gradients and stress-free boundaries.

A general algorithm using finite element method for aerodynamic configurations at low speeds

NASA Technical Reports Server (NTRS)

Balasubramanian, R.

1975-01-01

A finite element algorithm for numerical simulation of two-dimensional, incompressible, viscous flows was developed. The Navier-Stokes equations are suitably modelled to facilitate direct solution for the essential flow parameters. A leap-frog time differencing and Galerkin minimization of these model equations yields the finite element algorithm. The finite elements are triangular with bicubic shape functions approximating the solution space. The finite element matrices are unsymmetrically banded to facilitate savings in storage. An unsymmetric L-U decomposition is performed on the finite element matrices to obtain the solution for the boundary value problem.

Orientation of doubly rotated quartz plates.

PubMed

Sherman, J R

1989-01-01

A derivation from classical spherical trigonometry of equations to compute the orientation of doubly-rotated quartz blanks from Bragg X-ray data is discussed. These are usually derived by compact and efficient vector methods, which are reviewed briefly. They are solved by generating a quadratic equation with numerical coefficients. Two methods exist for performing the computation from measurements against two planes: a direct solution by a quadratic equation and a process of convergent iteration. Both have a spurious solution. Measurement against three lattice planes yields a set of three linear equations the solution of which is an unambiguous result.

Analytical Solutions for the Surface States of Bi1-xSbx (0 ≤ x ≲ 0.1)

NASA Astrophysics Data System (ADS)

Fuseya, Yuki; Fukuyama, Hidetoshi

2018-04-01

Analytical solutions for the surface state (SS) of an extended Wolff Hamiltonian, which is a common Hamiltonian for strongly spin-orbit coupled systems, are obtained both for semi-infinite and finite-thickness boundary conditions. For the semi-infinite system, there are two types of SS solutions: (I-a) linearly crossing SSs in the direct bulk band gap, and (I-b) SSs with linear dispersions entering the bulk conduction or valence bands away from the band edge. For the finite-thickness system, a gap opens in the SS of solution I-a. Numerical solutions for the SS are also obtained based on the tight-binding model of Liu and Allen [Phys. Rev. B 52, 1566 (1995)] for Bi1-xSbx (0 ≤ x ≤ 0.1). A perfect correspondence between the analytic and numerical solutions is obtained around the \\bar{M} point including their thickness dependence. This is the first time that the character of the SS numerically obtained is identified with the help of analytical solutions. The size of the gap for I-a SS can be larger than that of bulk band gap even for a "thick" films ( ≲ 200 bilayers ≃ 80 nm) of pure bismuth. Consequently, in such a film of Bi1-xSbx, there is no apparent change in the SSs through the band inversion at x ≃ 0.04, even though the nature of the SS is changed from solution I-a to I-b. Based on our theoretical results, the experimental results on the SS of Bi1-xSbx (0 ≤ x ≲ 0.1) are discussed.

Numerical Asymptotic Solutions Of Differential Equations

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.

1992-01-01

Numerical algorithms derived and compared with classical analytical methods. In method, expansions replaced with integrals evaluated numerically. Resulting numerical solutions retain linear independence, main advantage of asymptotic solutions.

Solution of the lossy nonlinear Tricomi equation with application to sonic boom focusing

NASA Astrophysics Data System (ADS)

Salamone, Joseph A., III

Sonic boom focusing theory has been augmented with new terms that account for mean flow effects in the direction of propagation and also for atmospheric absorption/dispersion due to molecular relaxation due to oxygen and nitrogen. The newly derived model equation was numerically implemented using a computer code. The computer code was numerically validated using a spectral solution for nonlinear propagation of a sinusoid through a lossy homogeneous medium. An additional numerical check was performed to verify the linear diffraction component of the code calculations. The computer code was experimentally validated using measured sonic boom focusing data from the NASA sponsored Superboom Caustic and Analysis Measurement Program (SCAMP) flight test. The computer code was in good agreement with both the numerical and experimental validation. The newly developed code was applied to examine the focusing of a NASA low-boom demonstration vehicle concept. The resulting pressure field was calculated for several supersonic climb profiles. The shaping efforts designed into the signatures were still somewhat evident despite the effects of sonic boom focusing.

Symplectic partitioned Runge-Kutta scheme for Maxwell's equations

NASA Astrophysics Data System (ADS)

Huang, Zhi-Xiang; Wu, Xian-Liang

Using the symplectic partitioned Runge-Kutta (PRK) method, we construct a new scheme for approximating the solution to infinite dimensional nonseparable Hamiltonian systems of Maxwell's equations for the first time. The scheme is obtained by discretizing the Maxwell's equations in the time direction based on symplectic PRK method, and then evaluating the equation in the spatial direction with a suitable finite difference approximation. Several numerical examples are presented to verify the efficiency of the scheme.

Direct discontinuous Galerkin method and its variations for second order elliptic equations

DOE PAGES

Huang, Hongying; Chen, Zheng; Li, Jin; ...

2016-08-23

In this study, we study direct discontinuous Galerkin method (Liu and Yan in SIAM J Numer Anal 47(1):475–698, 2009) and its variations (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010; Vidden and Yan in J Comput Math 31(6):638–662, 2013; Yan in J Sci Comput 54(2–3):663–683, 2013) for 2nd order elliptic problems. A priori error estimate under energy norm is established for all four methods. Optimal error estimate under L 2 norm is obtained for DDG method with interface correction (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010) and symmetric DDG method (Vidden and Yan in J Comput Mathmore » 31(6):638–662, 2013). A series of numerical examples are carried out to illustrate the accuracy and capability of the schemes. Numerically we obtain optimal (k+1)th order convergence for DDG method with interface correction and symmetric DDG method on nonuniform and unstructured triangular meshes. An interface problem with discontinuous diffusion coefficients is investigated and optimal (k+1)th order accuracy is obtained. Peak solutions with sharp transitions are captured well. Highly oscillatory wave solutions of Helmholz equation are well resolved.« less

Direct discontinuous Galerkin method and its variations for second order elliptic equations

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

Huang, Hongying; Chen, Zheng; Li, Jin

In this study, we study direct discontinuous Galerkin method (Liu and Yan in SIAM J Numer Anal 47(1):475–698, 2009) and its variations (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010; Vidden and Yan in J Comput Math 31(6):638–662, 2013; Yan in J Sci Comput 54(2–3):663–683, 2013) for 2nd order elliptic problems. A priori error estimate under energy norm is established for all four methods. Optimal error estimate under L 2 norm is obtained for DDG method with interface correction (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010) and symmetric DDG method (Vidden and Yan in J Comput Mathmore » 31(6):638–662, 2013). A series of numerical examples are carried out to illustrate the accuracy and capability of the schemes. Numerically we obtain optimal (k+1)th order convergence for DDG method with interface correction and symmetric DDG method on nonuniform and unstructured triangular meshes. An interface problem with discontinuous diffusion coefficients is investigated and optimal (k+1)th order accuracy is obtained. Peak solutions with sharp transitions are captured well. Highly oscillatory wave solutions of Helmholz equation are well resolved.« less

Numerical computation of gravitational field for general axisymmetric objects

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

2016-10-01

We developed a numerical method to compute the gravitational field of a general axisymmetric object. The method (I) numerically evaluates a double integral of the ring potential by the split quadrature method using the double exponential rules, and (II) derives the acceleration vector by numerically differentiating the numerically integrated potential by Ridder's algorithm. Numerical comparison with the analytical solutions for a finite uniform spheroid and an infinitely extended object of the Miyamoto-Nagai density distribution confirmed the 13- and 11-digit accuracy of the potential and the acceleration vector computed by the method, respectively. By using the method, we present the gravitational potential contour map and/or the rotation curve of various axisymmetric objects: (I) finite uniform objects covering rhombic spindles and circular toroids, (II) infinitely extended spheroids including Sérsic and Navarro-Frenk-White spheroids, and (III) other axisymmetric objects such as an X/peanut-shaped object like NGC 128, a power-law disc with a central hole like the protoplanetary disc of TW Hya, and a tear-drop-shaped toroid like an axisymmetric equilibrium solution of plasma charge distribution in an International Thermonuclear Experimental Reactor-like tokamak. The method is directly applicable to the electrostatic field and will be easily extended for the magnetostatic field. The FORTRAN 90 programs of the new method and some test results are electronically available.

Exact self-similarity solution of the Navier-Stokes equations for a porous channel with orthogonally moving walls

NASA Astrophysics Data System (ADS)

Dauenhauer, Eric C.; Majdalani, Joseph

2003-06-01

This article describes a self-similarity solution of the Navier-Stokes equations for a laminar, incompressible, and time-dependent flow that develops within a channel possessing permeable, moving walls. The case considered here pertains to a channel that exhibits either injection or suction across two opposing porous walls while undergoing uniform expansion or contraction. Instances of direct application include the modeling of pulsating diaphragms, sweat cooling or heating, isotope separation, filtration, paper manufacturing, irrigation, and the grain regression during solid propellant combustion. To start, the stream function and the vorticity equation are used in concert to yield a partial differential equation that lends itself to a similarity transformation. Following this similarity transformation, the original problem is reduced to solving a fourth-order differential equation in one similarity variable η that combines both space and time dimensions. Since two of the four auxiliary conditions are of the boundary value type, a numerical solution becomes dependent upon two initial guesses. In order to achieve convergence, the governing equation is first transformed into a function of three variables: The two guesses and η. At the outset, a suitable numerical algorithm is applied by solving the resulting set of twelve first-order ordinary differential equations with two unspecified start-up conditions. In seeking the two unknown initial guesses, the rapidly converging inverse Jacobian method is applied in an iterative fashion. Numerical results are later used to ascertain a deeper understanding of the flow character. The numerical scheme enables us to extend the solution range to physical settings not considered in previous studies. Moreover, the numerical approach broadens the scope to cover both suction and injection cases occurring with simultaneous wall motion.

Exact solution for an optimal impermeable parachute problem

NASA Astrophysics Data System (ADS)

Lupu, Mircea; Scheiber, Ernest

2002-10-01

In the paper there are solved direct and inverse boundary problems and analytical solutions are obtained for optimization problems in the case of some nonlinear integral operators. It is modeled the plane potential flow of an inviscid, incompressible and nonlimited fluid jet, witch encounters a symmetrical, curvilinear obstacle--the deflector of maximal drag. There are derived integral singular equations, for direct and inverse problems and the movement in the auxiliary canonical half-plane is obtained. Next, the optimization problem is solved in an analytical manner. The design of the optimal airfoil is performed and finally, numerical computations concerning the drag coefficient and other geometrical and aerodynamical parameters are carried out. This model corresponds to the Helmholtz impermeable parachute problem.

Convective and morphological instabilities during crystal growth: Effect of gravity modulation

NASA Technical Reports Server (NTRS)

Coreill, S. R.; Murray, B. T.; Mcfadden, G. B.; Wheeler, A. A.; Saunders, B. V.

1992-01-01

During directional solidification of a binary alloy at constant velocity in the vertical direction, morphological and convective instabilities may occur due to the temperature and solute gradients associated with the solidification process. The effect of time-periodic modulation (vibration) is studied by considering a vertical gravitational acceleration which is sinusoidal in time. The conditions for the onset of solutal convection are calculated numerically, employing two distinct computational procedures based on Floquet theory. In general, a stable state can be destabilized by modulation and an unstable state can be stabilized. In the limit of high frequency modulation, the method of averaging and multiple-scale asymptotic analysis can be used to simplify the calculations.

Direct Numerical Simulation of Passive Scalar Mixing in Shock Turbulence Interaction

NASA Astrophysics Data System (ADS)

Gao, Xiangyu; Bermejo-Moreno, Ivan; Larsson, Johan

2017-11-01

Passive scalar mixing in the canonical shock-turbulence interaction configuration is investigated through shock-capturing Direct Numerical Simulations (DNS). Scalar fields with different Schmidt numbers are transported by an initially isotropic turbulent flow field passing across a nominally planar shock wave. A solution-adaptive hybrid numerical scheme on Cartesian structured grids is used, that combines a fifth-order WENO scheme near shocks and a sixth-order central-difference scheme away from shocks. The simulations target variations in the shock Mach number, M (from 1.5 to 3), turbulent Mach number, Mt (from 0.1 to 0.4, including wrinkled- and broken-shock regimes), and scalar Schmidt numbers, Sc (from 0.5 to 2), while keeping the Taylor microscale Reynolds number constant (Reλ 40). The effects on passive scalar statistics are investigated, including the streamwise evolution of scalar variance budgets, pdfs and spectra, in comparison with their temporal evolution in decaying isotropic turbulence.

Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices

NASA Astrophysics Data System (ADS)

da Luz, H. L. F.; Abdullaev, F. Kh.; Gammal, A.; Salerno, M.; Tomio, Lauro

2010-10-01

The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.

Towards Perfectly Absorbing Boundary Conditions for Euler Equations

NASA Technical Reports Server (NTRS)

Hayder, M. Ehtesham; Hu, Fang Q.; Hussaini, M. Yousuff

1997-01-01

In this paper, we examine the effectiveness of absorbing layers as non-reflecting computational boundaries for the Euler equations. The absorbing-layer equations are simply obtained by splitting the governing equations in the coordinate directions and introducing absorption coefficients in each split equation. This methodology is similar to that used by Berenger for the numerical solutions of Maxwell's equations. Specifically, we apply this methodology to three physical problems shock-vortex interactions, a plane free shear flow and an axisymmetric jet- with emphasis on acoustic wave propagation. Our numerical results indicate that the use of absorbing layers effectively minimizes numerical reflection in all three problems considered.

TEMPEST/N33.5. Computational Fluid Dynamics Package For Incompressible, 3D, Time Dependent Pro

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

Trent, Dr.D.S.; Eyler, Dr.L.L.

TEMPESTN33.5 provides numerical solutions to general incompressible flow problems with coupled heat transfer in fluids and solids. Turbulence is created with a k-e model and gas, liquid or solid constituents may be included with the bulk flow. Problems may be modeled in Cartesian or cylindrical coordinates. Limitations include incompressible flow, Boussinesq approximation, and passive constituents. No direct steady state solution is available; steady state is obtained as the limit of a transient.

Evaluation of solution procedures for material and/or geometrically nonlinear structural analysis by the direct stiffness method.

NASA Technical Reports Server (NTRS)

Stricklin, J. A.; Haisler, W. E.; Von Riesemann, W. A.

1972-01-01

This paper presents an assessment of the solution procedures available for the analysis of inelastic and/or large deflection structural behavior. A literature survey is given which summarized the contribution of other researchers in the analysis of structural problems exhibiting material nonlinearities and combined geometric-material nonlinearities. Attention is focused at evaluating the available computation and solution techniques. Each of the solution techniques is developed from a common equation of equilibrium in terms of pseudo forces. The solution procedures are applied to circular plates and shells of revolution in an attempt to compare and evaluate each with respect to computational accuracy, economy, and efficiency. Based on the numerical studies, observations and comments are made with regard to the accuracy and economy of each solution technique.

On the Eikonal equation in the pedestrian flow problem

NASA Astrophysics Data System (ADS)

Felcman, J.; Kubera, P.

2017-07-01

We consider the Pedestrian Flow Equations (PFEs) as the coupled system formed by the Eikonal equation and the first order hyperbolic system with the source term. The hyperbolic system consists of the continuity equation and momentum equation of fluid dynamics. Specifying the social and pressure forces in the momentum equation we come to the assumption that each pedestrian is trying to move in a desired direction (e.g. to the exit in the panic situation) with a desired velocity, where his velocity and the direction of movement depend on the density of pedestrians in his neighborhood. In [1] we used the model, where the desired direction of movement is given by the solution of the Eikonal equation (more precisely by the gradient of the solution). Here we avoid the solution of the Eikonal equation, which is the novelty of the paper. Based on the fact that the solution of the Eikonal equation has the meaning of the shortest time to reach the exit, we define explicitly such a function in the framework of the Dijkstra's algorithm for the shortest path in the graph. This is done at the discrete level of the solution. As the graph we use the underlying triangulation, where the norm of each edge is density depending and has the dimension of the time. The numerical examples of the solution of the PFEs with and without the solution of the Eikonal equation are presented.

Analytic solution of the Spencer-Lewis angular-spatial moments equations

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

Filippone, W.L.

A closed-form solution for the angular-spatial moments of the Spencer-Lewis equation is presented that is valid for infinite homogeneous media. From the moments, the electron density distribution as a function of position and path length (energy) is reconstructed for several sample problems involving plane isotropic sources of electrons in aluminium. The results are in excellent agreement with those determined numerically using the streaming ray method. The primary use of the closed form solution will most likely be to generate accurate electron transport benchmark solutions. In principle, the electron density as a function of space, path length, and direction can bemore » determined for planar sources of arbitrary angular distribution.« less

A Numerical Comparison of Barrier and Modified Barrier Methods for Large-Scale Bound-Constrained Optimization

NASA Technical Reports Server (NTRS)

Nash, Stephen G.; Polyak, R.; Sofer, Ariela

1994-01-01

When a classical barrier method is applied to the solution of a nonlinear programming problem with inequality constraints, the Hessian matrix of the barrier function becomes increasingly ill-conditioned as the solution is approached. As a result, it may be desirable to consider alternative numerical algorithms. We compare the performance of two methods motivated by barrier functions. The first is a stabilized form of the classical barrier method, where a numerically stable approximation to the Newton direction is used when the barrier parameter is small. The second is a modified barrier method where a barrier function is applied to a shifted form of the problem, and the resulting barrier terms are scaled by estimates of the optimal Lagrange multipliers. The condition number of the Hessian matrix of the resulting modified barrier function remains bounded as the solution to the constrained optimization problem is approached. Both of these techniques can be used in the context of a truncated-Newton method, and hence can be applied to large problems, as well as on parallel computers. In this paper, both techniques are applied to problems with bound constraints and we compare their practical behavior.

Food applications of natural antimicrobial compounds.

PubMed

Lucera, Annalisa; Costa, Cristina; Conte, Amalia; Del Nobile, Matteo A

2012-01-01

In agreement with the current trend of giving value to natural and renewable resources, the use of natural antimicrobial compounds, particularly in food and biomedical applications, becomes very frequent. The direct addition of natural compounds to food is the most common method of application, even if numerous efforts have been made to find alternative solutions to the aim of avoiding undesirable inactivation. Dipping, spraying, and coating treatment of food with active solutions are currently applied to product prior to packaging as valid options. The aim of the current work is to give an overview on the use of natural compounds in food sector. In particular, the review will gather numerous case-studies of meat, fish, dairy products, minimally processed fruit and vegetables, and cereal-based products where these compounds found application.

Food applications of natural antimicrobial compounds

PubMed Central

Lucera, Annalisa; Costa, Cristina; Conte, Amalia; Del Nobile, Matteo A.

2012-01-01

In agreement with the current trend of giving value to natural and renewable resources, the use of natural antimicrobial compounds, particularly in food and biomedical applications, becomes very frequent. The direct addition of natural compounds to food is the most common method of application, even if numerous efforts have been made to find alternative solutions to the aim of avoiding undesirable inactivation. Dipping, spraying, and coating treatment of food with active solutions are currently applied to product prior to packaging as valid options. The aim of the current work is to give an overview on the use of natural compounds in food sector. In particular, the review will gather numerous case-studies of meat, fish, dairy products, minimally processed fruit and vegetables, and cereal-based products where these compounds found application. PMID:23060862

The boundary element method applied to 3D magneto-electro-elastic dynamic problems

NASA Astrophysics Data System (ADS)

Igumnov, L. A.; Markov, I. P.; Kuznetsov, Iu A.

2017-11-01

Due to the coupling properties, the magneto-electro-elastic materials possess a wide number of applications. They exhibit general anisotropic behaviour. Three-dimensional transient analyses of magneto-electro-elastic solids can hardly be found in the literature. 3D direct boundary element formulation based on the weakly-singular boundary integral equations in Laplace domain is presented in this work for solving dynamic linear magneto-electro-elastic problems. Integral expressions of the three-dimensional fundamental solutions are employed. Spatial discretization is based on a collocation method with mixed boundary elements. Convolution quadrature method is used as a numerical inverse Laplace transform scheme to obtain time domain solutions. Numerical examples are provided to illustrate the capability of the proposed approach to treat highly dynamic problems.

On computing special functions in marine engineering

NASA Astrophysics Data System (ADS)

Constantinescu, E.; Bogdan, M.

2015-11-01

Important modeling applications in marine engineering conduct us to a special class of solutions for difficult differential equations with variable coefficients. In order to be able to solve and implement such models (in wave theory, in acoustics, in hydrodynamics, in electromagnetic waves, but also in many other engineering fields), it is necessary to compute so called special functions: Bessel functions, modified Bessel functions, spherical Bessel functions, Hankel functions. The aim of this paper is to develop numerical solutions in Matlab for the above mentioned special functions. Taking into account the main properties for Bessel and modified Bessel functions, we shortly present analytically solutions (where possible) in the form of series. Especially it is studied the behavior of these special functions using Matlab facilities: numerical solutions and plotting. Finally, it will be compared the behavior of the special functions and point out other directions for investigating properties of Bessel and spherical Bessel functions. The asymptotic forms of Bessel functions and modified Bessel functions allow determination of important properties of these functions. The modified Bessel functions tend to look more like decaying and growing exponentials.

Comparison of viscous-shock-layer solutions by time-asymptotic and steady-state methods. [flow distribution around a Jupiter entry probe

NASA Technical Reports Server (NTRS)

Gupta, R. N.; Moss, J. N.; Simmonds, A. L.

1982-01-01

Two flow-field codes employing the time- and space-marching numerical techniques were evaluated. Both methods were used to analyze the flow field around a massively blown Jupiter entry probe under perfect-gas conditions. In order to obtain a direct point-by-point comparison, the computations were made by using identical grids and turbulence models. For the same degree of accuracy, the space-marching scheme takes much less time as compared to the time-marching method and would appear to provide accurate results for the problems with nonequilibrium chemistry, free from the effect of local differences in time on the final solution which is inherent in time-marching methods. With the time-marching method, however, the solutions are obtainable for the realistic entry probe shapes with massive or uniform surface blowing rates; whereas, with the space-marching technique, it is difficult to obtain converged solutions for such flow conditions. The choice of the numerical method is, therefore, problem dependent. Both methods give equally good results for the cases where results are compared with experimental data.

An analytic solution for numerical modeling validation in electromagnetics: the resistive sphere

NASA Astrophysics Data System (ADS)

Swidinsky, Andrei; Liu, Lifei

2017-11-01

We derive the electromagnetic response of a resistive sphere to an electric dipole source buried in a conductive whole space. The solution consists of an infinite series of spherical Bessel functions and associated Legendre polynomials, and follows the well-studied problem of a conductive sphere buried in a resistive whole space in the presence of a magnetic dipole. Our result is particularly useful for controlled-source electromagnetic problems using a grounded electric dipole transmitter and can be used to check numerical methods of calculating the response of resistive targets (such as finite difference, finite volume, finite element and integral equation). While we elect to focus on the resistive sphere in our examples, the expressions in this paper are completely general and allow for arbitrary source frequency, sphere radius, transmitter position, receiver position and sphere/host conductivity contrast so that conductive target responses can also be checked. Commonly used mesh validation techniques consist of comparisons against other numerical codes, but such solutions may not always be reliable or readily available. Alternatively, the response of simple 1-D models can be tested against well-known whole space, half-space and layered earth solutions, but such an approach is inadequate for validating models with curved surfaces. We demonstrate that our theoretical results can be used as a complementary validation tool by comparing analytic electric fields to those calculated through a finite-element analysis; the software implementation of this infinite series solution is made available for direct and immediate application.

Nonlinear ion-acoustic cnoidal waves in a dense relativistic degenerate magnetoplasma.

PubMed

El-Shamy, E F

2015-03-01

The complex pattern and propagation characteristics of nonlinear periodic ion-acoustic waves, namely, ion-acoustic cnoidal waves, in a dense relativistic degenerate magnetoplasma consisting of relativistic degenerate electrons and nondegenerate cold ions are investigated. By means of the reductive perturbation method and appropriate boundary conditions for nonlinear periodic waves, a nonlinear modified Korteweg-de Vries (KdV) equation is derived and its cnoidal wave is analyzed. The various solutions of nonlinear ion-acoustic cnoidal and solitary waves are presented numerically with the Sagdeev potential approach. The analytical solution and numerical simulation of nonlinear ion-acoustic cnoidal waves of the nonlinear modified KdV equation are studied. Clearly, it is found that the features (amplitude and width) of nonlinear ion-acoustic cnoidal waves are proportional to plasma number density, ion cyclotron frequency, and direction cosines. The numerical results are applied to high density astrophysical situations, such as in superdense white dwarfs. This research will be helpful in understanding the properties of compact astrophysical objects containing cold ions with relativistic degenerate electrons.

Numerical studies of the fluid and optical fields associated with complex cavity flows

NASA Technical Reports Server (NTRS)

Atwood, Christopher A.

1992-01-01

Numerical solutions for the flowfield about several cavity configurations have been computed using the Reynolds averaged Navier-Stokes equations. Comparisons between numerical and experimental results are made in two dimensions for free shear layers and a rectangular cavity, and in three dimensions for the transonic aero-window problem of the Stratospheric Observatory for Infrared Astronomy (SOFIA). Results show that dominant acoustic frequencies and magnitudes of the self excited resonant cavity flows compare well with the experiment. In addition, solution sensitivity to artificial dissipation and grid resolution levels are determined. Optical path distortion due to the flow field is modelled geometrically and is found to match the experiment. The fluid field was computed using a diagonalized scheme within an overset mesh framework. An existing code, OVERFLOW, was utilized with the additions of characteristic boundary condition and output routines required for reduction of the unsteady data. The newly developed code is directly applicable to a generalized three dimensional structured grid zone. Details are provided in a paper included in Appendix A.

Transient heat transfer in viscous rarefied gas between concentric cylinders. Effect of curvature

NASA Astrophysics Data System (ADS)

Gospodinov, P.; Roussinov, V.; Dankov, D.

2015-10-01

The thermoacoustic waves arising in cylindrical or planar Couette rarefied gas flow between rotating cylinders is studied in the cases of suddenly cylinder (active) wall velocity direction turn on. An unlimited increase in the radius of the inner cylinder flow can be interpreted as Couette flow between the two flat plates. Based on the developed in previous publications Navier-Stockes-Fourier (NSF) model and Direct Simulation Monte Carlo (DSMC) method and their numerical solutions, are considered transient processes in the gas phase. Macroscopic flow characteristics (velocity, density, temperature) are received. The cylindrical flow cases for fixed velocity and temperature of the both walls are considered. The curvature effects over the wave's distribution and attenuation are studied numerically.

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.

Direct numerical simulation of axisymmetric turbulence

NASA Astrophysics Data System (ADS)

Qu, Bo; Bos, Wouter J. T.; Naso, Aurore

2017-09-01

The dynamics of decaying, strictly axisymmetric, incompressible turbulence is investigated using direct numerical simulations. It is found that the angular momentum is a robust invariant of the system. It is further shown that long-lived coherent structures are generated by the flow. These structures can be associated with stationary solutions of the Euler equations. The structures obey relations in agreement with predictions from selective decay principles, compatible with the decay laws of the system. Two different types of decay scenarios are highlighted. The first case results in a quasi-two-dimensional flow with a dynamical behavior in the poloidal plane similar to freely decaying two-dimensional turbulence. In a second regime, the long-time dynamics is dominated by a single three-dimensional mode.

Mathematical modeling and numerical simulation of unilateral dynamic rupture propagation along very-long reverse faults

NASA Astrophysics Data System (ADS)

Hirano, S.

2017-12-01

For some great earthquakes, dynamic rupture propagates unilaterally along a horizontal direction of very-long reverse faults (e.g., the Mw9.1 Sumatra earthquake in 2004, the Mw8.0 Wenchuan earthquake in 2008, and the Mw8.8 Maule earthquake in 2010, etc.). It seems that barriers or creeping sections may not lay along the opposite region of the co-seismically ruptured direction. In fact, in the case of Sumatra, the Mw8.6 earthquake occurred in the opposite region only three months after the mainshock. Mechanism of unilateral mode-II rupture along a material interface has been investigated theoretically and numerically. For mode-II rupture propagating along a material interface, an analytical solution implies that co-seismic stress perturbation depends on the rupture direction (Weertman, 1980 JGR; Hirano & Yamashita, 2016 BSSA), and numerical modeling of plastic yielding contributes to simulating the unilateral rupture (DeDonteny et al., 2011 JGR). However, mode-III rupture may dominate for the very-long reverse faults, and it can be shown that stress perturbation due to mode-III rupture does not depend on the rupture direction. Hence, an effect of the material interface is insufficient to understand the mechanism of unilateral rupture along the very-long reverse faults. In this study, I consider a two-dimensional bimaterial system with interfacial dynamic mode-III rupture under an obliquely pre-stressed configuration (i.e., the maximum shear direction of the background stress is inclined from the interfacial fault). First, I derived an analytical solution of regularized elastic stress field around a steady-state interfacial slip pulse using the method of Rice et al. (2005 BSSA). Then I found that the total stress, which is the sum of the background stress and co-seismic stress perturbation, depends on the rupture direction even in the mode-III case. Second, I executed a finite difference numerical simulation with a plastic yielding model of Andrews (1978 JGR; 2005 JGR) and succeeded in a simulation of unilateral rupture propagation in some parameter ranges (see figure). This unilateral rupture might be caused by energy dissipation due to the plastic yielding process that concentrates in the vicinity of only one rupture tip depending on the rupture direction.

Multi-modal vibration amplitudes of taut inclined cables due to direct and/or parametric excitation

NASA Astrophysics Data System (ADS)

Macdonald, J. H. G.

2016-02-01

Cables are often prone to potentially damaging large amplitude vibrations. The dynamic excitation may be from external loading or motion of the cable ends, the latter including direct excitation, normally from components of end motion transverse to the cable, and parametric excitation induced by axial components of end motion causing dynamic tension variations. Geometric nonlinearity can be important, causing stiffening behaviour and nonlinear modal coupling. Previous analyses of the vibrations, often neglecting sag, have generally dealt with direct and parametric excitation separately or have reverted to numerical solutions of the responses. Here a nonlinear cable model is adopted, applicable to taut cables such as on cable-stayed bridges, that allows for cable inclination, small sag (such that the vibration modes are similar to those of a taut string), multiple modes in both planes and end motion and/or external forcing close to any natural frequency. Based on the method of scaling and averaging it is found that, for sinusoidal inputs and positive damping, non-zero steady state responses can only occur in the modes in each plane with natural frequencies close to the excitation frequency and those with natural frequencies close to half this frequency. Analytical solutions, in the form of non-dimensional polynomial equations, are derived for the steady state vibration amplitudes in up to three modes simultaneously: the directly excited mode, the corresponding nonlinearly coupled mode in the orthogonal plane and a parametrically excited mode with half the natural frequency. The stability of the solutions is also identified. The outputs of the equations are consistent with previous results, where available. Example results from the analytical solutions are presented for a typical inclined bridge cable subject to vertical excitation of the lower end, and they are validated by numerical integration of the equations of motion and against some previous experimental results. It is shown that the modal interactions and sag (although very small) affect the responses significantly.

Interior-Point Methods for Linear Programming: A Challenge to the Simplex Method

DTIC Science & Technology

1988-07-01

subsequently found that the method was first proposed by Dikin in 1967 [6]. Search directions are generated by the same system (5). Any hint of quadratic...1982). Inexact Newton methods, SIAM Journal on Numerical Analysis 19, 400-408. [6] I. I. Dikin (1967). Iterative solution of problems of linear and

Nonlocal dark solitons under competing cubic-quintic nonlinearities.

PubMed

Chen, L; Wang, Q; Shen, M; Zhao, H; Lin, Y-Y; Jeng, C-C; Lee, R-K; Krolikowski, W

2013-01-01

We investigate properties of dark solitons under competing nonlocal cubic-local quintic nonlinearities. Analytical results, based on a variational approach and confirmed by direct numerical simulations, reveal the existence of a unique dark soliton solutions with their width being independent of the degree of nonlocality, due to the competing cubic-quintic nonlinearities.

Variational Perturbation Treatment of the Confined Hydrogen Atom

ERIC Educational Resources Information Center

Montgomery, H. E., Jr.

2011-01-01

The Schrodinger equation for the ground state of a hydrogen atom confined at the centre of an impenetrable cavity is treated using variational perturbation theory. Energies calculated from variational perturbation theory are comparable in accuracy to the results from a direct numerical solution. The goal of this exercise is to introduce the…

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.

Optimal control, optimization and asymptotic analysis of Purcell's microswimmer model

NASA Astrophysics Data System (ADS)

Wiezel, Oren; Or, Yizhar

2016-11-01

Purcell's swimmer (1977) is a classic model of a three-link microswimmer that moves by performing periodic shape changes. Becker et al. (2003) showed that the swimmer's direction of net motion is reversed upon increasing the stroke amplitude of joint angles. Tam and Hosoi (2007) used numerical optimization in order to find optimal gaits for maximizing either net displacement or Lighthill's energetic efficiency. In our work, we analytically derive leading-order expressions as well as next-order corrections for both net displacement and energetic efficiency of Purcell's microswimmer. Using these expressions enables us to explicitly show the reversal in direction of motion, as well as obtaining an estimate for the optimal stroke amplitude. We also find the optimal swimmer's geometry for maximizing either displacement or energetic efficiency. Additionally, the gait optimization problem is revisited and analytically formulated as an optimal control system with only two state variables, which can be solved using Pontryagin's maximum principle. It can be shown that the optimal solution must follow a "singular arc". Numerical solution of the boundary value problem is obtained, which exactly reproduces Tam and Hosoi's optimal gait.

Direct handling of equality constraints in multilevel optimization

NASA Technical Reports Server (NTRS)

Renaud, John E.; Gabriele, Gary A.

1990-01-01

In recent years there have been several hierarchic multilevel optimization algorithms proposed and implemented in design studies. Equality constraints are often imposed between levels in these multilevel optimizations to maintain system and subsystem variable continuity. Equality constraints of this nature will be referred to as coupling equality constraints. In many implementation studies these coupling equality constraints have been handled indirectly. This indirect handling has been accomplished using the coupling equality constraints' explicit functional relations to eliminate design variables (generally at the subsystem level), with the resulting optimization taking place in a reduced design space. In one multilevel optimization study where the coupling equality constraints were handled directly, the researchers encountered numerical difficulties which prevented their multilevel optimization from reaching the same minimum found in conventional single level solutions. The researchers did not explain the exact nature of the numerical difficulties other than to associate them with the direct handling of the coupling equality constraints. The coupling equality constraints are handled directly, by employing the Generalized Reduced Gradient (GRG) method as the optimizer within a multilevel linear decomposition scheme based on the Sobieski hierarchic algorithm. Two engineering design examples are solved using this approach. The results show that the direct handling of coupling equality constraints in a multilevel optimization does not introduce any problems when the GRG method is employed as the internal optimizer. The optimums achieved are comparable to those achieved in single level solutions and in multilevel studies where the equality constraints have been handled indirectly.

Characterization of a Method for Inverse Heat Conduction Using Real and Simulated Thermocouple Data

NASA Technical Reports Server (NTRS)

Pizzo, Michelle E.; Glass, David E.

2017-01-01

It is often impractical to instrument the external surface of high-speed vehicles due to the aerothermodynamic heating. Temperatures can instead be measured internal to the structure using embedded thermocouples, and direct and inverse methods can then be used to estimate temperature and heat flux on the external surface. Two thermocouples embedded at different depths are required to solve direct and inverse problems, and filtering schemes are used to reduce noise in the measured data. Accuracy in the estimated surface temperature and heat flux is dependent on several factors. Factors include the thermocouple location through the thickness of a material, the sensitivity of the surface solution to the error in the specified location of the embedded thermocouples, and the sensitivity to the error in thermocouple data. The effect of these factors on solution accuracy is studied using the methodology discussed in the work of Pizzo, et. al.1 A numerical study is performed to determine if there is an optimal depth at which to embed one thermocouple through the thickness of a material assuming that a second thermocouple is installed on the back face. Solution accuracy will be discussed for a range of embedded thermocouple depths. Moreover, the sensitivity of the surface solution to (a) the error in the specified location of the embedded thermocouple and to (b) the error in the thermocouple data are quantified using numerical simulation, and the results are discussed.

Stability of the iterative solutions of integral equations as one phase freezing criterion.

PubMed

Fantoni, R; Pastore, G

2003-10-01

A recently proposed connection between the threshold for the stability of the iterative solution of integral equations for the pair correlation functions of a classical fluid and the structural instability of the corresponding real fluid is carefully analyzed. Direct calculation of the Lyapunov exponent of the standard iterative solution of hypernetted chain and Percus-Yevick integral equations for the one-dimensional (1D) hard rods fluid shows the same behavior observed in 3D systems. Since no phase transition is allowed in such 1D system, our analysis shows that the proposed one phase criterion, at least in this case, fails. We argue that the observed proximity between the numerical and the structural instability in 3D originates from the enhanced structure present in the fluid but, in view of the arbitrary dependence on the iteration scheme, it seems uneasy to relate the numerical stability analysis to a robust one-phase criterion for predicting a thermodynamic phase transition.

A numerical cloud model for the support of laboratory experimentation

NASA Technical Reports Server (NTRS)

Hagen, D. E.

1979-01-01

A numerical cloud model is presented which can describe the evolution of a cloud starting from moist aerosol-laden air through the diffusional growth regime. The model is designed for the direct support of cloud chamber laboratory experimentation, i.e., experiment preparation, real-time control and data analysis. In the model the thermodynamics is uncoupled from the droplet growth processes. Analytic solutions for the cloud droplet growth equations are developed which can be applied in most laboratory situations. The model is applied to a variety of representative experiments.

Reconstruction Of The Permittivity Profile Of A Stratified Dielectric Layer

NASA Astrophysics Data System (ADS)

Vogelzang, E.; Ferwerda, H. A.; Yevick, D.

1985-03-01

A numerical procedure is given for the reconstruction of the permittivity profile of a dielectric slab on a perfect conductor. Profiles not supporting guided modes are reconstructed from the complex reflection amplitude for TE-polarized, monochromatic plane waves incident from different directions using the Marchenko theory. The contribution of guided modes is incorporated in the reconstruction procedure through the Gelfand-Levitan equations. An advantage of our approach is that a unique solution for the permittivity profile is obtained without the use of complicated regularization techniques. Some illustrative numerical examples are presented.

Numerical parametric studies of spray combustion instability

NASA Technical Reports Server (NTRS)

Pindera, M. Z.

1993-01-01

A coupled numerical algorithm has been developed for studies of combustion instabilities in spray-driven liquid rocket engines. The model couples gas and liquid phase physics using the method of fractional steps. Also introduced is a novel, efficient methodology for accounting for spray formation through direct solution of liquid phase equations. Preliminary parametric studies show marked sensitivity of spray penetration and geometry to droplet diameter, considerations of liquid core, and acoustic interactions. Less sensitivity was shown to the combustion model type although more rigorous (multi-step) formulations may be needed for the differences to become apparent.

A computational study of the topology of vortex breakdown

NASA Technical Reports Server (NTRS)

Spall, Robert E.; Gatski, Thomas B.

1991-01-01

A fully three-dimensional numerical simulation of vortex breakdown using the unsteady, incompressible Navier-Stokes equations has been performed. Solutions to four distinct types of breakdown are identified and compared with experimental results. The computed solutions include weak helical, double helix, spiral, and bubble-type breakdowns. The topological structure of the various breakdowns as well as their interrelationship are studied. The data reveal that the asymmetric modes of breakdown may be subject to additional breakdowns as the vortex core evolves in the streamwise direction. The solutions also show that the freestream axial velocity distribution has a significant effect on the position and type of vortex breakdown.

Transport processes in directional solidification and their effects on microstructure development

NASA Astrophysics Data System (ADS)

Mazumder, Prantik

The processing of materials with unique electronic, mechanical, optical and thermal properties plays a crucial role in modern technology. The quality of these materials depend strongly on the microstructures and the solute/dopant fields in the solid product, that are strongly influenced by the intricate coupling of heat and mass transfer and melt flow in the growth systems. An integrated research program is developed that include precisely characterized experiments and detailed physical and numerical modeling of the complex transport and dynamical processes. Direct numerical simulation of the solidification process is carried out that takes into account the unsteady thermo-solutal convection in the vertical Bridgman crystal growth system, and accurately models the thermal interaction between the furnace and the ampoule by appropriately using experimentally measured thermal profiles. The flow instabilities and transitions and the nonlinear evolution following the transitions are investigated by time series and flow pattern analysis. A range of complex dynamical behavior is predicted with increasing thermal Rayleigh number. The route to chaos appears as: steady convection --> transient mono-periodic --> transient bi-periodic --> transient quasiperiodic --> transient intermittent oscillation- relaxation --> stable intermittent oscillation-relaxation attractor. The spatio-temporal dynamics of the melt flow is found to be directly related to the spatial patterns observed experimentally in the solidified crystals. The application of the model to two phase Sn-Cd peritectic alloys showed that a new class of tree-like oscillating microstructure develops in the solid phase due to unsteady thermo-solutal convection in the liquid melt. These oscillating layered structures can give the illusion of band structures on a plane of polish. The model is applied to single phase solidification in the Al-Cu and Pb-Sn systems to characterize the effect of convection on the macroscopic shape and disorder in the primary arm spacing of the cellular/dendritic freezing front. The apparently puzzling experimental observation of higher disorder in the weakly convective Al-Cu system than that in the highly convective Pb-Sn system is explained by the numerical calculations.

On similarity solutions of a boundary layer problem with an upstream moving wall

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Lakin, W. D.; Nachman, A.

1986-01-01

The problem of a boundary layer on a flat plate which has a constant velocity opposite in direction to that of the uniform mainstream is examined. It was previously shown that the solution of this boundary value problem is crucially dependent on the parameter which is the ratio of the velocity of the plate to the velocity of the free stream. In particular, it was proved that a solution exists only if this parameter does not exceed a certain critical value, and numerical evidence was adduced to show that this solution is nonunique. Using Crocco formulation the present work proves this nonuniqueness. Also considered are the analyticity of solutions and the derivation of upper bounds on the critical value of wall velocity parameter.

Exact solutions of the population balance equation including particle transport, using group analysis

NASA Astrophysics Data System (ADS)

Lin, Fubiao; Meleshko, Sergey V.; Flood, Adrian E.

2018-06-01

The population balance equation (PBE) has received an unprecedented amount of attention in recent years from both academics and industrial practitioners because of its long history, widespread use in engineering, and applicability to a wide variety of particulate and discrete-phase processes. However it is typically impossible to obtain analytical solutions, although in almost every case a numerical solution of the PBEs can be obtained. In this article, the symmetries of PBEs with homogeneous coagulation kernels involving aggregation, breakage and growth processes and particle transport in one dimension are found by direct solving the determining equations. Using the optimal system of one and two-dimensional subalgebras, all invariant solutions and reduced equations are obtained. In particular, an explicit analytical physical solution is also presented.

Stokes flow inside an evaporating liquid line for any contact angle

NASA Astrophysics Data System (ADS)

Petsi, A. J.; Burganos, V. N.

2008-09-01

Evaporation of droplets or liquid films lying on a substrate induces internal viscous flow, which affects the transport of suspended particles and, thus, the final deposit profile in numerous applications. In this work, the problem of Stokes flow inside a two-dimensional droplet, representing the cross section of an evaporating liquid line lying on a flat surface, is considered. The stream function formulation is adopted, leading to the biharmonic equation in bipolar coordinates. A solution in closed form is obtained for any contact angle in (0,π) and is, thus, valid for both hydrophilic and hydrophobic substrates. The solution can be used with any type of evaporation mechanism, including diffusion, convection, or kinetically controlled modes. Both pinned and depinned contact lines are considered. For the boundary conditions to be compatible at the contact lines, the Navier slip boundary condition is applied on the substrate. Numerical results are presented for kinetically and diffusion controlled evaporation. For pinned contact lines, the flow inside the evaporating liquid line is directed towards the edges, thus, promoting the coffee stain phenomenon. In the case of depinned contact lines and contact angle less than π/2 , the flow is directed towards the center of the droplet, whereas, for strongly hydrophobic substrates it is directed outwards.

A direct method for the solution of unsteady two-dimensional incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ghia, K. N.; Osswald, G. A.; Ghia, U.

1983-01-01

The unsteady incompressible Navier-Stokes equations are formulated in terms of vorticity and stream function in generalized curvilinear orthogonal coordinates to facilitiate analysis of flow configurations with general geometries. The numerical method developed solves the conservative form of the transport equation using the alternating-direction implicit method, whereas the stream-function equation is solved by direct block Gaussian elimination. The method is applied to a model problem of flow over a back-step in a doubly infinite channel, using clustered conformal coordinates. One-dimensional stretching functions, dependent on the Reynolds number and the asymptotic behavior of the flow, are used to provide suitable grid distribution in the separation and reattachment regions, as well as in the inflow and outflow regions. The optimum grid distribution selected attempts to honor the multiple length scales of the separated-flow model problem. The asymptotic behavior of the finite-differenced transport equation near infinity is examined and the numerical method is carefully developed so as to lead to spatially second-order accurate wiggle-free solutions, i.e., with minimum dispersive error. Results have been obtained in the entire laminar range for the backstep channel and are in good agreement with the available experimental data for this flow problem.

Self-interacting inelastic dark matter: a viable solution to the small scale structure problems

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

Blennow, Mattias; Clementz, Stefan; Herrero-Garcia, Juan, E-mail: emb@kth.se, E-mail: scl@kth.se, E-mail: juan.herrero-garcia@adelaide.edu.au

2017-03-01

Self-interacting dark matter has been proposed as a solution to the small-scale structure problems, such as the observed flat cores in dwarf and low surface brightness galaxies. If scattering takes place through light mediators, the scattering cross section relevant to solve these problems may fall into the non-perturbative regime leading to a non-trivial velocity dependence, which allows compatibility with limits stemming from cluster-size objects. However, these models are strongly constrained by different observations, in particular from the requirements that the decay of the light mediator is sufficiently rapid (before Big Bang Nucleosynthesis) and from direct detection. A natural solution tomore » reconcile both requirements are inelastic endothermic interactions, such that scatterings in direct detection experiments are suppressed or even kinematically forbidden if the mass splitting between the two-states is sufficiently large. Using an exact solution when numerically solving the Schrödinger equation, we study such scenarios and find regions in the parameter space of dark matter and mediator masses, and the mass splitting of the states, where the small scale structure problems can be solved, the dark matter has the correct relic abundance and direct detection limits can be evaded.« less

Modelling solid solutions with cluster expansion, special quasirandom structures, and thermodynamic approaches

NASA Astrophysics Data System (ADS)

Saltas, V.; Horlait, D.; Sgourou, E. N.; Vallianatos, F.; Chroneos, A.

2017-12-01

Modelling solid solutions is fundamental in understanding the properties of numerous materials which are important for a range of applications in various fields including nanoelectronics and energy materials such as fuel cells, nuclear materials, and batteries, as the systematic understanding throughout the composition range of solid solutions for a range of conditions can be challenging from an experimental viewpoint. The main motivation of this review is to contribute to the discussion in the community of the applicability of methods that constitute the investigation of solid solutions computationally tractable. This is important as computational modelling is required to calculate numerous defect properties and to act synergistically with experiment to understand these materials. This review will examine in detail two examples: silicon germanium alloys and MAX phase solid solutions. Silicon germanium alloys are technologically important in nanoelectronic devices and are also relevant considering the recent advances in ternary and quaternary groups IV and III-V semiconductor alloys. MAX phase solid solutions display a palette of ceramic and metallic properties and it is anticipated that via their tuning they can have applications ranging from nuclear to aerospace industries as well as being precursors for particular MXenes. In the final part, a brief summary assesses the limitations and possibilities of the methodologies discussed, whereas there is discussion on the future directions and examples of solid solution systems that should prove fruitful to consider.

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.

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

NASA Astrophysics Data System (ADS)

Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

2017-07-01

This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

Symmetry-plane model of 3D Euler flows: Mapping to regular systems and numerical solutions of blowup

NASA Astrophysics Data System (ADS)

Mulungye, Rachel M.; Lucas, Dan; Bustamante, Miguel D.

2014-11-01

We introduce a family of 2D models describing the dynamics on the so-called symmetry plane of the full 3D Euler fluid equations. These models depend on a free real parameter and can be solved analytically. For selected representative values of the free parameter, we apply the method introduced in [M.D. Bustamante, Physica D: Nonlinear Phenom. 240, 1092 (2011)] to map the fluid equations bijectively to globally regular systems. By comparing the analytical solutions with the results of numerical simulations, we establish that the numerical simulations of the mapped regular systems are far more accurate than the numerical simulations of the original systems, at the same spatial resolution and CPU time. In particular, the numerical integrations of the mapped regular systems produce robust estimates for the growth exponent and singularity time of the main blowup quantity (vorticity stretching rate), converging well to the analytically-predicted values even beyond the time at which the flow becomes under-resolved (i.e. the reliability time). In contrast, direct numerical integrations of the original systems develop unstable oscillations near the reliability time. We discuss the reasons for this improvement in accuracy, and explain how to extend the analysis to the full 3D case. Supported under the programme for Research in Third Level Institutions (PRTLI) Cycle 5 and co-funded by the European Regional Development Fund.

Electroelastic fields in a layered piezoelectric cylindrical shell under dynamic load

NASA Astrophysics Data System (ADS)

Saviz, M. R.; Shakeri, M.; Yas, M. H.

2007-10-01

The objective of this paper is to demonstrate layerwise theory for the analysis of thick laminated piezoelectric shell structures. A general finite element formulation using the layerwise theory is developed for a laminated cylindrical shell with piezoelectric layers, subjected to dynamic loads. The quadratic approximation of the displacement and electric potential in the thickness direction is considered. The governing equations are reduced to two-dimensional (2D) differential equations. The three-dimensional (3D) elasticity solution is also presented. The resulting equations are solved by a proper finite element method. The numerical results for static loading are compared with exact solutions of benchmark problems. Numerical examples of the dynamic problem are presented. The convergence is studied, as is the influence of the electromechanical coupling on the axisymmetric free-vibration characteristics of a thick cylinder.

Vortex breakdown simulation

NASA Technical Reports Server (NTRS)

Hafez, M.; Ahmad, J.; Kuruvila, G.; Salas, M. D.

1987-01-01

In this paper, steady, axisymmetric inviscid, and viscous (laminar) swirling flows representing vortex breakdown phenomena are simulated using a stream function-vorticity-circulation formulation and two numerical methods. The first is based on an inverse iteration, where a norm of the solution is prescribed and the swirling parameter is calculated as a part of the output. The second is based on direct Newton iterations, where the linearized equations, for all the unknowns, are solved simultaneously by an efficient banded Gaussian elimination procedure. Several numerical solutions for inviscid and viscous flows are demonstrated, followed by a discussion of the results. Some improvements on previous work have been achieved: first order upwind differences are replaced by second order schemes, line relaxation procedure (with linear convergence rate) is replaced by Newton's iterations (which converge quadratically), and Reynolds numbers are extended from 200 up to 1000.

Direct determination of one-dimensional interphase structures using normalized crystal truncation rod analysis

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

Kawaguchi, Tomoya; Liu, Yihua; Reiter, Anthony

Here, a one-dimensional non-iterative direct method was employed for normalized crystal truncation rod analysis. The non-iterative approach, utilizing the Kramers–Kronig relation, avoids the ambiguities due to an improper initial model or incomplete convergence in the conventional iterative methods. The validity and limitations of the present method are demonstrated through both numerical simulations and experiments with Pt(111) in a 0.1 M CsF aqueous solution. The present method is compared with conventional iterative phase-retrieval methods.

Direct determination of one-dimensional interphase structures using normalized crystal truncation rod analysis

DOE PAGES

Kawaguchi, Tomoya; Liu, Yihua; Reiter, Anthony; ...

2018-04-20

Here, a one-dimensional non-iterative direct method was employed for normalized crystal truncation rod analysis. The non-iterative approach, utilizing the Kramers–Kronig relation, avoids the ambiguities due to an improper initial model or incomplete convergence in the conventional iterative methods. The validity and limitations of the present method are demonstrated through both numerical simulations and experiments with Pt(111) in a 0.1 M CsF aqueous solution. The present method is compared with conventional iterative phase-retrieval methods.

Numerical solution of the stochastic parabolic equation with the dependent operator coefficient

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

Ashyralyev, Allaberen; Department of Mathematics, ITTU, Ashgabat; Okur, Ulker

2015-09-18

In the present paper, a single step implicit difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is presented. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, this abstract result permits us to obtain the convergence estimates for the solution of difference schemes for the numerical solution of initial boundary value problems for parabolic equations. The theoretical statements for the solution of this difference scheme are supported by the results of numerical experiments.

Sedimentary Geothermal Feasibility Study: October 2016

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

Augustine, Chad; Zerpa, Luis

The objective of this project is to analyze the feasibility of commercial geothermal projects using numerical reservoir simulation, considering a sedimentary reservoir with low permeability that requires productivity enhancement. A commercial thermal reservoir simulator (STARS, from Computer Modeling Group, CMG) is used in this work for numerical modeling. In the first stage of this project (FY14), a hypothetical numerical reservoir model was developed, and validated against an analytical solution. The following model parameters were considered to obtain an acceptable match between the numerical and analytical solutions: grid block size, time step and reservoir areal dimensions; the latter related to boundarymore » effects on the numerical solution. Systematic model runs showed that insufficient grid sizing generates numerical dispersion that causes the numerical model to underestimate the thermal breakthrough time compared to the analytic model. As grid sizing is decreased, the model results converge on a solution. Likewise, insufficient reservoir model area introduces boundary effects in the numerical solution that cause the model results to differ from the analytical solution.« less

Quantitative Thermochronology

NASA Astrophysics Data System (ADS)

Braun, Jean; van der Beek, Peter; Batt, Geoffrey

2006-05-01

Thermochronology, the study of the thermal history of rocks, enables us to quantify the nature and timing of tectonic processes. Quantitative Thermochronology is a robust review of isotopic ages, and presents a range of numerical modeling techniques to allow the physical implications of isotopic age data to be explored. The authors provide analytical, semi-analytical, and numerical solutions to the heat transfer equation in a range of tectonic settings and under varying boundary conditions. They then illustrate their modeling approach built around a large number of case studies. The benefits of different thermochronological techniques are also described. Computer programs on an accompanying website at www.cambridge.org/9780521830577 are introduced through the text and provide a means of solving the heat transport equation in the deforming Earth to predict the ages of rocks and compare them directly to geological and geochronological data. Several short tutorials, with hints and solutions, are also included. Numerous case studies help geologists to interpret age data and relate it to Earth processes Essential background material to aid understanding and using thermochronological data Provides a thorough treatise on numerical modeling of heat transport in the Earth's crust Supported by a website hosting relevant computer programs and colour slides of figures from the book for use in teaching

Numerical Solution of 3D Poisson-Nernst-Planck Equations Coupled with Classical Density Functional Theory for Modeling Ion and Electron Transport in a Confined Environment

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

Meng, Da; Zheng, Bin; Lin, Guang

2014-08-29

We have developed efficient numerical algorithms for the solution of 3D steady-state Poisson-Nernst-Planck equations (PNP) with excess chemical potentials described by the classical density functional theory (cDFT). The coupled PNP equations are discretized by finite difference scheme and solved iteratively by Gummel method with relaxation. The Nernst-Planck equations are transformed into Laplace equations through the Slotboom transformation. Algebraic multigrid method is then applied to efficiently solve the Poisson equation and the transformed Nernst-Planck equations. A novel strategy for calculating excess chemical potentials through fast Fourier transforms is proposed which reduces computational complexity from O(N2) to O(NlogN) where N is themore » number of grid points. Integrals involving Dirac delta function are evaluated directly by coordinate transformation which yields more accurate result compared to applying numerical quadrature to an approximated delta function. Numerical results for ion and electron transport in solid electrolyte for Li ion batteries are shown to be in good agreement with the experimental data and the results from previous studies.« less

A new flux-conserving numerical scheme for the steady, incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Scott, James R.

1994-01-01

This paper is concerned with the continued development of a new numerical method, the space-time solution element (STS) method, for solving conservation laws. The present work focuses on the two-dimensional, steady, incompressible Navier-Stokes equations. Using first an integral approach, and then a differential approach, the discrete flux conservation equations presented in a recent paper are rederived. Here a simpler method for determining the flux expressions at cell interfaces is given; a systematic and rigorous derivation of the conditions used to simulate the differential form of the governing conservation law(s) is provided; necessary and sufficient conditions for a discrete approximation to satisfy a conservation law in E2 are derived; and an estimate of the local truncation error is given. A specific scheme is then constructed for the solution of the thin airfoil boundary layer problem. Numerical results are presented which demonstrate the ability of the scheme to accurately resolve the developing boundary layer and wake regions using grids which are much coarser than those employed by other numerical methods. It is shown that ten cells in the cross-stream direction are sufficient to accurately resolve the developing airfoil boundary layer.

3-D direct current resistivity anisotropic modelling by goal-oriented adaptive finite element methods

NASA Astrophysics Data System (ADS)

Ren, Zhengyong; Qiu, Lewen; Tang, Jingtian; Wu, Xiaoping; Xiao, Xiao; Zhou, Zilong

2018-01-01

Although accurate numerical solvers for 3-D direct current (DC) isotropic resistivity models are current available even for complicated models with topography, reliable numerical solvers for the anisotropic case are still an open question. This study aims to develop a novel and optimal numerical solver for accurately calculating the DC potentials for complicated models with arbitrary anisotropic conductivity structures in the Earth. First, a secondary potential boundary value problem is derived by considering the topography and the anisotropic conductivity. Then, two a posteriori error estimators with one using the gradient-recovery technique and one measuring the discontinuity of the normal component of current density are developed for the anisotropic cases. Combing the goal-oriented and non-goal-oriented mesh refinements and these two error estimators, four different solving strategies are developed for complicated DC anisotropic forward modelling problems. A synthetic anisotropic two-layer model with analytic solutions verified the accuracy of our algorithms. A half-space model with a buried anisotropic cube and a mountain-valley model are adopted to test the convergence rates of these four solving strategies. We found that the error estimator based on the discontinuity of current density shows better performance than the gradient-recovery based a posteriori error estimator for anisotropic models with conductivity contrasts. Both error estimators working together with goal-oriented concepts can offer optimal mesh density distributions and highly accurate solutions.

Weighted Non-linear Compact Schemes for the Direct Numerical Simulation of Compressible, Turbulent Flows

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

Ghosh, Debojyoti; Baeder, James D.

2014-01-21

A new class of compact-reconstruction weighted essentially non-oscillatory (CRWENO) schemes were introduced (Ghosh and Baeder in SIAM J Sci Comput 34(3): A1678–A1706, 2012) with high spectral resolution and essentially non-oscillatory behavior across discontinuities. The CRWENO schemes use solution-dependent weights to combine lower-order compact interpolation schemes and yield a high-order compact scheme for smooth solutions and a non-oscillatory compact scheme near discontinuities. The new schemes result in lower absolute errors, and improved resolution of discontinuities and smaller length scales, compared to the weighted essentially non-oscillatory (WENO) scheme of the same order of convergence. Several improvements to the smoothness-dependent weights, proposed inmore » the literature in the context of the WENO schemes, address the drawbacks of the original formulation. This paper explores these improvements in the context of the CRWENO schemes and compares the different formulations of the non-linear weights for flow problems with small length scales as well as discontinuities. Simplified one- and two-dimensional inviscid flow problems are solved to demonstrate the numerical properties of the CRWENO schemes and its different formulations. Canonical turbulent flow problems—the decay of isotropic turbulence and the shock-turbulence interaction—are solved to assess the performance of the schemes for the direct numerical simulation of compressible, turbulent flows« less

Perturbation-iteration theory for analyzing microwave striplines

NASA Technical Reports Server (NTRS)

Kretch, B. E.

1985-01-01

A perturbation-iteration technique is presented for determining the propagation constant and characteristic impedance of an unshielded microstrip transmission line. The method converges to the correct solution with a few iterations at each frequency and is equivalent to a full wave analysis. The perturbation-iteration method gives a direct solution for the propagation constant without having to find the roots of a transcendental dispersion equation. The theory is presented in detail along with numerical results for the effective dielectric constant and characteristic impedance for a wide range of substrate dielectric constants, stripline dimensions, and frequencies.

Bifurcation Analysis and Chaos Control in a Modified Finance System with Delayed Feedback

NASA Astrophysics Data System (ADS)

Yang, Jihua; Zhang, Erli; Liu, Mei

2016-06-01

We investigate the effect of delayed feedback on the finance system, which describes the time variation of the interest rate, for establishing the fiscal policy. By local stability analysis, we theoretically prove the existences of Hopf bifurcation and Hopf-zero bifurcation. By using the normal form method and center manifold theory, we determine the stability and direction of a bifurcating periodic solution. Finally, we give some numerical solutions, which indicate that when the delay passes through certain critical values, chaotic oscillation is converted into a stable equilibrium or periodic orbit.

Rapid Inversion of Angular Deflection Data for Certain Axisymmetric Refractive Index Distributions

NASA Technical Reports Server (NTRS)

Rubinstein, R.; Greenberg, P. S.

1994-01-01

Certain functions useful for representing axisymmetric refractive-index distributions are shown to have exact solutions for Abel transformation of the resulting angular deflection data. An advantage of this procedure over direct numerical Abel inversion is that least-squares curve fitting is a smoothing process that reduces the noise sensitivity of the computation

Radial Motion of Two Mutually Attracting Particles

ERIC Educational Resources Information Center

Mungan, Carl E.

2009-01-01

A pair of masses or opposite-sign charges released from rest will move directly toward each other under the action of the inverse-distance-squared force of attraction between them. An exact expression for the separation distance as a function of time can only be found by numerically inverting the solution of a differential equation. A simpler,…

On the wall-normal velocity of the compressible boundary-layer equations

NASA Technical Reports Server (NTRS)

Pruett, C. David

1991-01-01

Numerical methods for the compressible boundary-layer equations are facilitated by transformation from the physical (x,y) plane to a computational (xi,eta) plane in which the evolution of the flow is 'slow' in the time-like xi direction. The commonly used Levy-Lees transformation results in a computationally well-behaved problem for a wide class of non-similar boundary-layer flows, but it complicates interpretation of the solution in physical space. Specifically, the transformation is inherently nonlinear, and the physical wall-normal velocity is transformed out of the problem and is not readily recovered. In light of recent research which shows mean-flow non-parallelism to significantly influence the stability of high-speed compressible flows, the contribution of the wall-normal velocity in the analysis of stability should not be routinely neglected. Conventional methods extract the wall-normal velocity in physical space from the continuity equation, using finite-difference techniques and interpolation procedures. The present spectrally-accurate method extracts the wall-normal velocity directly from the transformation itself, without interpolation, leaving the continuity equation free as a check on the quality of the solution. The present method for recovering wall-normal velocity, when used in conjunction with a highly-accurate spectral collocation method for solving the compressible boundary-layer equations, results in a discrete solution which is extraordinarily smooth and accurate, and which satisfies the continuity equation nearly to machine precision. These qualities make the method well suited to the computation of the non-parallel mean flows needed by spatial direct numerical simulations (DNS) and parabolized stability equation (PSE) approaches to the analysis of stability.

Numerical integration of asymptotic solutions of ordinary differential equations

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.

1989-01-01

Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.

A Chebyshev Collocation Method for Moving Boundaries, Heat Transfer, and Convection During Directional Solidification

NASA Technical Reports Server (NTRS)

Zhang, Yiqiang; Alexander, J. I. D.; Ouazzani, J.

1994-01-01

Free and moving boundary problems require the simultaneous solution of unknown field variables and the boundaries of the domains on which these variables are defined. There are many technologically important processes that lead to moving boundary problems associated with fluid surfaces and solid-fluid boundaries. These include crystal growth, metal alloy and glass solidification, melting and name propagation. The directional solidification of semi-conductor crystals by the Bridgman-Stockbarger method is a typical example of such a complex process. A numerical model of this growth method must solve the appropriate heat, mass and momentum transfer equations and determine the location of the melt-solid interface. In this work, a Chebyshev pseudospectra collocation method is adapted to the problem of directional solidification. Implementation involves a solution algorithm that combines domain decomposition, finite-difference preconditioned conjugate minimum residual method and a Picard type iterative scheme.

Analysis of periodically excited non-linear systems by a parametric continuation technique

NASA Astrophysics Data System (ADS)

Padmanabhan, C.; Singh, R.

1995-07-01

The dynamic behavior and frequency response of harmonically excited piecewise linear and/or non-linear systems has been the subject of several recent investigations. Most of the prior studies employed harmonic balance or Galerkin schemes, piecewise linear techniques, analog simulation and/or direct numerical integration (digital simulation). Such techniques are somewhat limited in their ability to predict all of the dynamic characteristics, including bifurcations leading to the occurrence of unstable, subharmonic, quasi-periodic and/or chaotic solutions. To overcome this problem, a parametric continuation scheme, based on the shooting method, is applied specifically to a periodically excited piecewise linear/non-linear system, in order to improve understanding as well as to obtain the complete dynamic response. Parameter regions exhibiting bifurcations to harmonic, subharmonic or quasi-periodic solutions are obtained quite efficiently and systematically. Unlike other techniques, the proposed scheme can follow period-doubling bifurcations, and with some modifications obtain stable quasi-periodic solutions and their bifurcations. This knowledge is essential in establishing conditions for the occurrence of chaotic oscillations in any non-linear system. The method is first validated through the Duffing oscillator example, the solutions to which are also obtained by conventional one-term harmonic balance and perturbation methods. The second example deals with a clearance non-linearity problem for both harmonic and periodic excitations. Predictions from the proposed scheme match well with available analog simulation data as well as with multi-term harmonic balance results. Potential savings in computational time over direct numerical integration is demonstrated for some of the example cases. Also, this work has filled in some of the solution regimes for an impact pair, which were missed previously in the literature. Finally, one main limitation associated with the proposed procedure is discussed.

Porous media fracturing dynamics: stepwise crack advancement and fluid pressure oscillations

NASA Astrophysics Data System (ADS)

Cao, Toan D.; Hussain, Fazle; Schrefler, Bernhard A.

2018-02-01

We present new results explaining why fracturing in saturated porous media is not smooth and continuous but is a distinct stepwise process concomitant with fluid pressure oscillations. All exact solutions and almost all numerical models yield smooth fracture advancement and fluid pressure evolution, while recent experimental results, mainly from the oil industry, observation from geophysics and a very few numerical results for the quasi-static case indeed reveal the stepwise phenomenon. We summarize first these new experiments and these few numerical solutions for the quasi-static case. Both mechanical loading and pressure driven fractures are considered because their behaviours differ in the direction of the pressure jumps. Then we explore stepwise crack tip advancement and pressure fluctuations in dynamic fracturing with a hydro-mechanical model of porous media based on the Hybrid Mixture Theory. Full dynamic analyses of examples dealing with both hydraulic fracturing and mechanical loading are presented. The stepwise fracture advancement is confirmed in the dynamic setting as well as in the pressure fluctuations, but there are substantial differences in the frequency contents of the pressure waves in the two loading cases. Comparison between the quasi-static and fully dynamic solutions reveals that the dynamic response gives much more information such as the type of pressure oscillations and related frequencies and should be applied whenever there is a doubt about inertia forces playing a role - the case in most fracturing events. In the absence of direct relevant dynamic tests on saturated media some experimental results on dynamic fracture in dry materials, a fast hydraulic fracturing test and observations from geophysics confirm qualitatively the obtained results such as the type of pressure oscillations and the substantial difference in the behaviour under the two loading cases.

Benchmark Problems Used to Assess Computational Aeroacoustics Codes

NASA Technical Reports Server (NTRS)

Dahl, Milo D.; Envia, Edmane

2005-01-01

The field of computational aeroacoustics (CAA) encompasses numerical techniques for calculating all aspects of sound generation and propagation in air directly from fundamental governing equations. Aeroacoustic problems typically involve flow-generated noise, with and without the presence of a solid surface, and the propagation of the sound to a receiver far away from the noise source. It is a challenge to obtain accurate numerical solutions to these problems. The NASA Glenn Research Center has been at the forefront in developing and promoting the development of CAA techniques and methodologies for computing the noise generated by aircraft propulsion systems. To assess the technological advancement of CAA, Glenn, in cooperation with the Ohio Aerospace Institute and the AeroAcoustics Research Consortium, organized and hosted the Fourth CAA Workshop on Benchmark Problems. Participants from industry and academia from both the United States and abroad joined to present and discuss solutions to benchmark problems. These demonstrated technical progress ranging from the basic challenges to accurate CAA calculations to the solution of CAA problems of increasing complexity and difficulty. The results are documented in the proceedings of the workshop. Problems were solved in five categories. In three of the five categories, exact solutions were available for comparison with CAA results. A fourth category of problems representing sound generation from either a single airfoil or a blade row interacting with a gust (i.e., problems relevant to fan noise) had approximate analytical or completely numerical solutions. The fifth category of problems involved sound generation in a viscous flow. In this case, the CAA results were compared with experimental data.

A critical comparison of second order closures with direct numerical simulation of homogeneous turbulence

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Lumley, John L.

1991-01-01

Recently, several second order closure models have been proposed for closing the second moment equations, in which the velocity-pressure gradient (and scalar-pressure gradient) tensor and the dissipation rate tensor are two of the most important terms. In the literature, these correlation tensors are usually decomposed into a so called rapid term and a return-to-isotropy term. Models of these terms have been used in global flow calculations together with other modeled terms. However, their individual behavior in different flows have not been fully examined because they are un-measurable in the laboratory. Recently, the development of direct numerical simulation (DNS) of turbulence has given us the opportunity to do this kind of study. With the direct numerical simulation, we may use the solution to exactly calculate the values of these correlation terms and then directly compare them with the values from their modeled formulations (models). Here, we make direct comparisons of five representative rapid models and eight return-to-isotropy models using the DNS data of forty five homogeneous flows which were done by Rogers et al. (1986) and Lee et al. (1985). The purpose of these direct comparisons is to explore the performance of these models in different flows and identify the ones which give the best performance. The modeling procedure, model constraints, and the various evaluated models are described. The detailed results of the direct comparisons are discussed, and a few concluding remarks on turbulence models are given.

A GPU-accelerated semi-implicit fractional step method for numerical solutions of incompressible Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Ha, Sanghyun; Park, Junshin; You, Donghyun

2017-11-01

Utility of the computational power of modern Graphics Processing Units (GPUs) is elaborated for solutions of incompressible Navier-Stokes equations which are integrated using a semi-implicit fractional-step method. Due to its serial and bandwidth-bound nature, the present choice of numerical methods is considered to be a good candidate for evaluating the potential of GPUs for solving Navier-Stokes equations using non-explicit time integration. An efficient algorithm is presented for GPU acceleration of the Alternating Direction Implicit (ADI) and the Fourier-transform-based direct solution method used in the semi-implicit fractional-step method. OpenMP is employed for concurrent collection of turbulence statistics on a CPU while Navier-Stokes equations are computed on a GPU. Extension to multiple NVIDIA GPUs is implemented using NVLink supported by the Pascal architecture. Performance of the present method is experimented on multiple Tesla P100 GPUs compared with a single-core Xeon E5-2650 v4 CPU in simulations of boundary-layer flow over a flat plate. Supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (Ministry of Science, ICT and Future Planning NRF-2016R1E1A2A01939553, NRF-2014R1A2A1A11049599, and Ministry of Trade, Industry and Energy 201611101000230).

An unconditionally stable method for numerically solving solar sail spacecraft equations of motion

NASA Astrophysics Data System (ADS)

Karwas, Alex

Solar sails use the endless supply of the Sun's radiation to propel spacecraft through space. The sails use the momentum transfer from the impinging solar radiation to provide thrust to the spacecraft while expending zero fuel. Recently, the first solar sail spacecraft, or sailcraft, named IKAROS completed a successful mission to Venus and proved the concept of solar sail propulsion. Sailcraft experimental data is difficult to gather due to the large expenses of space travel, therefore, a reliable and accurate computational method is needed to make the process more efficient. Presented in this document is a new approach to simulating solar sail spacecraft trajectories. The new method provides unconditionally stable numerical solutions for trajectory propagation and includes an improved physical description over other methods. The unconditional stability of the new method means that a unique numerical solution is always determined. The improved physical description of the trajectory provides a numerical solution and time derivatives that are continuous throughout the entire trajectory. The error of the continuous numerical solution is also known for the entire trajectory. Optimal control for maximizing thrust is also provided within the framework of the new method. Verification of the new approach is presented through a mathematical description and through numerical simulations. The mathematical description provides details of the sailcraft equations of motion, the numerical method used to solve the equations, and the formulation for implementing the equations of motion into the numerical solver. Previous work in the field is summarized to show that the new approach can act as a replacement to previous trajectory propagation methods. A code was developed to perform the simulations and it is also described in this document. Results of the simulations are compared to the flight data from the IKAROS mission. Comparison of the two sets of data show that the new approach is capable of accurately simulating sailcraft motion. Sailcraft and spacecraft simulations are compared to flight data and to other numerical solution techniques. The new formulation shows an increase in accuracy over a widely used trajectory propagation technique. Simulations for two-dimensional, three-dimensional, and variable attitude trajectories are presented to show the multiple capabilities of the new technique. An element of optimal control is also part of the new technique. An additional equation is added to the sailcraft equations of motion that maximizes thrust in a specific direction. A technical description and results of an example optimization problem are presented. The spacecraft attitude dynamics equations take the simulation a step further by providing control torques using the angular rate and acceleration outputs of the numerical formulation.

Simulation of Channel Segregation During Directional Solidification of In—75 wt pct Ga. Qualitative Comparison with In Situ Observations

NASA Astrophysics Data System (ADS)

Saad, Ali; Gandin, Charles-André; Bellet, Michel; Shevchenko, Natalia; Eckert, Sven

2015-11-01

Freckles are common defects in industrial casting. They result from thermosolutal convection due to buoyancy forces generated from density variations in the liquid. The present paper proposes a numerical analysis for the formation of channel segregation using the three-dimensional (3D) cellular automaton (CA)—finite element (FE) model. The model integrates kinetics laws for the nucleation and growth of a microstructure with the solution of the conservation equations for the casting, while introducing an intermediate modeling scale for a direct representation of the envelope of the dendritic grains. Directional solidification of a cuboid cell is studied. Its geometry, the alloy chosen as well as the process parameters are inspired from experimental observations recently reported in the literature. Snapshots of the convective pattern, the solute distribution, and the morphology of the growth front are qualitatively compared. Similitudes are found when considering the coupled 3D CAFE simulations. Limitations of the model to reach direct simulation of the experiments are discussed.

Solutions of the benchmark problems by the dispersion-relation-preserving scheme

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.; Shen, H.; Kurbatskii, K. A.; Auriault, L.

1995-01-01

The 7-point stencil Dispersion-Relation-Preserving scheme of Tam and Webb is used to solve all the six categories of the CAA benchmark problems. The purpose is to show that the scheme is capable of solving linear, as well as nonlinear aeroacoustics problems accurately. Nonlinearities, inevitably, lead to the generation of spurious short wave length numerical waves. Often, these spurious waves would overwhelm the entire numerical solution. In this work, the spurious waves are removed by the addition of artificial selective damping terms to the discretized equations. Category 3 problems are for testing radiation and outflow boundary conditions. In solving these problems, the radiation and outflow boundary conditions of Tam and Webb are used. These conditions are derived from the asymptotic solutions of the linearized Euler equations. Category 4 problems involved solid walls. Here, the wall boundary conditions for high-order schemes of Tam and Dong are employed. These conditions require the use of one ghost value per boundary point per physical boundary condition. In the second problem of this category, the governing equations, when written in cylindrical coordinates, are singular along the axis of the radial coordinate. The proper boundary conditions at the axis are derived by applying the limiting process of r approaches 0 to the governing equations. The Category 5 problem deals with the numerical noise issue. In the present approach, the time-independent mean flow solution is computed first. Once the residual drops to the machine noise level, the incident sound wave is turned on gradually. The solution is marched in time until a time-periodic state is reached. No exact solution is known for the Category 6 problem. Because of this, the problem is formulated in two totally different ways, first as a scattering problem then as a direct simulation problem. There is good agreement between the two numerical solutions. This offers confidence in the computed results. Both formulations are solved as initial value problems. As such, no Kutta condition is required at the trailing edge of the airfoil.

Adaptive Grid Generation for Numerical Solution of Partial Differential Equations.

DTIC Science & Technology

1983-12-01

numerical solution of fluid dynamics problems is presented. However, the method is applicable to the numer- ical evaluation of any partial differential...emphasis is being placed on numerical solution of the governing differential equations by finite difference methods . In the past two decades, considerable...original equations presented in that paper. The solution of the second problem is more difficult. 2 The method of Thompson et al. provides control for

Alternative formulations of the Laplace transform boundary element (LTBE) numerical method for the solution of diffusion-type equations

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

Moridis, G.

1992-03-01

The Laplace Transform Boundary Element (LTBE) method is a recently introduced numerical method, and has been used for the solution of diffusion-type PDEs. It completely eliminates the time dependency of the problem and the need for time discretization, yielding solutions numerical in space and semi-analytical in time. In LTBE solutions are obtained in the Laplace spare, and are then inverted numerically to yield the solution in time. The Stehfest and the DeHoog formulations of LTBE, based on two different inversion algorithms, are investigated. Both formulations produce comparable, extremely accurate solutions.

Direct Quantification of Solute Diffusivity in Agarose and Articular Cartilage Using Correlation Spectroscopy.

PubMed

Shoga, Janty S; Graham, Brian T; Wang, Liyun; Price, Christopher

2017-10-01

Articular cartilage is an avascular tissue; diffusive transport is critical for its homeostasis. While numerous techniques have been used to quantify diffusivity within porous, hydrated tissues and tissue engineered constructs, these techniques have suffered from issues regarding invasiveness and spatial resolution. In the present study, we implemented and compared two separate correlation spectroscopy techniques, fluorescence correlation spectroscopy (FCS) and raster image correlation spectroscopy (RICS), for the direct, and minimally-invasive quantification of fluorescent solute diffusion in agarose and articular cartilage. Specifically, we quantified the diffusional properties of fluorescein and Alexa Fluor 488-conjugated dextrans (3k and 10k) in aqueous solutions, agarose gels of varying concentration (i.e. 1, 3, 5%), and in different zones of juvenile bovine articular cartilage explants (i.e. superficial, middle, and deep). In agarose, properties of solute diffusion obtained via FCS and RICS were inversely related to molecule size, gel concentration, and applied strain. In cartilage, the diffusional properties of solutes were similarly dependent upon solute size, cartilage zone, and compressive strain; findings that agree with work utilizing other quantification techniques. In conclusion, this study established the utility of FCS and RICS as simple and minimally invasive techniques for quantifying microscale solute diffusivity within agarose constructs and articular cartilage explants.

Numerical solution of potential flow about arbitrary 2-dimensional multiple bodies

NASA Technical Reports Server (NTRS)

Thompson, J. F.; Thames, F. C.

1982-01-01

A procedure for the finite-difference numerical solution of the lifting potential flow about any number of arbitrarily shaped bodies is given. The solution is based on a technique of automatic numerical generation of a curvilinear coordinate system having coordinate lines coincident with the contours of all bodies in the field, regardless of their shapes and number. The effects of all numerical parameters involved are analyzed and appropriate values are recommended. Comparisons with analytic solutions for single Karman-Trefftz airfoils and a circular cylinder pair show excellent agreement. The technique of application of the boundary-fitted coordinate systems to the numerical solution of partial differential equations is illustrated.

Differential geometry based solvation model I: Eulerian formulation

NASA Astrophysics Data System (ADS)

Chen, Zhan; Baker, Nathan A.; Wei, G. W.

2010-11-01

This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the solvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By optimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second-order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to both experimental and theoretical results in the literature.

Differential geometry based solvation model I: Eulerian formulation

PubMed Central

Chen, Zhan; Baker, Nathan A.; Wei, G. W.

2010-01-01

This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the salvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By minimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to both experimental and theoretical results in the literature. PMID:20938489

An Investigation into Solution Verification for CFD-DEM

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

Fullmer, William D.; Musser, Jordan

This report presents the study of the convergence behavior of the computational fluid dynamicsdiscrete element method (CFD-DEM) method, specifically National Energy Technology Laboratory’s (NETL) open source MFiX code (MFiX-DEM) with a diffusion based particle-tocontinuum filtering scheme. In particular, this study focused on determining if the numerical method had a solution in the high-resolution limit where the grid size is smaller than the particle size. To address this uncertainty, fixed particle beds of two primary configurations were studied: i) fictitious beds where the particles are seeded with a random particle generator, and ii) instantaneous snapshots from a transient simulation of anmore » experimentally relevant problem. Both problems considered a uniform inlet boundary and a pressure outflow. The CFD grid was refined from a few particle diameters down to 1/6 th of a particle diameter. The pressure drop between two vertical elevations, averaged across the bed cross-section was considered as the system response quantity of interest. A least-squares regression method was used to extrapolate the grid-dependent results to an approximate “grid-free” solution in the limit of infinite resolution. The results show that the diffusion based scheme does yield a converging solution. However, the convergence is more complicated than encountered in simpler, single-phase flow problems showing strong oscillations and, at times, oscillations superimposed on top of globally non-monotonic behavior. The challenging convergence behavior highlights the importance of using at least four grid resolutions in solution verification problems so that (over-determined) regression-based extrapolation methods may be applied to approximate the grid-free solution. The grid-free solution is very important in solution verification and VVUQ exercise in general as the difference between it and the reference solution largely determines the numerical uncertainty. By testing different randomized particle configurations of the same general problem (for the fictitious case) or different instances of freezing a transient simulation, the numerical uncertainties appeared to be on the same order of magnitude as ensemble or time averaging uncertainties. By testing different drag laws, almost all cases studied show that model form uncertainty in this one, very important closure relation was larger than the numerical uncertainty, at least with a reasonable CFD grid, roughly five particle diameters. In this study, the diffusion width (filtering length scale) was mostly set at a constant of six particle diameters. A few exploratory tests were performed to show that similar convergence behavior was observed for diffusion widths greater than approximately two particle diameters. However, this subject was not investigated in great detail because determining an appropriate filter size is really a validation question which must be determined by comparison to experimental or highly accurate numerical data. Future studies are being considered targeting solution verification of transient simulations as well as validation of the filter size with direct numerical simulation data.« less

Breather management in the derivative nonlinear Schrödinger equation with variable coefficients

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

Zhong, Wei-Ping, E-mail: zhongwp6@126.com; Texas A&M University at Qatar, P.O. Box 23874 Doha; Belić, Milivoj

2015-04-15

We investigate breather solutions of the generalized derivative nonlinear Schrödinger (DNLS) equation with variable coefficients, which is used in the description of femtosecond optical pulses in inhomogeneous media. The solutions are constructed by means of the similarity transformation, which reduces a particular form of the generalized DNLS equation into the standard one, with constant coefficients. Examples of bright and dark breathers of different orders, that ride on finite backgrounds and may be related to rogue waves, are presented. - Highlights: • Exact solutions of a generalized derivative NLS equation are obtained. • The solutions are produced by means of amore » transformation to the usual integrable equation. • The validity of the solutions is verified by comparing them to numerical counterparts. • Stability of the solutions is checked by means of direct simulations. • The model applies to the propagation of ultrashort pulses in optical media.« less

Exact solution for four-order acousto-optic Bragg diffraction with arbitrary initial conditions.

PubMed

Pieper, Ron; Koslover, Deborah; Poon, Ting-Chung

2009-03-01

An exact solution to the four-order acousto-optic (AO) Bragg diffraction problem with arbitrary initial conditions compatible with exact Bragg angle incident light is developed. The solution, obtained by solving a 4th-order differential equation, is formalized into a transition matrix operator predicting diffracted light orders at the exit of the AO cell in terms of the same diffracted light orders at the entrance. It is shown that the transition matrix is unitary and that this unitary matrix condition is sufficient to guarantee energy conservation. A comparison of analytical solutions with numerical predictions validates the formalism. Although not directly related to the approach used to obtain the solution, it was discovered that all four generated eigenvalues from the four-order AO differential matrix operator are expressed simply in terms of Euclid's Divine Proportion.

Spurious Numerical Solutions Of Differential Equations

NASA Technical Reports Server (NTRS)

Lafon, A.; Yee, H. C.

1995-01-01

Paper presents detailed study of spurious steady-state numerical solutions of differential equations that contain nonlinear source terms. Main objectives of this study are (1) to investigate how well numerical steady-state solutions of model nonlinear reaction/convection boundary-value problem mimic true steady-state solutions and (2) to relate findings of this investigation to implications for interpretation of numerical results from computational-fluid-dynamics algorithms and computer codes used to simulate reacting flows.

Numerical Simulation of Subsonic and Transonic Propeller Flow. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Snyder, Aaron

1988-01-01

The numerical simulation of 3-D transonic flow about a system of propeller blades is investigated. In particular, it is shown that the use of helical coordinates significantly simplifies the form of the governing equation when the propeller system is assumed to be surrounded by an irrotational flow field of an inviscid fluid. The unsteady small disturbance equation, valid for lightly loaded blades and expressed in helical coordinates, is derived from the general blade-fixed potential equation, given for an arbitrary coordinate system. The use of a coordinate system which inherently adapts to the mean flow results in a disturbance equation requiring relatively few terms to accurately model the physics of the flow. Furthermore, the helical coordinate system presented here is novel in that it is periodic in the circumferential direction while, simultaneously, maintaining orthogonal properties at the mean blade locations. The periodic characteristic allows a complete cascade of blades to be treated, and the orthogonality property affords straightforward treatment of blade boundary conditions. An ADI numerical scheme is used to compute the solution of the steady flow as an asymptotic limit of an unsteady flow. As an example of the method, solutions are presented for subsonic and transonic flow about a 5 percent thick bicircular arc blade of an 8-bladed cascade. Both high and low advance ratio cases are computed and include a lifting as well as nonlifting cases. The nonlifting solutions obtained are compared to solutions from a Euler code.

Strongly localized dark modes in binary discrete media with cubic-quintic nonlinearity within the anti-continuum limit

NASA Astrophysics Data System (ADS)

Taib, L. Abdul; Hadi, M. S. Abdul; Umarov, B. A.

2017-12-01

The existence of dark strongly localized modes of binary discrete media with cubic-quintic nonlinearity is numerically demonstrated by solving the relevant discrete nonlinear Schrödinger equations. In the model, the coupling coefficients between adjacent sites are set to be relatively small representing the anti-continuum limit. In addition, approximated analytical solutions for vectorial solitons with various topologies are derived. Stability analysis of the localized states was performed using the standard linearized eigenfrequency problem. The prediction from the stability analysis are furthermore verified by direct numerical integrations.

Improved numerical methods for turbulent viscous flows aerothermal modeling program, phase 2

NASA Technical Reports Server (NTRS)

Karki, K. C.; Patankar, S. V.; Runchal, A. K.; Mongia, H. C.

1988-01-01

The details of a study to develop accurate and efficient numerical schemes to predict complex flows are described. In this program, several discretization schemes were evaluated using simple test cases. This assessment led to the selection of three schemes for an in-depth evaluation based on two-dimensional flows. The scheme with the superior overall performance was incorporated in a computer program for three-dimensional flows. To improve the computational efficiency, the selected discretization scheme was combined with a direct solution approach in which the fluid flow equations are solved simultaneously rather than sequentially.

Effective equations and the inverse cascade theory for Kolmogorov flows

NASA Technical Reports Server (NTRS)

Weinan, E.; Shu, Chi-Wang

1992-01-01

We study the two dimensional Kolmogorov flows in the limit as the forcing frequency goes to infinity. Direct numerical simulation indicates that the low frequency energy spectrum evolves to a universal kappa (exp -4) decay law. We derive effective equations governing the behavior of the large scale flow quantities. We then present numerical evidence that with smooth initial data, the solution to the effective equation develops a kappa (exp -4) type singularity at a finite time. This gives a convenient explanation for the kappa (exp -4) decay law exhibited by the original Kolmogorov flows.

Numerical Solution of the Navier-Stokes Equations for Steady Magnetohydrodynamic Flow Between Two Parallel Porous Plates with an Angular Velocity

NASA Astrophysics Data System (ADS)

Delhi Babu, R.; Ganesh, S.

2018-04-01

The Steady Laminar stream of an electrically directing thick, incompressible liquid between two parallel permeable plates of a divert within the sight of a transverse attractive field with an angular velocity when the liquid is being pulled back through both the dividers of the channel at a similar rate with a precise speed is examined. Numerical arrangement is acquired for various estimations of R (Suction Reynolds number) utilizing R-K Gill's technique and the diagrams of dimensionless functions f ' and f have been drawn.

Wave Number Selection for Incompressible Parallel Jet Flows Periodic in Space

NASA Technical Reports Server (NTRS)

Miles, Jeffrey Hilton

1997-01-01

The temporal instability of a spatially periodic parallel flow of an incompressible inviscid fluid for various jet velocity profiles is studied numerically using Floquet Analysis. The transition matrix at the end of a period is evaluated by direct numerical integration. For verification, a method based on approximating a continuous function by a series of step functions was used. Unstable solutions were found only over a limited range of wave numbers and have a band type structure. The results obtained are analogous to the behavior observed in systems exhibiting complexity at the edge of order and chaos.

Numerical solution of a conspicuous consumption model with constant control delay☆

PubMed Central

Huschto, Tony; Feichtinger, Gustav; Hartl, Richard F.; Kort, Peter M.; Sager, Sebastian; Seidl, Andrea

2011-01-01

We derive optimal pricing strategies for conspicuous consumption products in periods of recession. To that end, we formulate and investigate a two-stage economic optimal control problem that takes uncertainty of the recession period length and delay effects of the pricing strategy into account. This non-standard optimal control problem is difficult to solve analytically, and solutions depend on the variable model parameters. Therefore, we use a numerical result-driven approach. We propose a structure-exploiting direct method for optimal control to solve this challenging optimization problem. In particular, we discretize the uncertainties in the model formulation by using scenario trees and target the control delays by introduction of slack control functions. Numerical results illustrate the validity of our approach and show the impact of uncertainties and delay effects on optimal economic strategies. During the recession, delayed optimal prices are higher than the non-delayed ones. In the normal economic period, however, this effect is reversed and optimal prices with a delayed impact are smaller compared to the non-delayed case. PMID:22267871

The conformal transformation of an airfoil into a straight line and its application to the inverse problem of airfoil theory

NASA Technical Reports Server (NTRS)

Mutterperl, William

1944-01-01

A method of conformal transformation is developed that maps an airfoil into a straight line, the line being chosen as the extended chord line of the airfoil. The mapping is accomplished by operating directly with the airfoil ordinates. The absence of any preliminary transformation is found to shorten the work substantially over that of previous methods. Use is made of the superposition of solutions to obtain a rigorous counterpart of the approximate methods of thin-airfoils theory. The method is applied to the solution of the direct and inverse problems for arbitrary airfoils and pressure distributions. Numerical examples are given. Applications to more general types of regions, in particular to biplanes and to cascades of airfoils, are indicated. (author)

Rapid computation of directional wellbore drawdown in a confined aquifer via Poisson resummation

NASA Astrophysics Data System (ADS)

Blumenthal, Benjamin J.; Zhan, Hongbin

2016-08-01

We have derived a rapidly computed analytical solution for drawdown caused by a partially or fully penetrating directional wellbore (vertical, horizontal, or slant) via Green's function method. The mathematical model assumes an anisotropic, homogeneous, confined, box-shaped aquifer. Any dimension of the box can have one of six possible boundary conditions: 1) both sides no-flux; 2) one side no-flux - one side constant-head; 3) both sides constant-head; 4) one side no-flux; 5) one side constant-head; 6) free boundary conditions. The solution has been optimized for rapid computation via Poisson Resummation, derivation of convergence rates, and numerical optimization of integration techniques. Upon application of the Poisson Resummation method, we were able to derive two sets of solutions with inverse convergence rates, namely an early-time rapidly convergent series (solution-A) and a late-time rapidly convergent series (solution-B). From this work we were able to link Green's function method (solution-B) back to image well theory (solution-A). We then derived an equation defining when the convergence rate between solution-A and solution-B is the same, which we termed the switch time. Utilizing the more rapidly convergent solution at the appropriate time, we obtained rapid convergence at all times. We have also shown that one may simplify each of the three infinite series for the three-dimensional solution to 11 terms and still maintain a maximum relative error of less than 10-14.

Formation mechanism of axial macrosegregation of primary phases induced by a static magnetic field during directional solidification

PubMed Central

Li, Xi; Fautrelle, Yves; Ren, Zhongming; Moreau, Rene

2017-01-01

Understanding the macrosegregation formed by applying magnetic fields is of high commercial importance. This work investigates how static magnetic fields control the solute and primary phase distributions in four directionally solidified alloys (i.e., Al-Cu, Al-Si, Al-Ni and Zn-Cu alloys). Experimental results demonstrate that significant axial macrosegregation of the solute and primary phases (i.e., Al2Cu, Si, Al3Ni and Zn5Cu phases) occurs at the initial solidification stage of the samples. This finding is accompanied by two interface transitions in the mushy zone: quasi planar → sloping → quasi planar. The amplitude of the macrosegregation of the primary phases under the magnetic field is related to the magnetic field intensity, temperature gradient and growth speed. The corresponding numerical simulations present a unidirectional thermoelectric (TE) magnetic convection pattern in the mushy zone as a consequence of the interaction between the magnetic field and TE current. Furthermore, a model is proposed to explain the peculiar macrosegregation phenomenon by considering the effect of the forced TE magnetic convection on the solute distribution. The present study not only offers a new approach to control the solute distribution by applying a static magnetic field but also facilitates the understanding of crystal growth in the solute that is controlled by the static magnetic field during directional solidification. PMID:28367991

Analytical and Numerical Solutions of Generalized Fokker-Planck Equations - Final Report

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

Prinja, Anil K.

The overall goal of this project was to develop advanced theoretical and numerical techniques to quantitatively describe the spreading of a collimated beam of charged particles in space, in angle, and in energy, as a result of small deflection, small energy transfer Coulomb collisions with the target nuclei and electrons. Such beams arise in several applications of great interest in nuclear engineering, and include electron and ion radiotherapy, ion beam modification of materials, accelerator transmutation of waste, and accelerator production of tritium, to name some important candidates. These applications present unique and difficult modeling challenges, but from the outset aremore » amenable to the language of ''transport theory'', which is very familiar to nuclear engineers and considerably less-so to physicists and material scientists. Thus, our approach has been to adopt a fundamental description based on transport equations, but the forward peakedness associated with charged particle interactions precludes a direct application of solution methods developed for neutral particle transport. Unique problem formulations and solution techniques are necessary to describe the transport and interaction of charged particles. In particular, we have developed the Generalized Fokker-Planck (GFP) approach to describe the angular and radial spreading of a collimated beam and a renormalized transport model to describe the energy-loss straggling of an initially monoenergetic distribution. Both analytic and numerical solutions have been investigated and in particular novel finite element numerical methods have been developed. In the first phase of the project, asymptotic methods were used to develop closed form solutions to the GFP equation for different orders of expansion, and was described in a previous progress report. In this final report we present a detailed description of (i) a novel energy straggling model based on a Fokker-Planck approximation but which is adapted for a multigroup transport setting, and (ii) two unique families of discontinuous finite element schemes, one linear and the other nonlinear.« less

Direct modeling for computational fluid dynamics

NASA Astrophysics Data System (ADS)

Xu, Kun

2015-06-01

All fluid dynamic equations are valid under their modeling scales, such as the particle mean free path and mean collision time scale of the Boltzmann equation and the hydrodynamic scale of the Navier-Stokes (NS) equations. The current computational fluid dynamics (CFD) focuses on the numerical solution of partial differential equations (PDEs), and its aim is to get the accurate solution of these governing equations. Under such a CFD practice, it is hard to develop a unified scheme that covers flow physics from kinetic to hydrodynamic scales continuously because there is no such governing equation which could make a smooth transition from the Boltzmann to the NS modeling. The study of fluid dynamics needs to go beyond the traditional numerical partial differential equations. The emerging engineering applications, such as air-vehicle design for near-space flight and flow and heat transfer in micro-devices, do require further expansion of the concept of gas dynamics to a larger domain of physical reality, rather than the traditional distinguishable governing equations. At the current stage, the non-equilibrium flow physics has not yet been well explored or clearly understood due to the lack of appropriate tools. Unfortunately, under the current numerical PDE approach, it is hard to develop such a meaningful tool due to the absence of valid PDEs. In order to construct multiscale and multiphysics simulation methods similar to the modeling process of constructing the Boltzmann or the NS governing equations, the development of a numerical algorithm should be based on the first principle of physical modeling. In this paper, instead of following the traditional numerical PDE path, we introduce direct modeling as a principle for CFD algorithm development. Since all computations are conducted in a discretized space with limited cell resolution, the flow physics to be modeled has to be done in the mesh size and time step scales. Here, the CFD is more or less a direct construction of discrete numerical evolution equations, where the mesh size and time step will play dynamic roles in the modeling process. With the variation of the ratio between mesh size and local particle mean free path, the scheme will capture flow physics from the kinetic particle transport and collision to the hydrodynamic wave propagation. Based on the direct modeling, a continuous dynamics of flow motion will be captured in the unified gas-kinetic scheme. This scheme can be faithfully used to study the unexplored non-equilibrium flow physics in the transition regime.

A study of various methods for calculating locations of lightning events

NASA Technical Reports Server (NTRS)

Cannon, John R.

1995-01-01

This article reports on the results of numerical experiments on finding the location of lightning events using different numerical methods. The methods include linear least squares, nonlinear least squares, statistical estimations, cluster analysis and angular filters and combinations of such techniques. The experiments involved investigations of methods for excluding fake solutions which are solutions that appear to be reasonable but are in fact several kilometers distant from the actual location. Some of the conclusions derived from the study are that bad data produces fakes, that no fool-proof method of excluding fakes was found, that a short base-line interferometer under development at Kennedy Space Center to measure the direction cosines of an event shows promise as a filter for excluding fakes. The experiments generated a number of open questions, some of which are discussed at the end of the report.

A method of measuring the effective thermal conductivity of thermoplastic foams

NASA Astrophysics Data System (ADS)

Asséko, André Chateau Akué; Cosson, Benoit; Chaki, Salim; Duborper, Clément; Lacrampe, Marie-France; Krawczak, Patricia

2017-10-01

An inverse method for determining the in-plane effective thermal conductivity of porous thermoplastics was implemented by coupling infrared thermography experiments and numerical solution of heat transfer in straight fins having temperature-dependent convective heat transfer coefficient. The obtained effective thermal conductivity values were compared with previous results obtained using a numerical solution based on periodic homogenization techniques (NSHT) in which the microstructure heterogeneity of extruded polymeric polyethylene (PE) foam in which pores are filled with air with different levels of open and closed porosity was taken into account and Transient Plane Source Technique (TPS) in order to verify the accuracy of the proposed method. The new method proposed in the present study is in good agreement with both NSHT and TPS. It is also applicable to structural materials such as composites, e.g. unidirectional fiber-reinforced plastics, where heat transfer is very different according to the fiber direction (parallel or transverse to the fibers).

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

Rubin, M. B.; Vorobiev, O.; Vitali, E.

Here, a large deformation thermomechanical model is developed for shock loading of a material that can exhibit elastic and inelastic anisotropy. Use is made of evolution equations for a triad of microstructural vectors m i(i=1,2,3) which model elastic deformations and directions of anisotropy. Specific constitutive equations are presented for a material with orthotropic elastic response. The rate of inelasticity depends on an orthotropic yield function that can be used to model weak fault planes with failure in shear and which exhibits a smooth transition to isotropic response at high compression. Moreover, a robust, strongly objective numerical algorithm is proposed formore » both rate-independent and rate-dependent response. The predictions of the continuum model are examined by comparison with exact steady-state solutions. Also, the constitutive equations are used to obtain a simplified continuum model of jointed rock which is compared with high fidelity numerical solutions that model a persistent system of joints explicitly in the rock medium.« less

A new anisotropic mesh adaptation method based upon hierarchical a posteriori error estimates

NASA Astrophysics Data System (ADS)

Huang, Weizhang; Kamenski, Lennard; Lang, Jens

2010-03-01

A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in some metric space, with the metric tensor being computed based on hierarchical a posteriori error estimates. A global hierarchical error estimate is employed in this study to obtain reliable directional information of the solution. Instead of solving the global error problem exactly, which is costly in general, we solve it iteratively using the symmetric Gauß-Seidel method. Numerical results show that a few GS iterations are sufficient for obtaining a reasonably good approximation to the error for use in anisotropic mesh adaptation. The new method is compared with several strategies using local error estimators or recovered Hessians. Numerical results are presented for a selection of test examples and a mathematical model for heat conduction in a thermal battery with large orthotropic jumps in the material coefficients.

Reduced-Order Direct Numerical Simulation of Solute Transport in Porous Media

NASA Astrophysics Data System (ADS)

Mehmani, Yashar; Tchelepi, Hamdi

2017-11-01

Pore-scale models are an important tool for analyzing fluid dynamics in porous materials (e.g., rocks, soils, fuel cells). Current direct numerical simulation (DNS) techniques, while very accurate, are computationally prohibitive for sample sizes that are statistically representative of the porous structure. Reduced-order approaches such as pore-network models (PNM) aim to approximate the pore-space geometry and physics to remedy this problem. Predictions from current techniques, however, have not always been successful. This work focuses on single-phase transport of a passive solute under advection-dominated regimes and delineates the minimum set of approximations that consistently produce accurate PNM predictions. Novel network extraction (discretization) and particle simulation techniques are developed and compared to high-fidelity DNS simulations for a wide range of micromodel heterogeneities and a single sphere pack. Moreover, common modeling assumptions in the literature are analyzed and shown that they can lead to first-order errors under advection-dominated regimes. This work has implications for optimizing material design and operations in manufactured (electrodes) and natural (rocks) porous media pertaining to energy systems. This work was supported by the Stanford University Petroleum Research Institute for Reservoir Simulation (SUPRI-B).

A new time domain random walk method for solute transport in 1-D heterogeneous media

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

Banton, O.; Delay, F.; Porel, G.

A new method to simulate solute transport in 1-D heterogeneous media is presented. This time domain random walk method (TDRW), similar in concept to the classical random walk method, calculates the arrival time of a particle cloud at a given location (directly providing the solute breakthrough curve). The main advantage of the method is that the restrictions on the space increments and the time steps which exist with the finite differences and random walk methods are avoided. In a homogeneous zone, the breakthrough curve (BTC) can be calculated directly at a given distance using a few hundred particles or directlymore » at the boundary of the zone. Comparisons with analytical solutions and with the classical random walk method show the reliability of this method. The velocity and dispersivity calculated from the simulated results agree within two percent with the values used as input in the model. For contrasted heterogeneous media, the random walk can generate high numerical dispersion, while the time domain approach does not.« less

Direct computation of stochastic flow in reservoirs with uncertain parameters

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

Dainton, M.P.; Nichols, N.K.; Goldwater, M.H.

1997-01-15

A direct method is presented for determining the uncertainty in reservoir pressure, flow, and net present value (NPV) using the time-dependent, one phase, two- or three-dimensional equations of flow through a porous medium. The uncertainty in the solution is modelled as a probability distribution function and is computed from given statistical data for input parameters such as permeability. The method generates an expansion for the mean of the pressure about a deterministic solution to the system equations using a perturbation to the mean of the input parameters. Hierarchical equations that define approximations to the mean solution at each point andmore » to the field convariance of the pressure are developed and solved numerically. The procedure is then used to find the statistics of the flow and the risked value of the field, defined by the NPV, for a given development scenario. This method involves only one (albeit complicated) solution of the equations and contrasts with the more usual Monte-Carlo approach where many such solutions are required. The procedure is applied easily to other physical systems modelled by linear or nonlinear partial differential equations with uncertain data. 14 refs., 14 figs., 3 tabs.« less

Nano-particle drag prediction at low Reynolds number using a direct Boltzmann-BGK solution approach

NASA Astrophysics Data System (ADS)

Evans, B.

2018-01-01

This paper outlines a novel approach for solution of the Boltzmann-BGK equation describing molecular gas dynamics applied to the challenging problem of drag prediction of a 2D circular nano-particle at transitional Knudsen number (0.0214) and low Reynolds number (0.25-2.0). The numerical scheme utilises a discontinuous-Galerkin finite element discretisation for the physical space representing the problem particle geometry and a high order discretisation for molecular velocity space describing the molecular distribution function. The paper shows that this method produces drag predictions that are aligned well with the range of drag predictions for this problem generated from the alternative numerical approaches of molecular dynamics codes and a modified continuum scheme. It also demonstrates the sensitivity of flow-field solutions and therefore drag predictions to the wall absorption parameter used to construct the solid wall boundary condition used in the solver algorithm. The results from this work has applications in fields ranging from diagnostics and therapeutics in medicine to the fields of semiconductors and xerographics.

A boundary integral equation method using auxiliary interior surface approach for acoustic radiation and scattering in two dimensions.

PubMed

Yang, S A

2002-10-01

This paper presents an effective solution method for predicting acoustic radiation and scattering fields in two dimensions. The difficulty of the fictitious characteristic frequency is overcome by incorporating an auxiliary interior surface that satisfies certain boundary condition into the body surface. This process gives rise to a set of uniquely solvable boundary integral equations. Distributing monopoles with unknown strengths over the body and interior surfaces yields the simple source formulation. The modified boundary integral equations are further transformed to ordinary ones that contain nonsingular kernels only. This implementation allows direct application of standard quadrature formulas over the entire integration domain; that is, the collocation points are exactly the positions at which the integration points are located. Selecting the interior surface is an easy task. Moreover, only a few corresponding interior nodal points are sufficient for the computation. Numerical calculations consist of the acoustic radiation and scattering by acoustically hard elliptic and rectangular cylinders. Comparisons with analytical solutions are made. Numerical results demonstrate the efficiency and accuracy of the current solution method.

Comparison of updated Lagrangian FEM with arbitrary Lagrangian Eulerian method for 3D thermo-mechanical extrusion of a tube profile

NASA Astrophysics Data System (ADS)

Kronsteiner, J.; Horwatitsch, D.; Zeman, K.

2017-10-01

Thermo-mechanical numerical modelling and simulation of extrusion processes faces several serious challenges. Large plastic deformations in combination with a strong coupling of thermal with mechanical effects leads to a high numerical demand for the solution as well as for the handling of mesh distortions. The two numerical methods presented in this paper also reflect two different ways to deal with mesh distortions. Lagrangian Finite Element Methods (FEM) tackle distorted elements by building a new mesh (called re-meshing) whereas Arbitrary Lagrangian Eulerian (ALE) methods use an "advection" step to remap the solution from the distorted to the undistorted mesh. Another difference between conventional Lagrangian and ALE methods is the separate treatment of material and mesh in ALE, allowing the definition of individual velocity fields. In theory, an ALE formulation contains the Eulerian formulation as a subset to the Lagrangian description of the material. The investigations presented in this paper were dealing with the direct extrusion of a tube profile using EN-AW 6082 aluminum alloy and a comparison of experimental with Lagrangian and ALE results. The numerical simulations cover the billet upsetting and last until one third of the billet length is extruded. A good qualitative correlation of experimental and numerical results could be found, however, major differences between Lagrangian and ALE methods concerning thermo-mechanical coupling lead to deviations in the thermal results.

Recovery of the parameters of cancellous bone by inversion of effective velocities, and transmission and reflection coefficients

NASA Astrophysics Data System (ADS)

Buchanan, James L.; Gilbert, Robert P.; Ou, Miao-jung Y.

2011-12-01

Estimating the parameters of an elastic or poroelastic medium from reflected or transmitted acoustic data is an important but difficult problem. Use of the Nelder-Mead simplex method to minimize an objective function measuring the discrepancy between some observable and its value calculated from a model for a trial set of parameters has been tried by several authors. In this paper, the difficulty with this direct approach, which is the existence of numerous local minima of the objective function, is documented for the in vitro experiment in which a specimen in a water tank is subject to an ultrasonic pulse. An indirect approach, based on the numerical solution of the equations for a set of ‘effective’ velocities and transmission coefficients, is then observed empirically to ameliorate the difficulties posed by the direct approach.

Numerical Algorithm for Delta of Asian Option

PubMed Central

Zhang, Boxiang; Yu, Yang; Wang, Weiguo

2015-01-01

We study the numerical solution of the Greeks of Asian options. In particular, we derive a close form solution of Δ of Asian geometric option and use this analytical form as a control to numerically calculate Δ of Asian arithmetic option, which is known to have no explicit close form solution. We implement our proposed numerical method and compare the standard error with other classical variance reduction methods. Our method provides an efficient solution to the hedging strategy with Asian options. PMID:26266271

Numerical simulation of freckle formation in directional solidification of binary alloys

NASA Technical Reports Server (NTRS)

Felicelli, Sergio D.; Heinrich, Juan C.; Poirier, David R.

1992-01-01

A mathematical model of solidification is presented which simulates the formation of segregation models known as 'freckles' during directional solidification of binary alloys. The growth of the two-phase or dendritic zone is calculated by solving the coupled equations of momentum, energy, and solute transport, as well as maintaining the thermodynamic constraints dictated by the phase diagram of the alloy. Calculations for lead-tin alloys show that the thermosolutal convection in the dendritic zone during solidification can produce heavily localized inhomogeneities in the composition of the final alloy.

Stability and Hopf bifurcation in a simplified BAM neural network with two time delays.

PubMed

Cao, Jinde; Xiao, Min

2007-03-01

Various local periodic solutions may represent different classes of storage patterns or memory patterns, and arise from the different equilibrium points of neural networks (NNs) by applying Hopf bifurcation technique. In this paper, a bidirectional associative memory NN with four neurons and multiple delays is considered. By applying the normal form theory and the center manifold theorem, analysis of its linear stability and Hopf bifurcation is performed. An algorithm is worked out for determining the direction and stability of the bifurcated periodic solutions. Numerical simulation results supporting the theoretical analysis are also given.

Noniterative three-dimensional grid generation using parabolic partial differential equations

NASA Technical Reports Server (NTRS)

Edwards, T. A.

1985-01-01

A new algorithm for generating three-dimensional grids has been developed and implemented which numerically solves a parabolic partial differential equation (PDE). The solution procedure marches outward in two coordinate directions, and requires inversion of a scalar tridiagonal system in the third. Source terms have been introduced to control the spacing and angle of grid lines near the grid boundaries, and to control the outer boundary point distribution. The method has been found to generate grids about 100 times faster than comparable grids generated via solution of elliptic PDEs, and produces smooth grids for finite-difference flow calculations.

Numerical simulation of KdV equation by finite difference method

NASA Astrophysics Data System (ADS)

Yokus, A.; Bulut, H.

2018-05-01

In this study, the numerical solutions to the KdV equation with dual power nonlinearity by using the finite difference method are obtained. Discretize equation is presented in the form of finite difference operators. The numerical solutions are secured via the analytical solution to the KdV equation with dual power nonlinearity which is present in the literature. Through the Fourier-Von Neumann technique and linear stable, we have seen that the FDM is stable. Accuracy of the method is analyzed via the L2 and L_{∞} norm errors. The numerical, exact approximations and absolute error are presented in tables. We compare the numerical solutions with the exact solutions and this comparison is supported with the graphic plots. Under the choice of suitable values of parameters, the 2D and 3D surfaces for the used analytical solution are plotted.

Finite-analytic numerical solution of heat transfer in two-dimensional cavity flow

NASA Technical Reports Server (NTRS)

Chen, C.-J.; Naseri-Neshat, H.; Ho, K.-S.

1981-01-01

Heat transfer in cavity flow is numerically analyzed by a new numerical method called the finite-analytic method. The basic idea of the finite-analytic method is the incorporation of local analytic solutions in the numerical solutions of linear or nonlinear partial differential equations. In the present investigation, the local analytic solutions for temperature, stream function, and vorticity distributions are derived. When the local analytic solution is evaluated at a given nodal point, it gives an algebraic relationship between a nodal value in a subregion and its neighboring nodal points. A system of algebraic equations is solved to provide the numerical solution of the problem. The finite-analytic method is used to solve heat transfer in the cavity flow at high Reynolds number (1000) for Prandtl numbers of 0.1, 1, and 10.

Determination of unknown coefficient in a non-linear elliptic problem related to the elastoplastic torsion of a bar

NASA Astrophysics Data System (ADS)

Hasanov, Alemdar; Erdem, Arzu

2008-08-01

The inverse problem of determining the unknown coefficient of the non-linear differential equation of torsional creep is studied. The unknown coefficient g = g({xi}2) depends on the gradient{xi} : = |{nabla}u| of the solution u(x), x [isin] {Omega} [sub] Rn, of the direct problem. It is proved that this gradient is bounded in C-norm. This permits one to choose the natural class of admissible coefficients for the considered inverse problem. The continuity in the norm of the Sobolev space H1({Omega}) of the solution u(x;g) of the direct problem with respect to the unknown coefficient g = g({xi}2) is obtained in the following sense: ||u(x;g) - u(x;gm)||1 [->] 0 when gm({eta}) [->] g({eta}) point-wise as m [->] {infty}. Based on these results, the existence of a quasi-solution of the inverse problem in the considered class of admissible coefficients is obtained. Numerical examples related to determination of the unknown coefficient are presented.

Development of a model of space station solar array

NASA Technical Reports Server (NTRS)

Bosela, Paul A.

1990-01-01

Space structures, such as the space station solar arrays, must be extremely lightweight, flexible structures. Accurate prediction of the natural frequencies and mode shapes is essential for determining the structural adequacy of components, and designing a control system. The tension preload in the blanket of photovoltaic solar collectors, and the free/free boundary conditions of a structure in space, causes serious reservations on the use of standard finite element techniques of solution. In particular, a phenomena known as grounding, or false stiffening, of the stiffness matrix occurs during rigid body rotation. The grounding phenomena is examined in detail. Numerous stiffness matrices developed by others are examined for rigid body rotation capability, and found lacking. Various techniques are used for developing new stiffness matrices from the rigorous solutions of the differential equations, including the solution of the directed force problem. A new directed force stiffness matrix developed by the author provides all the rigid body capabilities for the beam in space.

A reduced-order model from high-dimensional frictional hysteresis

PubMed Central

Biswas, Saurabh; Chatterjee, Anindya

2014-01-01

Hysteresis in material behaviour includes both signum nonlinearities as well as high dimensionality. Available models for component-level hysteretic behaviour are empirical. Here, we derive a low-order model for rate-independent hysteresis from a high-dimensional massless frictional system. The original system, being given in terms of signs of velocities, is first solved incrementally using a linear complementarity problem formulation. From this numerical solution, to develop a reduced-order model, basis vectors are chosen using the singular value decomposition. The slip direction in generalized coordinates is identified as the minimizer of a dissipation-related function. That function includes terms for frictional dissipation through signum nonlinearities at many friction sites. Luckily, it allows a convenient analytical approximation. Upon solution of the approximated minimization problem, the slip direction is found. A final evolution equation for a few states is then obtained that gives a good match with the full solution. The model obtained here may lead to new insights into hysteresis as well as better empirical modelling thereof. PMID:24910522

A stability analysis on forced convection boundary layer stagnation-point slip flow in Darcy-Forchheimer porous medium towards a shrinking sheet

NASA Astrophysics Data System (ADS)

Bakar, Shahirah Abu; Arifin, Norihan Md; Ali, Fadzilah Md; Bachok, Norfifah; Nazar, Roslinda

2017-08-01

The stagnation-point flow over a shrinking sheet in Darcy-Forchheimer porous medium is numerically studied. The governing partial differential equations are transformed into ordinary differential equations using a similarity transformation, and then solved numerically by using shooting technique method with Maple implementation. Dual solutions are observed in a certain range of the shrinking parameter. Regarding on numerical solutions, we prepared stability analysis to identify which solution is stable between non-unique solutions by bvp4c solver in Matlab. Further we obtain numerical results or each solution, which enable us to discuss the features of the respective solutions.

A combined numerical and experimental framework for determining permeability properties of the arterial media.

PubMed

Comerford, A; Chooi, K Y; Nowak, M; Weinberg, P D; Sherwin, S J

2015-04-01

The medial layer of the arterial wall may play an important role in the regulation of water and solute transport across the wall. In particular, a high medial resistance to transport could cause accumulation of lipid-carrying molecules in the inner wall. In this study, the water transport properties of medial tissue were characterised in a numerical model, utilising experimentally obtained data for the medial microstructure and the relative permeability of different constituents. For the model, a new solver for flow in porous materials, based on a high-order splitting scheme, was implemented in the spectral/hp element library nektar++ and validated. The data were obtained by immersing excised aortic bifurcations in a solution of fluorescent protein tracer and subsequently imaging them with a confocal microscope. Cuboidal regions of interest were selected in which the microstructure and relative permeability of different structures were transformed to a computational mesh. Impermeable objects were treated fictitiously in the numerical scheme. On this cube, a pressure drop was applied in the three coordinate directions and the principal components of the permeability tensor were determined. The reconstructed images demonstrated the arrangement of elastic lamellae and interspersed smooth muscle cells in rat aortic media; the distribution and alignment of the smooth muscle cells varied spatially within the extracellular matrix. The numerical simulations highlighted that the heterogeneity of the medial structure is important in determining local water transport properties of the tissue, resulting in regional and directional variation of the permeability tensor. A major factor in this variation is the alignment and density of smooth muscle cells in the media, particularly adjacent to the adventitial layer.

Numerical simulations of electromagnetic scattering by Solar system objects

NASA Astrophysics Data System (ADS)

Dlugach, Janna M.

2016-11-01

Having been profoundly stimulated by the seminal work of Viktor V. Sobolev, I have been involved in multi-decadal research in the fields of radiative transfer, electromagnetic scattering by morphologically complex particles and particulate media, and planetary remote sensing. Much of this research has been done in close collaboration with other "descendants" of Academician Sobolev. This tutorial paper gives a representative overview of the results of extensive numerical simulations (in the vast majority carried out in collaboration with Michael Mishchenko) used to analyze remote-sensing observations of Solar system objects and based on highly accurate methods of the radiative transfer theory and direct computer solvers of the Maxwell equations. Using the atmosphere of Jupiter as a proving ground and performing T-matrix and radiative-transfer calculations helps demonstrate the strong effect of aerosol-particle shapes on the accuracy of remote-sensing retrievals. I then discuss the application of the T-matrix method, a numerically exact solution of the vector radiative transfer equation, and the theory of coherent backscattering to an analysis of polarimetric radar observations of Saturn's rings. Numerical modeling performed by using the superposition T-matrix method in application to cometary dust in the form of aggregates serves to reproduce the results of polarimetric observations of the distant comet C/2010 S1. On the basis of direct computer solutions of the Maxwell equations, it is demonstrated that all backscattering effects predicted by the low-density theories of radiative transfer and coherent backscattering can also be identified for media with volume packing densities typically encountered in natural and artificial environments. This result implies that spectacular opposition effects observed for some high-albedo atmoshereless Solar system bodies can be attributed to coherent backscattering of sunlight by regolith layers composed of microscopic particles.

Effect of Channel Geometry and Properties of a Vapor-Gas Mixture on Volume Condensation in a Flow through a Nozzle

NASA Astrophysics Data System (ADS)

Sidorov, A. A.; Yastrebov, A. K.

2018-01-01

A method of direct numerical solution of the kinetic equation for the droplet size distribution function was used for the numerical investigation of volume condensation in a supersonic vapor-gas flow. Distributions of temperature for the gas phase and droplets, degree of supersaturation, pressure, fraction of droplets by weight, the number of droplets per unit mass, and of the nucleation rate along the channel were determined. The influence of nozzle geometry, mixture composition, and temperature dependence of the mixture properties on the investigated process was evaluated. It has been found that the nozzle divergence angle determines the vapor-gas mixture expansion rate: an increase in the divergence angle enhances the temperature decrease rate and the supersaturation degree raise rate. With an increase or decrease in the partial pressure of incondensable gas, the droplet temperature approaches the gas phase temperature or the saturation temperature at the partial gas pressure, respectively. A considerable effect of the temperature dependence of the liquid surface tension and properties on gas phase parameters and the integral characteristics of condensation aerosol was revealed. However, the difference in results obtained with or without considering the temperature dependence of evaporation heat is negligible. The predictions are compared with experimental data of other investigations for two mixtures: a mixture of heavy water vapor with nitrogen (incondensable gas) or n-nonane vapor with nitrogen. The predictions agree quite well qualitatively and quantitatively with the experiment. The comparison of the predictions with numerical results from other publications obtained using the method of moments demonstrates the usefulness of the direct numerical solution method and the method of moments in a wide range of input data.

A numerical solution for two-dimensional Fredholm integral equations of the second kind with kernels of the logarithmic potential form

NASA Technical Reports Server (NTRS)

Gabrielsen, R. E.; Uenal, A.

1981-01-01

Two dimensional Fredholm integral equations with logarithmic potential kernels are numerically solved. The explicit consequence of these solutions to their true solutions is demonstrated. The results are based on a previous work in which numerical solutions were obtained for Fredholm integral equations of the second kind with continuous kernels.

Control of sound radiation from a wavepacket over a curved surface

NASA Technical Reports Server (NTRS)

Maestrello, Lucio; El Hady, Nabil M.

1989-01-01

Active control of acoustic pressure in the far field resulting from the growth and decay of a wavepacket convecting in a boundary layer over a concave-convex surface is investigated numerically using direct computations of the Navier-Stokes equations. The resulting sound radiation is computed using linearized Euler equations with the pressure from the Navier-Stokes solution as a time-dependent boundary condition. The acoustic far field exhibits directivity type of behavior that points upstream to the flow direction. A fixed control algorithm is used where the attenuation signal is synthesized by a filter which actively adapt it to the amplitude-time response of the outgoing acoustic wave.

Homogenization of a Directed Dispersal Model for Animal Movement in a Heterogeneous Environment.

PubMed

Yurk, Brian P

2016-10-01

The dispersal patterns of animals moving through heterogeneous environments have important ecological and epidemiological consequences. In this work, we apply the method of homogenization to analyze an advection-diffusion (AD) model of directed movement in a one-dimensional environment in which the scale of the heterogeneity is small relative to the spatial scale of interest. We show that the large (slow) scale behavior is described by a constant-coefficient diffusion equation under certain assumptions about the fast-scale advection velocity, and we determine a formula for the slow-scale diffusion coefficient in terms of the fast-scale parameters. We extend the homogenization result to predict invasion speeds for an advection-diffusion-reaction (ADR) model with directed dispersal. For periodic environments, the homogenization approximation of the solution of the AD model compares favorably with numerical simulations. Invasion speed approximations for the ADR model also compare favorably with numerical simulations when the spatial period is sufficiently small.

Transparent 'solution' of ultrathin magnesium hydroxide nanocrystals for flexible and transparent nanocomposite films.

PubMed

Wang, Jie-Xin; Sun, Qian; Chen, Bo; Wu, Xi; Zeng, Xiao-Fei; Zhang, Cong; Zou, Hai-Kui; Chen, Jian-Feng

2015-05-15

Transparent solutions of nanocrystals exhibit many unique properties, and are thus attractive materials for numerous applications. However, the synthesis of transparent nanocrystal solutions of magnesium hydroxide (MH) with wide applications is yet to be realized. Here, we report a facile two-step process, which includes a direct reactive precipitation in alcohol phase instead of aqueous phase combined with a successive surface modification, to prepare transparent alcohol solutions containing lamellar MH nanocrystals with an average size of 52 nm and an ultrathin thickness of 1-2 nm, which is the thinnest MH nanoplatelet reported in the literatures. Further, highly flexible and transparent nanocomposite films are fabricated with a solution mixing method by adding the transparent MH nanocrystal solutions into PVB solution. Considering the simplicity of the fabrication process, high transparency and good flexibility, this MH/polymer nanocomposite film is promising for flame-resistant applications in plastic electronics and optical devices with high transparency, such as flexible displays, optical filters, and flexible solar cells.

A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity

NASA Technical Reports Server (NTRS)

Yau, J. F.; Wang, S. S.; Corten, H. T.

1980-01-01

A simple and convenient method of analysis for studying two-dimensional mixed-mode crack problems is presented. The analysis is formulated on the basis of conservation laws of elasticity and of fundamental relationships in fracture mechanics. The problem is reduced to the determination of mixed-mode stress-intensity factor solutions in terms of conservation integrals involving known auxiliary solutions. One of the salient features of the present analysis is that the stress-intensity solutions can be determined directly by using information extracted in the far field. Several examples with solutions available in the literature are solved to examine the accuracy and other characteristics of the current approach. This method is demonstrated to be superior in its numerical simplicity and computational efficiency to other approaches. Solutions of more complicated and practical engineering fracture problems dealing with the crack emanating from a circular hole are presented also to illustrate the capacity of this method

Solute drag in polycrystalline materials: Derivation and numerical analysis of a variational model for the effect of solute on the motion of boundaries and junctions during coarsening

NASA Astrophysics Data System (ADS)

Wilson, Seth Robert

A mathematical model that results in an expression for the local acceleration of a network of sharp interfaces interacting with an ambient solute field is proposed. This expression comprises a first-order differential equation for the local velocity that, given the appropriate initial conditions, may be used to predict the subsequent time evolution of the system, including non-steady state absorption and desorption of solute. Evolution equations for both interfaces and the junction of interfaces are derived by maximizing a functional approximating the rate at which the local Gibbs free energy density decreases, as a function of the local solute content and the instantaneous velocity. The model has been formulated in three dimensions, and non-equilibrium effects such as grain boundary diffusion, solute gradients, and time-dependant segregation are taken into account. As a consequence of this model, it is shown that both interfaces and the junctions between interfaces obey evolution equations that closely resemble Newton's second law. In particular, the concept of "thrust" in variable-mass systems is shown to have a direct analog in solute-interface interaction. Numerical analysis of the equations that result reveals that a double cusp catastrophe governs the behavior of the solute-interface system, for which trajectories that include hysteresis, slip-stick motion, and jerky motion are all conceivable. The geometry of the cusp catastrophe is quantified, and a number of relations between physical parameters and system behavior are consequently predicted.

Panel flutter optimization by gradient projection

NASA Technical Reports Server (NTRS)

Pierson, B. L.

1975-01-01

A gradient projection optimal control algorithm incorporating conjugate gradient directions of search is described and applied to several minimum weight panel design problems subject to a flutter speed constraint. New numerical solutions are obtained for both simply-supported and clamped homogeneous panels of infinite span for various levels of inplane loading and minimum thickness. The minimum thickness inequality constraint is enforced by a simple transformation of variables.

Research on Aero-Thermodynamic Distortion Induced Structural Dynamic Response of Multi-Stage Compressor Blading.

DTIC Science & Technology

1988-01-15

However. only very engineering limited experimental data exists to assess the Director, Thermal Sciences and range of validity and to direct the... experimental results of Goldstein et. al. "A 1111 and also the Navier Stokes numerical solutions of Morihara 1121. Diffuser The predicted stream function...Unsteady Aerodynamic Interactions in a Multistage Compressor............................................................ 53 I APPENDIX VI. Experimental

Synchronization between two coupled direct current glow discharge plasma sources

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

Chaubey, Neeraj; Mukherjee, S.; Sen, A.

2015-02-15

Experimental results on the nonlinear dynamics of two coupled glow discharge plasma sources are presented. A variety of nonlinear phenomena including frequency synchronization and frequency pulling are observed as the coupling strength is varied. Numerical solutions of a model representation of the experiment consisting of two coupled asymmetric Van der Pol type equations are found to be in good agreement with the observed results.

Permeable Reactive Barriers: Lessons Learned/New Directions

DTIC Science & Technology

2005-02-01

set up to treat simulated mine drainage indicates that the sulfide minerals form in close proximity to the organic solids (Waybrant, Ptacek, and...both vertically and horizontally along the PRB installation area. Groundwater and solute transport modeling can be used to simulate representative...2001; Elder, Benson, and Eykholt 2002). The numerical simulations show that the spatial variations in the hydraulic conductivity of both the aquifer

A Discrete Approximation Framework for Hereditary Systems.

DTIC Science & Technology

1980-05-01

schemes which are included in the general framework and which may be implemented directly on high-speed computing machines are developed. A numerical...an appropriately chosen Hilbert space. We then proceed to develop general approximation schemes for the solutions to the homogeneous AEE which in turn...rich classes of these schemes . In addition, two particular families of approximation schemes included in the general framework are developed and

Updates to Simulation of a Single-Element Lean-Direct Injection Combustor Using a Polyhedral Mesh Derived From Hanging-Node Elements

NASA Technical Reports Server (NTRS)

Wey, Changju Thomas; Liu, Nan-Suey

2014-01-01

This paper summarizes the procedures of inserting a thin-layer mesh to existing inviscid polyhedral mesh either with or without hanging-node elements as well as presents sample results from its applications to the numerical solution of a single-element LDI combustor using a releasable edition of the National Combustion Code (NCC).

Updates to Simulation of a Single-Element Lean-Direct Injection Combustor Using a Polyhedral Mesh Derived from Hanging-Node Elements

NASA Technical Reports Server (NTRS)

Wey, Thomas; Liu, Nan-Suey

2014-01-01

This paper summarizes the procedures of inserting a thin-layer mesh to existing inviscid polyhedral mesh either with or without hanging-node elements as well as presents sample results from its applications to the numerical solution of a single-element LDI combustor using a releasable edition of the National Combustion Code (NCC).

Phase space reconstruction and estimation of the largest Lyapunov exponent for gait kinematic data

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

Josiński, Henryk; Świtoński, Adam; Silesian University of Technology, Akademicka 16, 44-100 Gliwice

The authors describe an example of application of nonlinear time series analysis directed at identifying the presence of deterministic chaos in human motion data by means of the largest Lyapunov exponent. The method was previously verified on the basis of a time series constructed from the numerical solutions of both the Lorenz and the Rössler nonlinear dynamical systems.

Breathing chimera in a system of phase oscillators

NASA Astrophysics Data System (ADS)

Bolotov, M. I.; Smirnov, L. A.; Osipov, G. V.; Pikovsky, A. S.

2017-09-01

Chimera states consisting of synchronous and asynchronous domains in a medium of nonlinearly coupled phase oscillators have been considered. Stationary inhomogeneous solutions of the Ott-Antonsen equation for a complex order parameter that correspond to fundamental chimeras have been constructed. The direct numerical simulation has shown that these structures under certain conditions are transformed to oscillatory (breathing) chimera regimes because of the development of instability.

The resolvent of singular integral equations. [of kernel functions in mixed boundary value problems

NASA Technical Reports Server (NTRS)

Williams, M. H.

1977-01-01

The investigation reported is concerned with the construction of the resolvent for any given kernel function. In problems with ill-behaved inhomogeneous terms as, for instance, in the aerodynamic problem of flow over a flapped airfoil, direct numerical methods become very difficult. A description is presented of a solution method by resolvent which can be employed in such problems.

Numerical Solution for Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Warsi, Z. U. A.; Weed, R. A.; Thompson, J. F.

1982-01-01

Carefully selected blend of computational techniques solves complete set of equations for viscous, unsteady, hypersonic flow in general curvilinear coordinates. New algorithm has tested computation of axially directed flow about blunt body having shape similar to that of such practical bodies as wide-body aircraft or artillery shells. Method offers significant computational advantages because of conservation-law form of equations and because it reduces amount of metric data required.

On the accuracy of analytical models of impurity segregation during directional melt crystallization and their applicability for quantitative calculations

NASA Astrophysics Data System (ADS)

Voloshin, A. E.; Prostomolotov, A. I.; Verezub, N. A.

2016-11-01

The paper deals with the analysis of the accuracy of some one-dimensional (1D) analytical models of the axial distribution of impurities in the crystal grown from a melt. The models proposed by Burton-Prim-Slichter, Ostrogorsky-Muller and Garandet with co-authors are considered, these models are compared to the results of a two-dimensional (2D) numerical simulation. Stationary solutions as well as solutions for the initial transient regime obtained using these models are considered. The sources of errors are analyzed, a conclusion is made about the applicability of 1D analytical models for quantitative estimates of impurity incorporation into the crystal sample as well as for the solution of the inverse problems.

Gust Acoustics Computation with a Space-Time CE/SE Parallel 3D Solver

NASA Technical Reports Server (NTRS)

Wang, X. Y.; Himansu, A.; Chang, S. C.; Jorgenson, P. C. E.; Reddy, D. R. (Technical Monitor)

2002-01-01

The benchmark Problem 2 in Category 3 of the Third Computational Aero-Acoustics (CAA) Workshop is solved using the space-time conservation element and solution element (CE/SE) method. This problem concerns the unsteady response of an isolated finite-span swept flat-plate airfoil bounded by two parallel walls to an incident gust. The acoustic field generated by the interaction of the gust with the flat-plate airfoil is computed by solving the 3D (three-dimensional) Euler equations in the time domain using a parallel version of a 3D CE/SE solver. The effect of the gust orientation on the far-field directivity is studied. Numerical solutions are presented and compared with analytical solutions, showing a reasonable agreement.

The development and application of CFD technology in mechanical engineering

NASA Astrophysics Data System (ADS)

Wei, Yufeng

2017-12-01

Computational Fluid Dynamics (CFD) is an analysis of the physical phenomena involved in fluid flow and heat conduction by computer numerical calculation and graphical display. The numerical method simulates the complexity of the physical problem and the precision of the numerical solution, which is directly related to the hardware speed of the computer and the hardware such as memory. With the continuous improvement of computer performance and CFD technology, it has been widely applied to the field of water conservancy engineering, environmental engineering and industrial engineering. This paper summarizes the development process of CFD, the theoretical basis, the governing equations of fluid mechanics, and introduces the various methods of numerical calculation and the related development of CFD technology. Finally, CFD technology in the mechanical engineering related applications are summarized. It is hoped that this review will help researchers in the field of mechanical engineering.

Three-dimensional supersonic flow around double compression ramp with finite span

NASA Astrophysics Data System (ADS)

Lee, H. S.; Lee, J. H.; Park, G.; Park, S. H.; Byun, Y. H.

2017-01-01

Three-dimensional flows of Mach number 3 around a double-compression ramp with finite span have been investigated numerically. Shadowgraph visualisation images obtained in a supersonic wind tunnel are used for comparison. A three-dimensional Reynolds-averaged Navier-Stokes solver was used to obtain steady numerical solutions. Two-dimensional numerical results are also compared. Four different cases were studied: two different second ramp angles of 30° and 45° in configurations with and without sidewalls, respectively. Results showed that there is a leakage of mass and momentum fluxes heading outwards in the spanwise direction for three-dimensional cases without sidewalls. The leakage changed the flow characteristics of the shock-induced boundary layer and resulted in the discrepancy between the experimental data and two-dimensional numerical results. It is found that suppressing the flow leakage by attaching the sidewalls enhances the two-dimensionality of the experimental data for the double-compression ramp flow.

Numerical analysis of the asymptotic two-point boundary value solution for N-body trajectories.

NASA Technical Reports Server (NTRS)

Lancaster, J. E.; Allemann, R. A.

1972-01-01

Previously published asymptotic solutions for lunar and interplanetary trajectories have been modified and combined to formulate a general analytical boundary value solution applicable to a broad class of trajectory problems. In addition, the earlier first-order solutions have been extended to second-order to determine if improved accuracy is possible. Comparisons between the asymptotic solution and numerical integration for several lunar and interplanetary trajectories show that the asymptotic solution is generally quite accurate. Also, since no iterations are required, a solution to the boundary value problem is obtained in a fraction of the time required for numerically integrated solutions.

A numerical method for solving systems of linear ordinary differential equations with rapidly oscillating solutions

NASA Technical Reports Server (NTRS)

Bernstein, Ira B.; Brookshaw, Leigh; Fox, Peter A.

1992-01-01

The present numerical method for accurate and efficient solution of systems of linear equations proceeds by numerically developing a set of basis solutions characterized by slowly varying dependent variables. The solutions thus obtained are shown to have a computational overhead largely independent of the small size of the scale length which characterizes the solutions; in many cases, the technique obviates series solutions near singular points, and its known sources of error can be easily controlled without a substantial increase in computational time.

Temperature-dependent poroelastic and viscoelastic effects on microscale-modelling of seismic reflections in heavy oil reservoirs

NASA Astrophysics Data System (ADS)

Ciz, Radim; Saenger, Erik H.; Gurevich, Boris; Shapiro, Serge A.

2009-03-01

We develop a new model for elastic properties of rocks saturated with heavy oil. The heavy oil is represented by a viscoelastic material, which at low frequencies and/or high temperatures behaves as a Newtonian fluid, and at high frequencies and/or low temperatures as a nearly elastic solid. The bulk and shear moduli of a porous rock saturated with such viscoelastic material are then computed using approximate extended Gassmann equations of Ciz and Shapiro by replacing the elastic moduli of the pore filling material with complex and frequency-dependent moduli of the viscoelastic pore fill. We test the proposed model by comparing its predictions with numerical simulations based on a direct finite-difference solution of equations of dynamic viscoelasticity. The simulations are performed for the reflection coefficient from an interface between a homogeneous fluid and a porous medium. The numerical tests are performed both for an idealized porous medium consisting of alternating solid and viscoelastic layers, and for a more realistic 3-D geometry of the pore space. Both sets of numerical tests show a good agreement between the predictions of the proposed viscoelastic workflow and numerical simulations for relatively high viscosities where viscoelastic effects are important. The results confirm that application of extended Gassmann equations in conjunction with the complex and frequency-dependent moduli of viscoelastic pore filling material, such as heavy oil, provides a good approximation for the elastic moduli of rocks saturated with such material. By construction, this approximation is exactly consistent with the classical Gassmann's equation for sufficiently low frequencies or high temperature when heavy oil behaves like a fluid. For higher frequencies and/or lower temperatures, the predictions are in good agreement with the direct numerical solution of equations of dynamic viscoelasticity on the microscale. This demonstrates that the proposed methodology provides realistic estimates of elastic properties of heavy oil rocks.

Design of transonic airfoil sections using a similarity theory

NASA Technical Reports Server (NTRS)

Nixon, D.

1978-01-01

A study of the available methods for transonic airfoil and wing design indicates that the most powerful technique is the numerical optimization procedure. However, the computer time for this method is relatively large because of the amount of computation required in the searches during optimization. The optimization method requires that base and calibration solutions be computed to determine a minimum drag direction. The design space is then computationally searched in this direction; it is these searches that dominate the computation time. A recent similarity theory allows certain transonic flows to be calculated rapidly from the base and calibration solutions. In this paper the application of the similarity theory to design problems is examined with the object of at least partially eliminating the costly searches of the design optimization method. An example of an airfoil design is presented.

Analytical solutions of travel time to a pumping well with variable evapotranspiration.

PubMed

Chen, Tian-Fei; Wang, Xu-Sheng; Wan, Li; Li, Hailong

2014-01-01

Analytical solutions of groundwater travel time to a pumping well in an unconfined aquifer have been developed in previous studies, however, the change in evapotranspiration was not considered. Here, we develop a mathematical model of unconfined flow toward a discharge well with redistribution of groundwater evapotranspiration for travel time analysis. Dependency of groundwater evapotranspiration on the depth to water table is described using a linear formula with an extinction depth. Analytical solutions of groundwater level and travel time are obtained. For a typical hypothetical example, these solutions perfectly agree with the numerical simulation results based on MODFLOW and MODPATH. As indicated in a dimensionless framework, a lumped parameter which is proportional to the pumping rate controls the distributions of groundwater evapotranspiration rate and the travel time along the radial direction. © 2013, National Ground Water Association.

Accumulation of organic compounds leached from plastic materials used in biopharmaceutical process containers.

PubMed

Jenke, Dennis R; Zietlow, David; Garber, Mary Jo; Sadain, Salma; Reiber, Duane; Terbush, William

2007-01-01

Plastic materials are widely used in medical items, such as solution containers, transfusion sets, transfer tubing, and devices. An emerging trend in the biotechnology industry is the utilization of plastic containers to prepare, transport, and store an assortment of solutions including buffers, media, and in-process and finished product. The direct contact of such containers with the product at one or more points in its lifetime raises the possibility that container leachables may accumulate in the finished product. The interaction between several commercially available container materials and numerous model test solutions (representative of buffers and media used in biopharmaceutical applications) was investigated. This paper summarizes the identification of leachables associated with the container materials and documents the levels to which targeted leachables accumulate in the test solutions under defined storage conditions.

Evaporation-induced flow in an inviscid liquid line at any contact angle

NASA Astrophysics Data System (ADS)

Petsi, A. J.; Burganos, V. N.

2006-04-01

The problem of potential flow inside an evaporating liquid line, shaped as an infinitely long cylindrical segment lying on a flat surface, is considered and an analytical solution is obtained for any contact angle in (0,π) . In this way, microflow details inside linear liquid bodies evaporating on hydrophilic, hydrophobic, and strongly hydrophobic substrates can now be obtained. The mathematical formulation employs the velocity potential and stream function formulations in bipolar coordinates and the solution is obtained using the technique of Fourier transform. Both pinned and depinned contact lines are considered. The solution is applicable to any evaporation mechanism but for illustration purposes numerical results are presented here for the particular case of kinetically controlled evaporation. For hydrophilic substrates, the flow inside the evaporating liquid line is directed towards the edges for pinned contact lines, thus, promoting a coffee stain effect. The opposite flow direction is observed for depinned contact lines. However, for strongly hydrophobic substrates, flow is directed outwards for both pinned and depinned contact lines, but owing to its low magnitude compared to that on hydrophilic substrates, a craterlike colloidal deposit should be expected rather than a ringlike deposit, in agreement with experimental observations.

Algorithms for the computation of solutions of the Ornstein-Zernike equation.

PubMed

Peplow, A T; Beardmore, R E; Bresme, F

2006-10-01

We introduce a robust and efficient methodology to solve the Ornstein-Zernike integral equation using the pseudoarc length (PAL) continuation method that reformulates the integral equation in an equivalent but nonstandard form. This enables the computation of solutions in regions where the compressibility experiences large changes or where the existence of multiple solutions and so-called branch points prevents Newton's method from converging. We illustrate the use of the algorithm with a difficult problem that arises in the numerical solution of integral equations, namely the evaluation of the so-called no-solution line of the Ornstein-Zernike hypernetted chain (HNC) integral equation for the Lennard-Jones potential. We are able to use the PAL algorithm to solve the integral equation along this line and to connect physical and nonphysical solution branches (both isotherms and isochores) where appropriate. We also show that PAL continuation can compute solutions within the no-solution region that cannot be computed when Newton and Picard methods are applied directly to the integral equation. While many solutions that we find are new, some correspond to states with negative compressibility and consequently are not physical.

Vectorization on the star computer of several numerical methods for a fluid flow problem

NASA Technical Reports Server (NTRS)

Lambiotte, J. J., Jr.; Howser, L. M.

1974-01-01

A reexamination of some numerical methods is considered in light of the new class of computers which use vector streaming to achieve high computation rates. A study has been made of the effect on the relative efficiency of several numerical methods applied to a particular fluid flow problem when they are implemented on a vector computer. The method of Brailovskaya, the alternating direction implicit method, a fully implicit method, and a new method called partial implicitization have been applied to the problem of determining the steady state solution of the two-dimensional flow of a viscous imcompressible fluid in a square cavity driven by a sliding wall. Results are obtained for three mesh sizes and a comparison is made of the methods for serial computation.

Direct Numerical Simulation of Acoustic Waves Interacting with a Shock Wave in a Quasi-1D Convergent-Divergent Nozzle Using an Unstructured Finite Volume Algorithm

NASA Technical Reports Server (NTRS)

Bui, Trong T.; Mankbadi, Reda R.

1995-01-01

Numerical simulation of a very small amplitude acoustic wave interacting with a shock wave in a quasi-1D convergent-divergent nozzle is performed using an unstructured finite volume algorithm with a piece-wise linear, least square reconstruction, Roe flux difference splitting, and second-order MacCormack time marching. First, the spatial accuracy of the algorithm is evaluated for steady flows with and without the normal shock by running the simulation with a sequence of successively finer meshes. Then the accuracy of the Roe flux difference splitting near the sonic transition point is examined for different reconstruction schemes. Finally, the unsteady numerical solutions with the acoustic perturbation are presented and compared with linear theory results.

Mean Field Type Control with Congestion (II): An Augmented Lagrangian Method

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

Achdou, Yves, E-mail: achdou@ljll.univ-paris-diderot.fr; Laurière, Mathieu

This work deals with a numerical method for solving a mean-field type control problem with congestion. It is the continuation of an article by the same authors, in which suitably defined weak solutions of the system of partial differential equations arising from the model were discussed and existence and uniqueness were proved. Here, the focus is put on numerical methods: a monotone finite difference scheme is proposed and shown to have a variational interpretation. Then an Alternating Direction Method of Multipliers for solving the variational problem is addressed. It is based on an augmented Lagrangian. Two kinds of boundary conditionsmore » are considered: periodic conditions and more realistic boundary conditions associated to state constrained problems. Various test cases and numerical results are presented.« less

Numerical simulations to the nonlinear model of interpersonal relationships with time fractional derivative

NASA Astrophysics Data System (ADS)

Gencoglu, Muharrem Tuncay; Baskonus, Haci Mehmet; Bulut, Hasan

2017-01-01

The main aim of this manuscript is to obtain numerical solutions for the nonlinear model of interpersonal relationships with time fractional derivative. The variational iteration method is theoretically implemented and numerically conducted only to yield the desired solutions. Numerical simulations of desired solutions are plotted by using Wolfram Mathematica 9. The authors would like to thank the reviewers for their comments that help improve the manuscript.

Unsteady boundary layer rotating flow and heat transfer in a copper-water nanofluid over a shrinking sheet

NASA Astrophysics Data System (ADS)

Dzulkifli, Nor Fadhilah; Bachok, Norfifah; Yacob, Nor Azizah; Arifin, Norihan Md; Rosali, Haliza

2017-04-01

The study of unsteady three-dimensional boundary layer rotating flow with heat transfer in Copper-water nanofluid over a shrinking sheet is discussed. The governing equations in terms of partial differential equations are transformed to ordinary differential equations by introducing the appropriate similarity variables which are then solved numerically by a shooting method with Maple software. The numerical results of velocity gradient in x and y directions, skin friction coefficient and local Nusselt number as well as dual velocity and temperature profiles are shown graphically. The study revealed that dual solutions exist in certain range of s > 0.

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

A Multiuser Detector Based on Artificial Bee Colony Algorithm for DS-UWB Systems

PubMed Central

Liu, Xiaohui

2013-01-01

Artificial Bee Colony (ABC) algorithm is an optimization algorithm based on the intelligent behavior of honey bee swarm. The ABC algorithm was developed to solve optimizing numerical problems and revealed premising results in processing time and solution quality. In ABC, a colony of artificial bees search for rich artificial food sources; the optimizing numerical problems are converted to the problem of finding the best parameter which minimizes an objective function. Then, the artificial bees randomly discover a population of initial solutions and then iteratively improve them by employing the behavior: moving towards better solutions by means of a neighbor search mechanism while abandoning poor solutions. In this paper, an efficient multiuser detector based on a suboptimal code mapping multiuser detector and artificial bee colony algorithm (SCM-ABC-MUD) is proposed and implemented in direct-sequence ultra-wideband (DS-UWB) systems under the additive white Gaussian noise (AWGN) channel. The simulation results demonstrate that the BER and the near-far effect resistance performances of this proposed algorithm are quite close to those of the optimum multiuser detector (OMD) while its computational complexity is much lower than that of OMD. Furthermore, the BER performance of SCM-ABC-MUD is not sensitive to the number of active users and can obtain a large system capacity. PMID:23983638

Fuel-optimal low-thrust formation reconfiguration via Radau pseudospectral method

NASA Astrophysics Data System (ADS)

Li, Jing

2016-07-01

This paper investigates fuel-optimal low-thrust formation reconfiguration near circular orbit. Based on the Clohessy-Wiltshire equations, first-order necessary optimality conditions are derived from the Pontryagin's maximum principle. The fuel-optimal impulsive solution is utilized to divide the low-thrust trajectory into thrust and coast arcs. By introducing the switching times as optimization variables, the fuel-optimal low-thrust formation reconfiguration is posed as a nonlinear programming problem (NLP) via direct transcription using multiple-phase Radau pseudospectral method (RPM), which is then solved by a sparse nonlinear optimization software SNOPT. To facilitate optimality verification and, if necessary, further refinement of the optimized solution of the NLP, formulas for mass costate estimation and initial costates scaling are presented. Numerical examples are given to show the application of the proposed optimization method. To fix the problem, generic fuel-optimal low-thrust formation reconfiguration can be simplified as reconfiguration without any initial and terminal coast arcs, whose optimal solutions can be efficiently obtained from the multiple-phase RPM at the cost of a slight fuel increment. Finally, influence of the specific impulse and maximum thrust magnitude on the fuel-optimal low-thrust formation reconfiguration is analyzed. Numerical results shown the links and differences between the fuel-optimal impulsive and low-thrust solutions.

Numerical study of magnetohydrodynamic viscous plasma flow in rotating porous media with Hall currents and inclined magnetic field influence

NASA Astrophysics Data System (ADS)

Bég, O. Anwar; Sim, Lik; Zueco, J.; Bhargava, R.

2010-02-01

A numerical solution is developed for the viscous, incompressible, magnetohydrodynamic flow in a rotating channel comprising two infinite parallel plates and containing a Darcian porous medium, the plates lying in the x-z plane, under constant pressure gradient. The system is subjected to a strong, inclined magnetic field orientated to the positive direction of the y-axis (rotational axis, normal to the x-z plane). The Navier-Stokes flow equations for a general rotating hydromagnetic flow are reduced to a pair of linear, viscous partial differential equations neglecting convective acceleration terms, for primary velocity (u‧) and secondary velocity (v‧) where these velocities are directed along the x and y axes. Only viscous terms are retained in the momenta equations. The model is non-dimensionalized and shown to be controlled by a number of dimensionless parameters. The resulting dimensionless ordinary differential equations are solved using a robust numerical method, Network Simulation Methodology. Full details of the numerics are provided. The present solutions are also benchmarked against the analytical solutions presented recently by Ghosh and Pop [Ghosh SK, Pop I. An analytical approach to MHD plasma behaviour of a rotating environment in the presence of an inclined magnetic field as compared to excitation frequency. Int J Appl Mech Eng 2006;11(4):845-856] for the case of a purely fluid medium (infinite permeability). We study graphically the influence of Hartmann number (Ha, magnetic field parameter), Ekman number (Ek, rotation parameter), Hall current parameter (Nh), Darcy number (Da, permeability parameter), pressure gradient (Np) and also magnetic field inclination (θ) on primary and secondary velocity fields. Additionally we investigate the effects of these multiphysical parameters on the dimensionless shear stresses at the plates. Both primary and secondary velocity are seen to be increased with a rise in Darcy number, owing to a simultaneous reduction in Darcian drag force. Primary velocity is seen to decrease with an increase in Hall current parameter (Nh) but there is a decrease in secondary velocity. The study finds important applications in magnetic materials processing, hydromagnetic plasma energy generators, magneto-geophysics and planetary astrophysics.

Two-dimensional fracture analysis of piezoelectric material based on the scaled boundary node method

NASA Astrophysics Data System (ADS)

Shen-Shen, Chen; Juan, Wang; Qing-Hua, Li

2016-04-01

A scaled boundary node method (SBNM) is developed for two-dimensional fracture analysis of piezoelectric material, which allows the stress and electric displacement intensity factors to be calculated directly and accurately. As a boundary-type meshless method, the SBNM employs the moving Kriging (MK) interpolation technique to an approximate unknown field in the circumferential direction and therefore only a set of scattered nodes are required to discretize the boundary. As the shape functions satisfy Kronecker delta property, no special techniques are required to impose the essential boundary conditions. In the radial direction, the SBNM seeks analytical solutions by making use of analytical techniques available to solve ordinary differential equations. Numerical examples are investigated and satisfactory solutions are obtained, which validates the accuracy and simplicity of the proposed approach. Project supported by the National Natural Science Foundation of China (Grant Nos. 11462006 and 21466012), the Foundation of Jiangxi Provincial Educational Committee, China (Grant No. KJLD14041), and the Foundation of East China Jiaotong University, China (Grant No. 09130020).

Numerical Analysis of an H 1-Galerkin Mixed Finite Element Method for Time Fractional Telegraph Equation

PubMed Central

Wang, Jinfeng; Zhao, Meng; Zhang, Min; Liu, Yang; Li, Hong

2014-01-01

We discuss and analyze an H 1-Galerkin mixed finite element (H 1-GMFE) method to look for the numerical solution of time fractional telegraph equation. We introduce an auxiliary variable to reduce the original equation into lower-order coupled equations and then formulate an H 1-GMFE scheme with two important variables. We discretize the Caputo time fractional derivatives using the finite difference methods and approximate the spatial direction by applying the H 1-GMFE method. Based on the discussion on the theoretical error analysis in L 2-norm for the scalar unknown and its gradient in one dimensional case, we obtain the optimal order of convergence in space-time direction. Further, we also derive the optimal error results for the scalar unknown in H 1-norm. Moreover, we derive and analyze the stability of H 1-GMFE scheme and give the results of a priori error estimates in two- or three-dimensional cases. In order to verify our theoretical analysis, we give some results of numerical calculation by using the Matlab procedure. PMID:25184148

A 2-D numerical simulation study on longitudinal solute transport and longitudinal dispersion coefficient

NASA Astrophysics Data System (ADS)

Zhang, Wei

2011-07-01

The longitudinal dispersion coefficient, DL, is a fundamental parameter of longitudinal solute transport models: the advection-dispersion (AD) model and various deadzone models. Since DL cannot be measured directly, and since its calibration using tracer test data is quite expensive and not always available, researchers have developed various methods, theoretical or empirical, for estimating DL by easier available cross-sectional hydraulic measurements (i.e., the transverse velocity profile, etc.). However, for known and unknown reasons, DL cannot be satisfactorily predicted using these theoretical/empirical formulae. Either there is very large prediction error for theoretical methods, or there is a lack of generality for the empirical formulae. Here, numerical experiments using Mike21, a software package that implements one of the most rigorous two-dimensional hydrodynamic and solute transport equations, for longitudinal solute transport in hypothetical streams, are presented. An analysis of the evolution of simulated solute clouds indicates that the two fundamental assumptions in Fischer's longitudinal transport analysis may be not reasonable. The transverse solute concentration distribution, and hence the longitudinal transport appears to be controlled by a dimensionless number ?, where Q is the average volumetric flowrate, Dt is a cross-sectional average transverse dispersion coefficient, and W is channel flow width. A simple empirical ? relationship may be established. Analysis and a revision of Fischer's theoretical formula suggest that ɛ influences the efficiency of transverse mixing and hence has restraining effect on longitudinal spreading. The findings presented here would improve and expand our understanding of longitudinal solute transport in open channel flow.

Theory of precipitation effects on dead cylindrical fuels

Treesearch

Michael A. Fosberg

1972-01-01

Numerical and analytical solutions of the Fickian diffusion equation were used to determine the effects of precipitation on dead cylindrical forest fuels. The analytical solution provided a physical framework. The numerical solutions were then used to refine the analytical solution through a similarity argument. The theoretical solutions predicted realistic rates of...

Can the Ocean's Heat Engine Control Horizontal Circulation? Insights From the Caspian Sea

NASA Astrophysics Data System (ADS)

Bruneau, Nicolas; Zika, Jan; Toumi, Ralf

2017-10-01

We investigate the role of the ocean's heat engine in setting horizontal circulation using a numerical model of the Caspian Sea. The Caspian Sea can be seen as a virtual laboratory—a compromise between realistic global models that are hampered by long equilibration times and idealized basin geometry models, which are not constrained by observations. We find that increases in vertical mixing drive stronger thermally direct overturning and consequent conversion of available potential to kinetic energy. Numerical solutions with water mass structures closest to observations overturn 0.02-0.04 × 106 m3/s (sverdrup) representing the first estimate of Caspian Sea overturning. Our results also suggest that the overturning is thermally forced increasing in intensity with increasing vertical diffusivity. Finally, stronger thermally direct overturning is associated with a stronger horizontal circulation in the Caspian Sea. This suggests that the ocean's heat engine can strongly impact broader horizontal circulations in the ocean.

Direct Numerical Simulation of a Coolant Jet in a Periodic Crossflow

NASA Technical Reports Server (NTRS)

Sharma, Chirdeep; Acharya, Sumanta

1998-01-01

A Direct Numerical Simulation of a coolant jet injected normally into a periodic crossflow is presented. The physical situation simulated represents a periodic module in a coolant hole array with a heated crossflow. A collocated finite difference scheme is used which is fifth-order accurate spatially and second-order accurate temporally. The scheme is based on a fractional step approach and requires the solution of a pressure-Poisson equation. The simulations are obtained for a blowing ratio of 0.25 and a channel Reynolds number of 5600. The simulations reveal the dynamics of several large scale structures including the Counter-rotating Vortex Pair (CVP), the horse-shoe vortex, the shear layer vortex, the wall vortex and the wake vortex. The origins and the interactions of these vortical structures are identified and explored. Also presented are the turbulence statistics and how they relate to the flow structures.

Pure quasi-P wave equation and numerical solution in 3D TTI media

NASA Astrophysics Data System (ADS)

Zhang, Jian-Min; He, Bing-Shou; Tang, Huai-Gu

2017-03-01

Based on the pure quasi-P wave equation in transverse isotropic media with a vertical symmetry axis (VTI media), a quasi-P wave equation is obtained in transverse isotropic media with a tilted symmetry axis (TTI media). This is achieved using projection transformation, which rotates the direction vector in the coordinate system of observation toward the direction vector for the coordinate system in which the z-component is parallel to the symmetry axis of the TTI media. The equation has a simple form, is easily calculated, is not influenced by the pseudo-shear wave, and can be calculated reliably when δ is greater than ɛ. The finite difference method is used to solve the equation. In addition, a perfectly matched layer (PML) absorbing boundary condition is obtained for the equation. Theoretical analysis and numerical simulation results with forward modeling prove that the equation can accurately simulate a quasi-P wave in TTI medium.

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.

The stability of a trailing-line vortex in compressible flow

NASA Technical Reports Server (NTRS)

Stott, Jillian A. K.; Duck, Peter W.

1992-01-01

We consider the inviscid stability of the Batchelor (1964) vortex in a compressible flow. The problem is tackled numerically and also asymptotically, in the limit of large (aximuthal and streamwise) wavenumbers, together with large Mach numbers. The nature of the solution passes through different regimes as the Mach number increases, relative to the wavenumbers. At very high wavenumbers and Mach numbers, the mode which is present in the incompressible case ceases to be unstable, while new 'center mode' forms, whose stability characteristics, are determined primarily by conditions close to the vortex axis. We find that generally the flow becomes less unstable as the Mach number increases, and that the regime of instability appears generally confined to disturbances in a direction counter to the direction of the rotation of the swirl of the vortex. Throughout the paper, comparison is made between our numerical results and results obtained from the various asymptotic theories.

Crank-Nicholson difference scheme for a stochastic parabolic equation with a dependent operator coefficient

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

Ashyralyev, Allaberen; Okur, Ulker

In the present paper, the Crank-Nicolson difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is considered. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, convergence estimates for the solution of difference schemes for the numerical solution of three mixed problems for parabolic equations are obtained. The numerical results are given.

A novel method for the production of core-shell microparticles by inverse gelation optimized with artificial intelligent tools.

PubMed

Rodríguez-Dorado, Rosalia; Landín, Mariana; Altai, Ayça; Russo, Paola; Aquino, Rita P; Del Gaudio, Pasquale

2018-03-01

Numerous studies have been focused on hydrophobic compounds encapsulation as oils. In fact, oils can provide numerous health benefits as synergic ingredient combined with other hydrophobic active ingredients. However, stable microparticles for pharmaceutical purposes are difficult to achieve when commonly techniques are used. In this work, sunflower oil was encapsulated in calcium-alginate capsules by prilling technique in co-axial configuration. Core-shell beads were produced by inverse gelation directly at the nozzle using a w/o emulsion containing aqueous calcium chloride solution in sunflower oil pumped through the inner nozzle while an aqueous alginate solution, coming out from the annular nozzle, produced the beads shell. To optimize process parameters artificial intelligence tools were proposed to optimize the numerous prilling process variables. Homogeneous and spherical microcapsules with narrow size distribution and a thin alginate shell were obtained when the parameters as w/o constituents, polymer concentrations, flow rates and frequency of vibration were optimized by two commercial software, FormRules® and INForm®, which implement neurofuzzy logic and Artificial Neural Networks together with genetic algorithms, respectively. This technique constitutes an innovative approach for hydrophobic compounds microencapsulation. Copyright © 2018 Elsevier B.V. All rights reserved.

Vibrations of a Mindlin plate subjected to a pair of inertial loads moving in opposite directions

NASA Astrophysics Data System (ADS)

Dyniewicz, Bartłomiej; Pisarski, Dominik; Bajer, Czesław I.

2017-01-01

A Mindlin plate subjected to a pair of inertial loads traveling at a constant high speed in opposite directions along arbitrary trajectory, straight or curved, is presented. The masses represent vehicles passing a bridge or track plates. A numerical solution is obtained using the space-time finite element method, since it allows a clear and simple derivation of the characteristic matrices of the time-stepping procedure. The transition from one spatial finite element to another must be energetically consistent. In the case of the moving inertial load the classical time-integration schemes are methodologically difficult, since we consider the Dirac delta term with a moving argument. The proposed numerical approach provides the correct definition of force equilibrium in the time interval. The given approach closes the problem of the numerical analysis of vibration of a structure subjected to inertial loads moving arbitrarily with acceleration. The results obtained for a massless and an inertial load traveling over a Mindlin plate at various speeds are compared with benchmark results obtained for a Kirchhoff plate. The pair of inertial forces traveling in opposite directions causes displacements and stresses more than twice as large as their corresponding quantities observed for the passage of a single mass.

The Linear Quadratic Gaussian Multistage Game with Nonclassical Information Pattern Using a Direct Solution Method

NASA Astrophysics Data System (ADS)

Clemens, Joshua William

Game theory has application across multiple fields, spanning from economic strategy to optimal control of an aircraft and missile on an intercept trajectory. The idea of game theory is fascinating in that we can actually mathematically model real-world scenarios and determine optimal decision making. It may not always be easy to mathematically model certain real-world scenarios, nonetheless, game theory gives us an appreciation for the complexity involved in decision making. This complexity is especially apparent when the players involved have access to different information upon which to base their decision making (a nonclassical information pattern). Here we will focus on the class of adversarial two-player games (sometimes referred to as pursuit-evasion games) with nonclassical information pattern. We present a two-sided (simultaneous) optimization solution method for the two-player linear quadratic Gaussian (LQG) multistage game. This direct solution method allows for further interpretation of each player's decision making (strategy) as compared to previously used formal solution methods. In addition to the optimal control strategies, we present a saddle point proof and we derive an expression for the optimal performance index value. We provide some numerical results in order to further interpret the optimal control strategies and to highlight real-world application of this game-theoretic optimal solution.

Three-dimensional finite amplitude electroconvection in dielectric liquids

NASA Astrophysics Data System (ADS)

Luo, Kang; Wu, Jian; Yi, Hong-Liang; Tan, He-Ping

2018-02-01

Charge injection induced electroconvection in a dielectric liquid lying between two parallel plates is numerically simulated in three dimensions (3D) using a unified lattice Boltzmann method (LBM). Cellular flow patterns and their subcritical bifurcation phenomena of 3D electroconvection are numerically investigated for the first time. A unit conversion is also derived to connect the LBM system to the real physical system. The 3D LBM codes are validated by three carefully chosen cases and all results are found to be highly consistent with the analytical solutions or other numerical studies. For strong injection, the steady state roll, polygon, and square flow patterns are observed under different initial disturbances. Numerical results show that the hexagonal cell with the central region being empty of charge and centrally downward flow is preferred in symmetric systems under random initial disturbance. For weak injection, the numerical results show that the flow directly passes from the motionless state to turbulence once the system loses its linear stability. In addition, the numerically predicted linear and finite amplitude stability criteria of different flow patterns are discussed.

Updates to Simulation of a Single-Element Lean-Direct Injection Combustor Using Arbitary Polyhedral Meshes

NASA Technical Reports Server (NTRS)

Wey, Thomas; Liu, Nan-Suey

2015-01-01

This paper summarizes the procedures of (1) generating control volumes anchored at the nodes of a mesh; and (2) generating staggered control volumes via mesh reconstructions, in terms of either mesh realignment or mesh refinement, as well as presents sample results from their applications to the numerical solution of a single-element LDI combustor using a releasable edition of the National Combustion Code (NCC).

Multiple scattering corrections to the Beer-Lambert law. 1: Open detector.

PubMed

Tam, W G; Zardecki, A

1982-07-01

Multiple scattering corrections to the Beer-Lambert law are analyzed by means of a rigorous small-angle solution to the radiative transfer equation. Transmission functions for predicting the received radiant power-a directly measured quantity in contrast to the spectral radiance in the Beer-Lambert law-are derived. Numerical algorithms and results relating to the multiple scattering effects for laser propagation in fog, cloud, and rain are presented.

Dynamics and Stability of Acoustic Wavefronts in the Ocean

DTIC Science & Technology

2011-09-01

developed to solve the eikonal equation and calculate wavefront and ray trajectory displacements, which are required to be small over a correlation length...with a direct modeling of acoustic wavefronts in the ocean through numerical solution of the eikonal equation lies in the eikonal (and acoustic...travel time) being a multi-valued function of position. A number of computational approaches to solve the eikonal equation without ray tracing have been

A mean spherical model for soft potentials: The hard core revealed as a perturbation

NASA Technical Reports Server (NTRS)

Rosenfeld, Y.; Ashcroft, N. W.

1978-01-01

The mean spherical approximation for fluids is extended to treat the case of dense systems interacting via soft-potentials. The extension takes the form of a generalized statement concerning the behavior of the direct correlation function c(r) and radial distribution g(r). From a detailed analysis that views the hard core portion of a potential as a perturbation on the whole, a specific model is proposed which possesses analytic solutions for both Coulomb and Yukawa potentials, in addition to certain other remarkable properties. A variational principle for the model leads to a relatively simple method for obtaining numerical solutions.

On the Propagation and Interaction of Spherical Blast Waves

NASA Technical Reports Server (NTRS)

Kandula, Max; Freeman, Robert

2007-01-01

The characteristics and the scaling laws of isolated spherical blast waves have been briefly reviewed. Both self-similar solutions and numerical solutions of isolated blast waves are discussed. Blast profiles in the near-field (strong shock region) and the far-field (weak shock region) are examined. Particular attention is directed at the blast overpressure and shock propagating speed. Consideration is also given to the interaction of spherical blast waves. Test data for the propagation and interaction of spherical blast waves emanating from explosives placed in the vicinity of a solid propellant stack are presented. These data are discussed with regard to the scaling laws concerning the decay of blast overpressure.

Assessment of an Explicit Algebraic Reynolds Stress Model

NASA Technical Reports Server (NTRS)

Carlson, Jan-Renee

2005-01-01

This study assesses an explicit algebraic Reynolds stress turbulence model in the in the three-dimensional Reynolds averaged Navier-Stokes (RANS) solver, ISAAC (Integrated Solution Algorithm for Arbitrary Con gurations). Additionally, it compares solutions for two select configurations between ISAAC and the RANS solver PAB3D. This study compares with either direct numerical simulation data, experimental data, or empirical models for several different geometries with compressible, separated, and high Reynolds number flows. In general, the turbulence model matched data or followed experimental trends well, and for the selected configurations, the computational results of ISAAC closely matched those of PAB3D using the same turbulence model.

Multigrid for Staggered Lattice Fermions

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

Brower, Richard C.; Clark, M. A.; Strelchenko, Alexei

Critical slowing down in Krylov methods for the Dirac operator presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. Here we formulate a multi-grid algorithm for the Kogut-Susskind (or staggered) fermion discretization which has proven difficult relative to Wilson multigrid due to its first-order anti-Hermitian structure. The solution is to introduce a novel spectral transformation by the K\\"ahler-Dirac spin structure prior to the Galerkin projection. We present numerical results for the two-dimensional, two-flavor Schwinger model, however, the general formalism is agnostic to dimension and is directly applicable to four-dimensional lattice QCD.

On the Directional Dependence and Null Space Freedom in Uncertainty Bound Identification

NASA Technical Reports Server (NTRS)

Lim, K. B.; Giesy, D. P.

1997-01-01

In previous work, the determination of uncertainty models via minimum norm model validation is based on a single set of input and output measurement data. Since uncertainty bounds at each frequency is directionally dependent for multivariable systems, this will lead to optimistic uncertainty levels. In addition, the design freedom in the uncertainty model has not been utilized to further reduce uncertainty levels. The above issues are addressed by formulating a min- max problem. An analytical solution to the min-max problem is given to within a generalized eigenvalue problem, thus avoiding a direct numerical approach. This result will lead to less conservative and more realistic uncertainty models for use in robust control.

Linear Instability of a Uni-Directional Transversely Sheared Mean Flow

NASA Technical Reports Server (NTRS)

Wundrow, David W.

1996-01-01

The effect of spanwise-periodic mean-flow distortions (i.e. streamwise-vortex structures) on the evolution of small-amplitude, single-frequency instability waves in an otherwise two-dimensional shear flow is investigated. The streamwise-vortex structures are taken to be just weak enough so that the spatially growing instability waves behave (locally) like linear perturbations about a uni-directional transversely sheared mean flow. Numerical solutions are computed and discussed for both the mean flow and the instability waves. The influence of the streamwise-vortex wavelength on the properties of the most rapidly growing instability wave is also discussed.

A constitutive material model for nonlinear finite element structural analysis using an iterative matrix approach

NASA Technical Reports Server (NTRS)

Koenig, Herbert A.; Chan, Kwai S.; Cassenti, Brice N.; Weber, Richard

1988-01-01

A unified numerical method for the integration of stiff time dependent constitutive equations is presented. The solution process is directly applied to a constitutive model proposed by Bodner. The theory confronts time dependent inelastic behavior coupled with both isotropic hardening and directional hardening behaviors. Predicted stress-strain responses from this model are compared to experimental data from cyclic tests on uniaxial specimens. An algorithm is developed for the efficient integration of the Bodner flow equation. A comparison is made with the Euler integration method. An analysis of computational time is presented for the three algorithms.

Breathing pulses in singularly perturbed reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Veerman, Frits

2015-07-01

The weakly nonlinear stability of pulses in general singularly perturbed reaction-diffusion systems near a Hopf bifurcation is determined using a centre manifold expansion. A general framework to obtain leading order expressions for the (Hopf) centre manifold expansion for scale separated, localised structures is presented. Using the scale separated structure of the underlying pulse, directly calculable expressions for the Hopf normal form coefficients are obtained in terms of solutions to classical Sturm-Liouville problems. The developed theory is used to establish the existence of breathing pulses in a slowly nonlinear Gierer-Meinhardt system, and is confirmed by direct numerical simulation.

Discrete is it enough? The revival of Piola-Hencky keynotes to analyze three-dimensional Elastica

NASA Astrophysics Data System (ADS)

Turco, Emilio

2018-04-01

Complex problems such as those concerning the mechanics of materials can be confronted only by considering numerical simulations. Analytical methods are useful to build guidelines or reference solutions but, for general cases of technical interest, they have to be solved numerically, especially in the case of large displacements and deformations. Probably continuous models arose for producing inspiring examples and stemmed from homogenization techniques. These techniques allowed for the solution of some paradigmatic examples but, in general, always require a discretization method for solving problems dictated by the applications. Therefore, and also by taking into account that computing powers are nowadays more largely available and cheap, the question arises: why not using directly a discrete model for 3D beams? In other words, it could be interesting to formulate a discrete model without using an intermediate continuum one, as this last, at the end, has to be discretized in any case. These simple considerations immediately evoke some very basic models developed many years ago when the computing powers were practically inexistent but the problem of finding simple solutions to beam deformation problem was already an emerging one. Actually, in recent years, the keynotes of Hencky and Piola attracted a renewed attention [see, one for all, the work (Turco et al. in Zeitschrift für Angewandte Mathematik und Physik 67(4):1-28, 2016)]: generalizing their results, in the present paper, a novel directly discrete three-dimensional beam model is presented and discussed, in the framework of geometrically nonlinear analysis. Using a stepwise algorithm based essentially on Newton's method to compute the extrapolations and on the Riks' arc-length method to perform the corrections, we could obtain some numerical simulations showing the computational effectiveness of presented model: Indeed, it presents a convenient balance between accuracy and computational cost.

The Role of Interfacial Water in Protein-Ligand Binding: Insights from the Indirect Solvent Mediated Potential of Mean Force.

PubMed

Cui, Di; Zhang, Bin W; Matubayasi, Nobuyuki; Levy, Ronald M

2018-02-13

Classical density functional theory (DFT) can be used to relate the thermodynamic properties of solutions to the indirect solvent mediated part of the solute-solvent potential of mean force (PMF). Standard, but powerful numerical methods can be used to estimate the solute-solvent PMF from which the indirect part can be extracted. In this work we show how knowledge of the direct and indirect parts of the solute-solvent PMF for water at the interface of a protein receptor can be used to gain insights about how to design tighter binding ligands. As we show, the indirect part of the solute-solvent PMF is equal to the sum of the 1-body (energy + entropy) terms in the inhomogeneous solvation theory (IST) expansion of the solvation free energy. To illustrate the effect of displacing interfacial water molecules with particular direct/indirect PMF signatures on the binding of ligands, we carry out simulations of protein binding with several pairs of congeneric ligands. We show that interfacial water locations that contribute favorably or unfavorably at the 1-body level (energy + entropy) to the solvation free energy of the solute can be targeted as part of the ligand design process. Water locations where the indirect PMF is larger in magnitude provide better targets for displacement when adding a functional group to a ligand core.

Analytical and Numerical solutions of a nonlinear alcoholism model via variable-order fractional differential equations

NASA Astrophysics Data System (ADS)

Gómez-Aguilar, J. F.

2018-03-01

In this paper, we analyze an alcoholism model which involves the impact of Twitter via Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives with constant- and variable-order. Two fractional mathematical models are considered, with and without delay. Special solutions using an iterative scheme via Laplace and Sumudu transform were obtained. We studied the uniqueness and existence of the solutions employing the fixed point postulate. The generalized model with variable-order was solved numerically via the Adams method and the Adams-Bashforth-Moulton scheme. Stability and convergence of the numerical solutions were presented in details. Numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient. Therefore, by including both the fractional derivatives and finite time delays in the alcoholism model studied, we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking.

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.

Comparison of NACA 0012 Laminar Flow Solutions: Structured and Unstructured Grid Methods

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Langer, S.

2016-01-01

In this paper we consider the solution of the compressible Navier-Stokes equations for a class of laminar airfoil flows. The principal objective of this paper is to demonstrate that members of this class of laminar flows have steady-state solutions. These laminar airfoil flow cases are often used to evaluate accuracy, stability and convergence of numerical solution algorithms for the Navier-Stokes equations. In recent years, such flows have also been used as test cases for high-order numerical schemes. While generally consistent steady-state solutions have been obtained for these flows using higher order schemes, a number of results have been published with various solutions, including unsteady ones. We demonstrate with two different numerical methods and a range of meshes with a maximum density that exceeds 8 × 106 grid points that steady-state solutions are obtained. Furthermore, numerical evidence is presented that even when solving the equations with an unsteady algorithm, one obtains steady-state solutions.

Petermann I and II spot size: Accurate semi analytical description involving Nelder-Mead method of nonlinear unconstrained optimization and three parameter fundamental modal field

NASA Astrophysics Data System (ADS)

Roy Choudhury, Raja; Roy Choudhury, Arundhati; Kanti Ghose, Mrinal

2013-01-01

A semi-analytical model with three optimizing parameters and a novel non-Gaussian function as the fundamental modal field solution has been proposed to arrive at an accurate solution to predict various propagation parameters of graded-index fibers with less computational burden than numerical methods. In our semi analytical formulation the optimization of core parameter U which is usually uncertain, noisy or even discontinuous, is being calculated by Nelder-Mead method of nonlinear unconstrained minimizations as it is an efficient and compact direct search method and does not need any derivative information. Three optimizing parameters are included in the formulation of fundamental modal field of an optical fiber to make it more flexible and accurate than other available approximations. Employing variational technique, Petermann I and II spot sizes have been evaluated for triangular and trapezoidal-index fibers with the proposed fundamental modal field. It has been demonstrated that, the results of the proposed solution identically match with the numerical results over a wide range of normalized frequencies. This approximation can also be used in the study of doped and nonlinear fiber amplifier.

Two-dimensional compressible flow in centrifugal compressors with straight blades

NASA Technical Reports Server (NTRS)

Stanitz, John D; Ellis, Gaylord O

1950-01-01

Six numerical examples are presented for steady, two-dimensional, compressible, nonviscous flow in centrifugal compressors with thin straight blades, the center lines of which generate the surface of a right circular cone when rotated about the axis of the compressor. A seventh example is presented for incompressible flow. The solutions were obtained in a region of the compressors, including the impeller tip, that was considered to be unaffected by the diffuser vanes or by the impeller-inlet configuration. Each solution applies to radial and mixed flow compressors with various cone angles but with the same angle between blades on the conic flow surface. The solution also apply to radial and mixed flow turbines with the rotation and the flow direction reversed. The effects of variations in the following parameters were investigated: (1) flow rate, (2) impeller-tip speed, (3) variation of passage height with radius, and (4) angle between blades on conic flow surface. The numerical results are presented in plots of the streamlines and constant Mach number lines. Correlation equations are developed whereby the flow conditions in any impeller with straight blades can be determined (in the region investigated by this analysis) for all operating conditions.

Turbulent solutions of the equations of fluid motion

NASA Technical Reports Server (NTRS)

Deissler, R. G.

1984-01-01

Some turbulent solutions of the unaveraged Navier-Stokes equations (equations of fluid motion) are reviewed. Those equations are solved numerically in order to study the nonlinear physics of incompressible turbulent flow. Initial three-dimensional cosine velocity fluctuations and periodic boundary conditions are used in most of the work considered. The three components of the mean-square velocity fluctuations are initially equal for the conditions chosen. The resulting solutions show characteristics of turbulence such as the linear and nonlinear excitation of small-scale fluctuations. For the stronger fluctuations, the initially nonrandom flow develops into an apparently random turbulence. Thus randomness or turbulence can arise as a consequence of the structure of the Navier-Stokes equations. The cases considered include turbulence which is statistically homogeneous or inhomogeneous and isotropic or anisotropic. A mean shear is present in some cases. A statistically steady-state turbulence is obtained by using a spatially periodic body force. Various turbulence processes, including the transfer of energy between eddy sizes and between directional components, and the production, dissipation, and spatial diffusion of turbulence, are considered. It is concluded that the physical processes occurring in turbulence can be profitably studied numerically.

Exergy optimization in a steady moving bed heat exchanger.

PubMed

Soria-Verdugo, A; Almendros-Ibáñez, J A; Ruiz-Rivas, U; Santana, D

2009-04-01

This work provides an energy and exergy optimization analysis of a moving bed heat exchanger (MBHE). The exchanger is studied as a cross-flow heat exchanger where one of the phases is a moving granular medium. The optimal MBHE dimensions and the optimal particle diameter are obtained for a range of incoming fluid flow rates. The analyses are carried out over operation data of the exchanger obtained in two ways: a numerical simulation of the steady-state problem and an analytical solution of the simplified equations, neglecting the conduction terms. The numerical simulation considers, for the solid, the convection heat transfer to the fluid and the diffusion term in both directions, and for the fluid only the convection heat transfer to the solid. The results are compared with a well-known analytical solution (neglecting conduction effects) for the temperature distribution in the exchanger. Next, the analytical solution is used to derive an expression for the exergy destruction. The optimal length of the MBHE depends mainly on the flow rate and does not depend on particle diameter unless they become very small (thus increasing sharply the pressure drop). The exergy optimal length is always smaller than the thermal one, although the difference is itself small.

Application of boundary element method to Stokes flows over a striped superhydrophobic surface with trapped gas bubbles

NASA Astrophysics Data System (ADS)

Ageev, A. I.; Golubkina, I. V.; Osiptsov, A. N.

2018-01-01

A slow steady flow of a viscous fluid over a superhydrophobic surface with a periodic striped system of 2D rectangular microcavities is considered. The microcavities contain small gas bubbles on the curved surface of which the shear stress vanishes. The general case is analyzed when the bubble occupies only a part of the cavity, and the flow velocity far from the surface is directed at an arbitrary angle to the cavity edge. Due to the linearity of the Stokes flow problem, the solution is split into two parts, corresponding to the flows perpendicular and along the cavities. Two variants of a boundary element method are developed and used to construct numerical solutions on the scale of a single cavity with periodic boundary conditions. By averaging these solutions, the average slip velocity and the slip length tensor components are calculated over a wide range of variation of governing parameters for the cases of a shear-driven flow and a pressure-driven channel flow. For a sufficiently high pressure drop in a microchannel of finite length, the variation of the bubble surface shift into the cavities induced by the streamwise pressure variation is estimated from numerical calculations.

A hybrid numerical technique for predicting the aerodynamic and acoustic fields of advanced turboprops

NASA Technical Reports Server (NTRS)

Homicz, G. F.; Moselle, J. R.

1985-01-01

A hybrid numerical procedure is presented for the prediction of the aerodynamic and acoustic performance of advanced turboprops. A hybrid scheme is proposed which in principle leads to a consistent simultaneous prediction of both fields. In the inner flow a finite difference method, the Approximate-Factorization Alternating-Direction-Implicit (ADI) scheme, is used to solve the nonlinear Euler equations. In the outer flow the linearized acoustic equations are solved via a Boundary-Integral Equation (BIE) method. The two solutions are iteratively matched across a fictitious interface in the flow so as to maintain continuity. At convergence the resulting aerodynamic load prediction will automatically satisfy the appropriate free-field boundary conditions at the edge of the finite difference grid, while the acoustic predictions will reflect the back-reaction of the radiated field on the magnitude of the loading source terms, as well as refractive effects in the inner flow. The equations and logic needed to match the two solutions are developed and the computer program implementing the procedure is described. Unfortunately, no converged solutions were obtained, due to unexpectedly large running times. The reasons for this are discussed and several means to alleviate the situation are suggested.

Experimental search for Exact Coherent Structures in turbulent small aspect ratio Taylor-Couette flow

NASA Astrophysics Data System (ADS)

Crowley, Christopher J.; Krygier, Michael; Grigoriev, Roman O.; Schatz, Michael F.

2017-11-01

Recent theoretical and experimental work suggests that the dynamics of turbulent flows are guided by unstable nonchaotic solutions to the Navier-Stokes equations. These solutions, known as exact coherent structures (ECS), play a key role in a fundamentally deterministic description of turbulence. In order to quantitatively demonstrate that actual turbulence in 3D flows is guided by ECS, high resolution, 3D-3C experimental measurements of the velocity need to be compared to solutions from direct numerical simulation of the Navier-Stokes equations. In this talk, we will present experimental measurements of fully time resolved, velocity measurements in a volume of turbulence in a counter-rotating, small aspect ratio Taylor-Couette flow. This work is supported by the Army Research Office (Contract # W911NF-16-1-0281).

Solution of the wave equation for open surfaces involving a line integral over the edge. [for supersonic propeller noise prediction

NASA Technical Reports Server (NTRS)

Farassat, F.

1984-01-01

A simple mathematical model of a stationary source distribution for the supersonic-propeller noise-prediction formula of Farassat (1983) is developed to test the validity of the formula solutions. The conventional thickness source term is used in place of the Isom thickness formula; the relative importance of the line and surface integrals in the solutions is evaluated; and the numerical results are compared with those obtained with a conventional retarded-time solution in tables. Good agreement is obtained over elevation angles from 10 to 90 deg, and the line-integral contribution is found to be significant at all elevation angles and of the same order of magnitude as the surface-integral contribution at angles less than 30 deg. The amplitude-normalized directivity patterns for the four cases computed (x = 1.5 or 10; k = 5.0 or 50) are presented graphically.

Using a derivative-free optimization method for multiple solutions of inverse transport problems

DOE PAGES

Armstrong, Jerawan C.; Favorite, Jeffrey A.

2016-01-14

Identifying unknown components of an object that emits radiation is an important problem for national and global security. Radiation signatures measured from an object of interest can be used to infer object parameter values that are not known. This problem is called an inverse transport problem. An inverse transport problem may have multiple solutions and the most widely used approach for its solution is an iterative optimization method. This paper proposes a stochastic derivative-free global optimization algorithm to find multiple solutions of inverse transport problems. The algorithm is an extension of a multilevel single linkage (MLSL) method where a meshmore » adaptive direct search (MADS) algorithm is incorporated into the local phase. Furthermore, numerical test cases using uncollided fluxes of discrete gamma-ray lines are presented to show the performance of this new algorithm.« less

The calculation of a turbulent diffusion flame in a free shear flow with a statistical turbulence model

NASA Astrophysics Data System (ADS)

Bywater, R. J.

1980-01-01

Solutions are presented for the turbulent diffusion flame in a two-dimensional shear layer based upon a kinetic theory of turbulence (KTT). The fuel and oxidizer comprising the two streams are considered to react infinitely fast according to a one-step, irreversible kinetic mechanism. The solutions are obtained by direct numerical calculation of the transverse velocity probability density function (PDF) and the associated species distributions. The mean reactant profiles calculated from the solutions display the characteristic thick, turbulent flame zone. The phenomena result from the fact that in the context of the KTT, species react only when in the same velocity cell. This coincides with the known physical requirement that molecular mixing precedes reaction. The solutions demonstrate this behavior by showing how reactants can coexist in the mean, even when infinite reaction rates are enforced at each point (t,x,u) of velocity space.

Streamwise-Localized Solutions with natural 1-fold symmetry

NASA Astrophysics Data System (ADS)

Altmeyer, Sebastian; Willis, Ashley; Hof, Björn

2014-11-01

It has been proposed in recent years that turbulence is organized around unstable invariant solutions, which provide the building blocks of the chaotic dynamics. In direct numerical simulations of pipe flow we show that when imposing a minimal symmetry constraint (reflection in an axial plane only) the formation of turbulence can indeed be explained by dynamical systems concepts. The hypersurface separating laminar from turbulent motion, the edge of turbulence, is spanned by the stable manifolds of an exact invariant solution, a periodic orbit of a spatially localized structure. The turbulent states themselves (turbulent puffs in this case) are shown to arise in a bifurcation sequence from a related localized solution (the upper branch orbit). The rather complex bifurcation sequence involves secondary Hopf bifurcations, frequency locking and a period doubling cascade until eventually turbulent puffs arise. In addition we report preliminary results of the transition sequence for pipe flow without symmetry constraints.

Fully inkjet-printed microfluidics: a solution to low-cost rapid three-dimensional microfluidics fabrication with numerous electrical and sensing applications

PubMed Central

Su, Wenjing; Cook, Benjamin S.; Fang, Yunnan; Tentzeris, Manos M.

2016-01-01

As the needs for low-cost rapidly-produced microfluidics are growing with the trend of Lab-on-a-Chip and distributed healthcare, the fully inkjet-printing of microfluidics can be a solution to it with numerous potential electrical and sensing applications. Inkjet-printing is an additive manufacturing technique featuring no material waste and a low equipment cost. Moreover, similar to other additive manufacturing techniques, inkjet-printing is easy to learn and has a high fabrication speed, while it offers generally a great planar resolution down to below 20 µm and enables flexible designs due to its inherent thin film deposition capabilities. Due to the thin film feature, the printed objects also usually obtain a high vertical resolution (such as 4.6 µm). This paper introduces a low-cost rapid three-dimensional fabrication process of microfluidics, that relies entirely on an inkjet-printer based single platform and can be implemented directly on top of virtually any substrates. PMID:27713545

Fully inkjet-printed microfluidics: a solution to low-cost rapid three-dimensional microfluidics fabrication with numerous electrical and sensing applications

NASA Astrophysics Data System (ADS)

Su, Wenjing; Cook, Benjamin S.; Fang, Yunnan; Tentzeris, Manos M.

2016-10-01

As the needs for low-cost rapidly-produced microfluidics are growing with the trend of Lab-on-a-Chip and distributed healthcare, the fully inkjet-printing of microfluidics can be a solution to it with numerous potential electrical and sensing applications. Inkjet-printing is an additive manufacturing technique featuring no material waste and a low equipment cost. Moreover, similar to other additive manufacturing techniques, inkjet-printing is easy to learn and has a high fabrication speed, while it offers generally a great planar resolution down to below 20 µm and enables flexible designs due to its inherent thin film deposition capabilities. Due to the thin film feature, the printed objects also usually obtain a high vertical resolution (such as 4.6 µm). This paper introduces a low-cost rapid three-dimensional fabrication process of microfluidics, that relies entirely on an inkjet-printer based single platform and can be implemented directly on top of virtually any substrates.

The solution of three-variable duct-flow equations

NASA Technical Reports Server (NTRS)

Stuart, A. R.; Hetherington, R.

1974-01-01

This paper establishes a numerical method for the solution of three-variable problems and is applied here to rotational flows through ducts of various cross sections. An iterative scheme is developed, the main feature of which is the addition of a duplicate variable to the forward component of velocity. Two forward components of velocity result from integrating two sets of first order ordinary differential equations for the streamline curvatures, in intersecting directions across the duct. Two pseudo-continuity equations are introduced with source/sink terms, whose strengths are dependent on the difference between the forward components of velocity. When convergence is obtained, the two forward components of velocity are identical, the source/sink terms are zero, and the original equations are satisfied. A computer program solves the exact equations and boundary conditions numerically. The method is economical and compares successfully with experiments on bent ducts of circular and rectangular cross section where secondary flows are caused by gradients of total pressure upstream.

Plastic zone size and crack tip opening displacement of a Dugdale crack interacting with a coated circular inclusion

NASA Astrophysics Data System (ADS)

Hoh, H. J.; Xiao, Z. M.; Luo, J.

2010-09-01

An analytical investigation on the plastic zone size of a crack near a coated circular inclusion under three different loading conditions of uniaxial tension, uniform tension and pure shear was carried out. Both the crack and coated circular inclusion are embedded in an infinite matrix, with the crack oriented along the radial direction of the inclusion. In the solution procedure, the crack is simulated as a continuous distribution of edge dislocations. With the Dugdale model of small-scale yielding [J. Mech. Phys. Solids 8 (1960) p. 100], two thin strips of yielded plastic zones are introduced at both crack tips. Using the solution for a coated circular inclusion interacting with a single dislocation as the Green's function, the physical problem is formulated into a set of singular integral equations. Using the method of Erdogan and Gupta [Q. J. Appl. Math. 29 (1972) p. 525] and iterative numerical procedures, the singular integral equations are solved numerically for the plastic zone sizes and crack tip opening displacement.

Discontinuous Galerkin finite element methods for radiative transfer in spherical symmetry

NASA Astrophysics Data System (ADS)

Kitzmann, D.; Bolte, J.; Patzer, A. B. C.

2016-11-01

The discontinuous Galerkin finite element method (DG-FEM) is successfully applied to treat a broad variety of transport problems numerically. In this work, we use the full capacity of the DG-FEM to solve the radiative transfer equation in spherical symmetry. We present a discontinuous Galerkin method to directly solve the spherically symmetric radiative transfer equation as a two-dimensional problem. The transport equation in spherical atmospheres is more complicated than in the plane-parallel case owing to the appearance of an additional derivative with respect to the polar angle. The DG-FEM formalism allows for the exact integration of arbitrarily complex scattering phase functions, independent of the angular mesh resolution. We show that the discontinuous Galerkin method is able to describe accurately the radiative transfer in extended atmospheres and to capture discontinuities or complex scattering behaviour which might be present in the solution of certain radiative transfer tasks and can, therefore, cause severe numerical problems for other radiative transfer solution methods.

Computational attributes of the integral form of the equation of transfer

NASA Technical Reports Server (NTRS)

Frankel, J. I.

1991-01-01

Difficulties can arise in radiative and neutron transport calculations when a highly anisotropic scattering phase function is present. In the presence of anisotropy, currently used numerical solutions are based on the integro-differential form of the linearized Boltzmann transport equation. This paper, departs from classical thought and presents an alternative numerical approach based on application of the integral form of the transport equation. Use of the integral formalism facilitates the following steps: a reduction in dimensionality of the system prior to discretization, the use of symbolic manipulation to augment the computational procedure, and the direct determination of key physical quantities which are derivable through the various Legendre moments of the intensity. The approach is developed in the context of radiative heat transfer in a plane-parallel geometry, and results are presented and compared with existing benchmark solutions. Encouraging results are presented to illustrate the potential of the integral formalism for computation. The integral formalism appears to possess several computational attributes which are well-suited to radiative and neutron transport calculations.

Time-dependent transport of energetic particles in magnetic turbulence: computer simulations versus analytical theory

NASA Astrophysics Data System (ADS)

Arendt, V.; Shalchi, A.

2018-06-01

We explore numerically the transport of energetic particles in a turbulent magnetic field configuration. A test-particle code is employed to compute running diffusion coefficients as well as particle distribution functions in the different directions of space. Our numerical findings are compared with models commonly used in diffusion theory such as Gaussian distribution functions and solutions of the cosmic ray Fokker-Planck equation. Furthermore, we compare the running diffusion coefficients across the mean magnetic field with solutions obtained from the time-dependent version of the unified non-linear transport theory. In most cases we find that particle distribution functions are indeed of Gaussian form as long as a two-component turbulence model is employed. For turbulence setups with reduced dimensionality, however, the Gaussian distribution can no longer be obtained. It is also shown that the unified non-linear transport theory agrees with simulated perpendicular diffusion coefficients as long as the pure two-dimensional model is excluded.

Applications of computer algebra to distributed parameter systems

NASA Technical Reports Server (NTRS)

Storch, Joel A.

1993-01-01

In the analysis of vibrations of continuous elastic systems, one often encounters complicated transcendental equations with roots directly related to the system's natural frequencies. Typically, these equations contain system parameters whose values must be specified before a numerical solution can be obtained. The present paper presents a method whereby the fundamental frequency can be obtained in analytical form to any desired degree of accuracy. The method is based upon truncation of rapidly converging series involving inverse powers of the system natural frequencies. A straightforward method to developing these series and summing them in closed form is presented. It is demonstrated how Computer Algebra can be exploited to perform the intricate analytical procedures which otherwise would render the technique difficult to apply in practice. We illustrate the method by developing two analytical approximations to the fundamental frequency of a vibrating cantilever carrying a rigid tip body. The results are compared to the numerical solution of the exact (transcendental) frequency equation over a range of system parameters.

Hybrid upwind discretization of nonlinear two-phase flow with gravity

NASA Astrophysics Data System (ADS)

Lee, S. H.; Efendiev, Y.; Tchelepi, H. A.

2015-08-01

Multiphase flow in porous media is described by coupled nonlinear mass conservation laws. For immiscible Darcy flow of multiple fluid phases, whereby capillary effects are negligible, the transport equations in the presence of viscous and buoyancy forces are highly nonlinear and hyperbolic. Numerical simulation of multiphase flow processes in heterogeneous formations requires the development of discretization and solution schemes that are able to handle the complex nonlinear dynamics, especially of the saturation evolution, in a reliable and computationally efficient manner. In reservoir simulation practice, single-point upwinding of the flux across an interface between two control volumes (cells) is performed for each fluid phase, whereby the upstream direction is based on the gradient of the phase-potential (pressure plus gravity head). This upwinding scheme, which we refer to as Phase-Potential Upwinding (PPU), is combined with implicit (backward-Euler) time discretization to obtain a Fully Implicit Method (FIM). Even though FIM suffers from numerical dispersion effects, it is widely used in practice. This is because of its unconditional stability and because it yields conservative, monotone numerical solutions. However, FIM is not unconditionally convergent. The convergence difficulties are particularly pronounced when the different immiscible fluid phases switch between co-current and counter-current states as a function of time, or (Newton) iteration. Whether the multiphase flow across an interface (between two control-volumes) is co-current, or counter-current, depends on the local balance between the viscous and buoyancy forces, and how the balance evolves in time. The sensitivity of PPU to small changes in the (local) pressure distribution exacerbates the problem. The common strategy to deal with these difficulties is to cut the timestep and try again. Here, we propose a Hybrid-Upwinding (HU) scheme for the phase fluxes, then HU is combined with implicit time discretization to yield a fully implicit method. In the HU scheme, the phase flux is divided into two parts based on the driving force. The viscous-driven and buoyancy-driven phase fluxes are upwinded differently. Specifically, the viscous flux, which is always co-current, is upwinded based on the direction of the total-velocity. The buoyancy-driven flux across an interface is always counter-current and is upwinded such that the heavier fluid goes downward and the lighter fluid goes upward. We analyze the properties of the Implicit Hybrid Upwinding (IHU) scheme. It is shown that IHU is locally conservative and produces monotone, physically-consistent numerical solutions. The IHU solutions show numerical diffusion levels that are slightly higher than those for standard FIM (i.e., implicit PPU). The primary advantage of the IHU scheme is that the numerical overall-flux of a fluid phase remains continuous and differentiable as the flow regime changes between co-current and counter-current conditions. This is in contrast to the standard phase-potential upwinding scheme, in which the overall fractional-flow (flux) function is non-differentiable across the boundary between co-current and counter-current flows.

A possible explanation for foreland thrust propagation

NASA Astrophysics Data System (ADS)

Panian, John; Pilant, Walter

1990-06-01

A common feature of thin-skinned fold and thrust belts is the sequential nature of foreland directed thrust systems. As a rule, younger thrusts develop in the footwalls of older thrusts, the whole sequence propagating towards the foreland in the transport direction. As each new younger thrust develops, the entire sequence is thickened; particularly in the frontal region. The compressive toe region can be likened to an advancing wave; as the mountainous thrust belt advanced the down-surface slope stresses drive thrusts ahead of it much like a surfboard rider. In an attempt to investigate the stresses in the frontal regions of thrustsheets, a numerical method has been devised from the algorithm given by McTigue and Mei [1981]. The algorithm yields a quickly computed approximate solution of the gravity- and tectonic-induced stresses of a two-dimensional homogeneous elastic half-space with an arbitrarily shaped free surface of small slope. A comparison of the numerical method with analytical examples shows excellent agreement. The numerical method was devised because it greatly facilitates the stress calculations and frees one from using the restrictive, simple topographic profiles necessary to obtain an analytical solution. The numerical version of the McTigue and Mei algorithm shows that there is a region of increased maximum resolved shear stress, τ, directly beneath the toe of the overthrust sheet. Utilizing the Mohr-Coulomb failure criterion, predicted fault lines are computed. It is shown that they flatten and become horizontal in some portions of this zone of increased τ. Thrust sheets are known to advance upon weak decollement zones. If there is a coincidence of increased τ, a weak rock layer, and a potential fault line parallel to this weak layer, we have in place all the elements necessary to initiate a new thrusting event. That is, this combination acts as a nucleating center to initiate a new thrusting event. Therefore, thrusts develop in sequence towards the foreland as a consequence of the stress concentrating abilities of the toe of the thrust sheet. The gravity- and tectonic-induced stresses due to the surface topography (usually ignored in previous analyses) of an advancing thrust sheet play a key role in the nature of shallow foreland thrust propagation.

Development of indirect EFBEM for radiating noise analysis including underwater problems

NASA Astrophysics Data System (ADS)

Kwon, Hyun-Wung; Hong, Suk-Yoon; Song, Jee-Hun

2013-09-01

For the analysis of radiating noise problems in medium-to-high frequency ranges, the Energy Flow Boundary Element Method (EFBEM) was developed. EFBEM is the analysis technique that applies the Boundary Element Method (BEM) to Energy Flow Analysis (EFA). The fundamental solutions representing spherical wave property for radiating noise problems in open field and considering the free surface effect in underwater are developed. Also the directivity factor is developed to express wave's directivity patterns in medium-to-high frequency ranges. Indirect EFBEM by using fundamental solutions and fictitious source was applied to open field and underwater noise problems successfully. Through numerical applications, the acoustic energy density distributions due to vibration of a simple plate model and a sphere model were compared with those of commercial code, and the comparison showed good agreement in the level and pattern of the energy density distributions.

Simple framework for understanding the universality of the maximum drag reduction asymptote in turbulent flow of polymer solutions

NASA Astrophysics Data System (ADS)

Li, Chang-Feng; Sureshkumar, Radhakrishna; Khomami, Bamin

2015-10-01

Self-consistent direct numerical simulations of turbulent channel flows of dilute polymer solutions exhibiting friction drag reduction (DR) show that an effective Deborah number defined as the ratio of polymer relaxation time to the time scale of fluctuations in the vorticity in the mean flow direction remains O (1) from the onset of DR to the maximum drag reduction (MDR) asymptote. However, the ratio of the convective time scale associated with streamwise vorticity fluctuations to the vortex rotation time decreases with increasing DR, and the maximum drag reduction asymptote is achieved when these two time scales become nearly equal. Based on these observations, a simple framework is proposed that adequately describes the influence of polymer additives on the extent of DR from the onset of DR to MDR as well as the universality of the MDR in wall-bounded turbulent flows with polymer additives.

Simple framework for understanding the universality of the maximum drag reduction asymptote in turbulent flow of polymer solutions.

PubMed

Li, Chang-Feng; Sureshkumar, Radhakrishna; Khomami, Bamin

2015-10-01

Self-consistent direct numerical simulations of turbulent channel flows of dilute polymer solutions exhibiting friction drag reduction (DR) show that an effective Deborah number defined as the ratio of polymer relaxation time to the time scale of fluctuations in the vorticity in the mean flow direction remains O(1) from the onset of DR to the maximum drag reduction (MDR) asymptote. However, the ratio of the convective time scale associated with streamwise vorticity fluctuations to the vortex rotation time decreases with increasing DR, and the maximum drag reduction asymptote is achieved when these two time scales become nearly equal. Based on these observations, a simple framework is proposed that adequately describes the influence of polymer additives on the extent of DR from the onset of DR to MDR as well as the universality of the MDR in wall-bounded turbulent flows with polymer additives.

4-D OCT in Developmental Cardiology

NASA Astrophysics Data System (ADS)

Jenkins, Michael W.; Rollins, Andrew M.

Although strong evidence exists to suggest that altered cardiac function can lead to CHDs, few studies have investigated the influential role of cardiac function and biophysical forces on the development of the cardiovascular system due to a lack of proper in vivo imaging tools. 4-D imaging is needed to decipher the complex spatial and temporal patterns of biomechanical forces acting upon the heart. Numerous solutions over the past several years have demonstrated 4-D OCT imaging of the developing cardiovascular system. This chapter will focus on these solutions and explain their context in the evolution of 4-D OCT imaging. The first sections describe the relevant techniques (prospective gating, direct 4-D imaging, retrospective gating), while later sections focus on 4-D Doppler imaging and measurements of force implementing 4-D OCT Doppler. Finally, the techniques are summarized, and some possible future directions are discussed.

A meshless method using radial basis functions for numerical solution of the two-dimensional KdV-Burgers equation

NASA Astrophysics Data System (ADS)

Zabihi, F.; Saffarian, M.

2016-07-01

The aim of this article is to obtain the numerical solution of the two-dimensional KdV-Burgers equation. We construct the solution by using a different approach, that is based on using collocation points. The solution is based on using the thin plate splines radial basis function, which builds an approximated solution with discretizing the time and the space to small steps. We use a predictor-corrector scheme to avoid solving the nonlinear system. The results of numerical experiments are compared with analytical solutions to confirm the accuracy and efficiency of the presented scheme.

Modeling flow and solute transport in irrigation furrows

USDA-ARS?s Scientific Manuscript database

This paper presents an internally coupled flow and solute transport model for free-draining irrigation furrows. Furrow hydraulics is simulated with a numerical zero-inertia model and solute transport is computed with a model based on a numerical solution of the cross-section averaged advection-dispe...

Fitted Fourier-pseudospectral methods for solving a delayed reaction-diffusion partial differential equation in biology

NASA Astrophysics Data System (ADS)

Adam, A. M. A.; Bashier, E. B. M.; Hashim, M. H. A.; Patidar, K. C.

2017-07-01

In this work, we design and analyze a fitted numerical method to solve a reaction-diffusion model with time delay, namely, a delayed version of a population model which is an extension of the logistic growth (LG) equation for a food-limited population proposed by Smith [F.E. Smith, Population dynamics in Daphnia magna and a new model for population growth, Ecology 44 (1963) 651-663]. Seeing that the analytical solution (in closed form) is hard to obtain, we seek for a robust numerical method. The method consists of a Fourier-pseudospectral semi-discretization in space and a fitted operator implicit-explicit scheme in temporal direction. The proposed method is analyzed for convergence and we found that it is unconditionally stable. Illustrative numerical results will be presented at the conference.

Automated smoother for the numerical decoupling of dynamics models.

PubMed

Vilela, Marco; Borges, Carlos C H; Vinga, Susana; Vasconcelos, Ana Tereza R; Santos, Helena; Voit, Eberhard O; Almeida, Jonas S

2007-08-21

Structure identification of dynamic models for complex biological systems is the cornerstone of their reverse engineering. Biochemical Systems Theory (BST) offers a particularly convenient solution because its parameters are kinetic-order coefficients which directly identify the topology of the underlying network of processes. We have previously proposed a numerical decoupling procedure that allows the identification of multivariate dynamic models of complex biological processes. While described here within the context of BST, this procedure has a general applicability to signal extraction. Our original implementation relied on artificial neural networks (ANN), which caused slight, undesirable bias during the smoothing of the time courses. As an alternative, we propose here an adaptation of the Whittaker's smoother and demonstrate its role within a robust, fully automated structure identification procedure. In this report we propose a robust, fully automated solution for signal extraction from time series, which is the prerequisite for the efficient reverse engineering of biological systems models. The Whittaker's smoother is reformulated within the context of information theory and extended by the development of adaptive signal segmentation to account for heterogeneous noise structures. The resulting procedure can be used on arbitrary time series with a nonstationary noise process; it is illustrated here with metabolic profiles obtained from in-vivo NMR experiments. The smoothed solution that is free of parametric bias permits differentiation, which is crucial for the numerical decoupling of systems of differential equations. The method is applicable in signal extraction from time series with nonstationary noise structure and can be applied in the numerical decoupling of system of differential equations into algebraic equations, and thus constitutes a rather general tool for the reverse engineering of mechanistic model descriptions from multivariate experimental time series.

A Planning Framework for the Deployment of Innovative Information and Communication Technologies in Procurement

NASA Astrophysics Data System (ADS)

Alard, Robert; Gustafsson, Martin; Nienhaus, Jörg

The management of buyer-supplier relations is a major topic for many enterprises today. Modern Information and Communication Technologies (ICT) offer interesting perspectives on opportunities and implementation approaches. Today, logistics and procurement departments of numerous enterprises are evaluating the possibilities and opportunities of new ICT solutions and especially of internet-based electronic procurement solutions for the optimisation and re-engineering of their buyer-supplier relationships. Due to the highly innovative character of the new ICT solutions and the scarcely available operational examples in the industry, only little guidance exists to support responsible managers during the evaluation, planning and designing of internet-based electronic procurement solutions. This paper describes a framework for the strategic evaluation and planning of the deployment of internet-based procurement solutions for direct materials. The presented approach supports enterprises in the analysis of procurement objects and procurement structuring, in the definition and management of buyer-supplier-relationships, in the requirements analysis of ICT solutions as well as the assessment of the potential to support procurement with innovative ICT and internet-based electronic procurement solutions.

Analytical solution for the normal emission portion of the averaged Yarkovsky-O'Keefe-Radzvieskii-Paddack coefficient for a single facet

NASA Astrophysics Data System (ADS)

Albuja, Antonella A.; Scheeres, Daniel J.

2015-02-01

The Yarkovsky-O'Keefe-Radzvieskii-Paddack (YORP) effect has been well studied for asteroids. This paper develops an analytic solution to find the normal emission YORP component for a single facet. The solution presented here does not account for self-shadowing or self-heating. The YORP coefficient for all facets can be summed together to find the total coefficient of the asteroid. The normal emission component of YORP has been shown to be the most important for asteroids and it directly affects the rate of change of the asteroid's spin period. The analytical solution found is a sole function of the facet's geometry and the obliquity of the asteroid. This solution is universal for any facet and its orientation. The behaviour of the coefficient is analysed with this analytical solution. The closed-form solution is used to find the total YORP coefficient for the asteroids Apollo and 1998 ML14 whose shape models are composed of different numbers of facets. The results are then compared to published results and those obtained through numerical quadrature for validation.

Automated Generation of Finite-Element Meshes for Aircraft Conceptual Design

NASA Technical Reports Server (NTRS)

Li, Wu; Robinson, Jay

2016-01-01

This paper presents a novel approach for automated generation of fully connected finite-element meshes for all internal structural components and skins of a given wing-body geometry model, controlled by a few conceptual-level structural layout parameters. Internal structural components include spars, ribs, frames, and bulkheads. Structural layout parameters include spar/rib locations in wing chordwise/spanwise direction and frame/bulkhead locations in longitudinal direction. A simple shell thickness optimization problem with two load conditions is used to verify versatility and robustness of the automated meshing process. The automation process is implemented in ModelCenter starting from an OpenVSP geometry and ending with a NASTRAN 200 solution. One subsonic configuration and one supersonic configuration are used for numerical verification. Two different structural layouts are constructed for each configuration and five finite-element meshes of different sizes are generated for each layout. The paper includes various comparisons of solutions of 20 thickness optimization problems, as well as discussions on how the optimal solutions are affected by the stress constraint bound and the initial guess of design variables.

Ensemble solute transport in two-dimensional operator-scaling random fields

NASA Astrophysics Data System (ADS)

Monnig, Nathan D.; Benson, David A.; Meerschaert, Mark M.

2008-02-01

Motivated by field measurements of aquifer hydraulic conductivity (K), recent techniques were developed to construct anisotropic fractal random fields in which the scaling, or self-similarity parameter, varies with direction and is defined by a matrix. Ensemble numerical results are analyzed for solute transport through these two-dimensional "operator-scaling" fractional Brownian motion ln(K) fields. Both the longitudinal and transverse Hurst coefficients, as well as the "radius of isotropy" are important to both plume growth rates and the timing and duration of breakthrough. It is possible to create operator-scaling fractional Brownian motion fields that have more "continuity" or stratification in the direction of transport. The effects on a conservative solute plume are continually faster-than-Fickian growth rates, highly non-Gaussian shapes, and a heavier tail early in the breakthrough curve. Contrary to some analytic stochastic theories for monofractal K fields, the plume growth rates never exceed A. Mercado's (1967) purely stratified aquifer growth rate of plume apparent dispersivity proportional to mean distance. Apparent superstratified growth must be the result of other demonstrable factors, such as initial plume size.

An efficient finite element method for simulation of droplet spreading on a topologically rough surface

NASA Astrophysics Data System (ADS)

Luo, Li; Wang, Xiao-Ping; Cai, Xiao-Chuan

2017-11-01

We study numerically the dynamics of a three-dimensional droplet spreading on a rough solid surface using a phase-field model consisting of the coupled Cahn-Hilliard and Navier-Stokes equations with a generalized Navier boundary condition (GNBC). An efficient finite element method on unstructured meshes is introduced to cope with the complex geometry of the solid surfaces. We extend the GNBC to surfaces with complex geometry by including its weak form along different normal and tangential directions in the finite element formulation. The semi-implicit time discretization scheme results in a decoupled system for the phase function, the velocity, and the pressure. In addition, a mass compensation algorithm is introduced to preserve the mass of the droplet. To efficiently solve the decoupled systems, we present a highly parallel solution strategy based on domain decomposition techniques. We validate the newly developed solution method through extensive numerical experiments, particularly for those phenomena that can not be achieved by two-dimensional simulations. On a surface with circular posts, we study how wettability of the rough surface depends on the geometry of the posts. The contact line motion for a droplet spreading over some periodic rough surfaces are also efficiently computed. Moreover, we study the spreading process of an impacting droplet on a microstructured surface, a qualitative agreement is achieved between the numerical and experimental results. The parallel performance suggests that the proposed solution algorithm is scalable with over 4,000 processors cores with tens of millions of unknowns.

Direct Numerical Simulation of Incompressible Pipe Flow Using a B-Spline Spectral Method

NASA Technical Reports Server (NTRS)

Loulou, Patrick; Moser, Robert D.; Mansour, Nagi N.; Cantwell, Brian J.

1997-01-01

A numerical method based on b-spline polynomials was developed to study incompressible flows in cylindrical geometries. A b-spline method has the advantages of possessing spectral accuracy and the flexibility of standard finite element methods. Using this method it was possible to ensure regularity of the solution near the origin, i.e. smoothness and boundedness. Because b-splines have compact support, it is also possible to remove b-splines near the center to alleviate the constraint placed on the time step by an overly fine grid. Using the natural periodicity in the azimuthal direction and approximating the streamwise direction as periodic, so-called time evolving flow, greatly reduced the cost and complexity of the computations. A direct numerical simulation of pipe flow was carried out using the method described above at a Reynolds number of 5600 based on diameter and bulk velocity. General knowledge of pipe flow and the availability of experimental measurements make pipe flow the ideal test case with which to validate the numerical method. Results indicated that high flatness levels of the radial component of velocity in the near wall region are physical; regions of high radial velocity were detected and appear to be related to high speed streaks in the boundary layer. Budgets of Reynolds stress transport equations showed close similarity with those of channel flow. However contrary to channel flow, the log layer of pipe flow is not homogeneous for the present Reynolds number. A topological method based on a classification of the invariants of the velocity gradient tensor was used. Plotting iso-surfaces of the discriminant of the invariants proved to be a good method for identifying vortical eddies in the flow field.

Hyporheic less-mobile porosity and solute transport in porous media

NASA Astrophysics Data System (ADS)

MahmoodPoorDehkordy, F.; Briggs, M. A.; Day-Lewis, F. D.; Scruggs, C.; Singha, K.; Zarnetske, J. P.; Lane, J. W., Jr.; Bagtzoglou, A. C.

2017-12-01

Solute transport and reactive processes are strongly influenced by hydrodynamic exchange with the hyporheic zone. Contaminant transport and redox zonation in the hyporheic zone and near-stream aquifer can be impacted by the exchange between mobile and less-mobile porosity zones in heterogeneous porous media. Less-mobile porosity zones can be created by fine materials with tight pore throats (e.g. clay, organics) and in larger, well-connected pores down gradient of flow obstructions (e.g. sand behind cobbles). Whereas fluid sampling is primarily responsive to the more-mobile domain, tracking solute tracer dynamics by geoelectrical methods provides direct information about both more- and less-mobile zones. During tracer injection through porous media of varied pore connectivity, a lag between fluid and bulk electrical conductivity is observed, creating a hysteresis loop when plotted in conductivity space. Thus, the combination of simultaneous fluid and bulk electrical conductivity measurements enables a much improved quantification of less-mobile solute dynamics compared to traditional fluid-only sampling approaches. We have demonstrated the less-mobile porosity exchange in laboratory-scale column experiments verified by simulation models. The experimental approach has also been applied to streambed sediments in column and reach-scale field experiments and verified using numerical simulation. Properties of the resultant hysteresis loops can be used to estimate exchange parameters of less-mobile porosity. Our integrated approach combining field experiments, laboratory experiments, and numerical modeling provides new insights into the effect of less-mobile porosity on solute transport in the hyporheic zone.

Flow and axial dispersion in a sinusoidal-walled tube: Effects of inertial and unsteady flows

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

Richmond, Marshall C.; Perkins, William A.; Scheibe, Timothy D.

2013-12-01

Dispersion in porous media flows has been the subject of much experimental, theoretical and numerical study. Here we consider a wavy-walled tube (a three-dimensional tube with sinusoidally-varying diameter) as a simplified conceptualization of flow in porous media, where constrictions represent pore throats and expansions pore bodies. A theoretical model for effective (macroscopic) longitudinal dispersion in this system has been developed by volume averaging the microscale velocity field. Direct numerical simulation using computational fluid dynamics (CFD) methods was used to compute velocity fields by solving the Navier-Stokes equations, and also to numerically solve the volume averaging closure problem, for a rangemore » of Reynolds numbers (Re) spanning the low-Re to inertial flow regimes, including one simulation at Re = 449 for which unsteady flow was observed. Dispersion values were computed using both the volume averaging solution and a random walk particle tracking method, and results of the two methods were shown to be consistent. Our results are compared to experimental measurements of dispersion in porous media and to previous theoretical results for the low-Re, Stokes flow regime. In the steady inertial regime we observe an power-law increase in effective longitudinal dispersion (DL) with Re, consistent with previous results. This rapid rate of increase is caused by trapping of solute in expansions due to flow separation (eddies). For the unsteady case (Re = 449), the rate of increase of DL with Re was smaller than that observed at lower Re. Velocity fluctuations in this regime lead to increased rates of solute mass transfer between the core flow and separated flow regions, thus diminishing the amount of tailing caused by solute trapping in eddies and thereby reducing longitudinal dispersion.« less

Gravity-Driven Thin Film Flow of an Ellis Fluid.

PubMed

Kheyfets, Vitaly O; Kieweg, Sarah L

2013-12-01

The thin film lubrication approximation has been studied extensively for moving contact lines of Newtonian fluids. However, many industrial and biological applications of the thin film equation involve shear-thinning fluids, which often also exhibit a Newtonian plateau at low shear. This study presents new numerical simulations of the three-dimensional (i.e. two-dimensional spreading), constant-volume, gravity-driven, free surface flow of an Ellis fluid. The numerical solution was validated with a new similarity solution, compared to previous experiments, and then used in a parametric study. The parametric study centered around rheological data for an example biological application of thin film flow: topical drug delivery of anti-HIV microbicide formulations, e.g. hydroxyethylcellulose (HEC) polymer solutions. The parametric study evaluated how spreading length and front velocity saturation depend on Ellis parameters. A lower concentration polymer solution with smaller zero shear viscosity ( η 0 ), τ 1/2 , and λ values spread further. However, when comparing any two fluids with any possible combinations of Ellis parameters, the impact of changing one parameter on spreading length depends on the direction and magnitude of changes in the other two parameters. In addition, the isolated effect of the shear-thinning parameter, λ , on the front velocity saturation depended on τ 1/2 . This study highlighted the relative effects of the individual Ellis parameters, and showed that the shear rates in this flow were in both the shear-thinning and plateau regions of rheological behavior, emphasizing the importance of characterizing the full range of shear-rates in rheological measurements. The validated numerical model and parametric study provides a useful tool for future steps to optimize flow of a fluid with rheological behavior well-described by the Ellis constitutive model, in a range of industrial and biological applications.

A digital matched filter for reverse time chaos.

PubMed

Bailey, J Phillip; Beal, Aubrey N; Dean, Robert N; Hamilton, Michael C

2016-07-01

The use of reverse time chaos allows the realization of hardware chaotic systems that can operate at speeds equivalent to existing state of the art while requiring significantly less complex circuitry. Matched filter decoding is possible for the reverse time system since it exhibits a closed form solution formed partially by a linear basis pulse. Coefficients have been calculated and are used to realize the matched filter digitally as a finite impulse response filter. Numerical simulations confirm that this correctly implements a matched filter that can be used for detection of the chaotic signal. In addition, the direct form of the filter has been implemented in hardware description language and demonstrates performance in agreement with numerical results.

Numerical studies of the KP line-solitons

NASA Astrophysics Data System (ADS)

Chakravarty, S.; McDowell, T.; Osborne, M.

2017-03-01

The Kadomtsev-Petviashvili (KP) equation admits a class of solitary wave solutions localized along distinct rays in the xy-plane, called the line-solitons, which describe the interaction of shallow water waves on a flat surface. These wave interactions have been observed on long, flat beaches, as well as have been recreated in laboratory experiments. In this paper, the line-solitons are investigated via direct numerical simulations of the KP equation, and the interactions of the evolved solitary wave patterns are studied. The objective is to obtain greater insight into solitary wave interactions in shallow water and to determine the extent the KP equation is a good model in describing these nonlinear interactions.

bhlight: General Relativistic Radiation Magnetohydrodynamics with Monte Carlo Transport

DOE PAGES

Ryan, Benjamin R; Dolence, Joshua C.; Gammie, Charles F.

2015-06-25

We present bhlight, a numerical scheme for solving the equations of general relativistic radiation magnetohydrodynamics using a direct Monte Carlo solution of the frequency-dependent radiative transport equation. bhlight is designed to evolve black hole accretion flows at intermediate accretion rate, in the regime between the classical radiatively efficient disk and the radiatively inefficient accretion flow (RIAF), in which global radiative effects play a sub-dominant but non-negligible role in disk dynamics. We describe the governing equations, numerical method, idiosyncrasies of our implementation, and a suite of test and convergence results. We also describe example applications to radiative Bondi accretion and tomore » a slowly accreting Kerr black hole in axisymmetry.« less

Numerical studies of the Bethe-Salpeter equation for a two-fermion bound state

NASA Astrophysics Data System (ADS)

de Paula, W.; Frederico, T.; Salmè, G.; Viviani, M.

2018-03-01

Some recent advances on the solution of the Bethe-Salpeter equation (BSE) for a two-fermion bound system directly in Minkowski space are presented. The calculations are based on the expression of the Bethe-Salpeter amplitude in terms of the so-called Nakanishi integral representation and on the light-front projection (i.e. the integration of the light-front variable k - = k 0 - k 3). The latter technique allows for the analytically exact treatment of the singularities plaguing the two-fermion BSE in Minkowski space. The good agreement observed between our results and those obtained using other existing numerical methods, based on both Minkowski and Euclidean space techniques, fully corroborate our analytical treatment.

Numerical prediction of marine propeller noise in non-uniform inflow

NASA Astrophysics Data System (ADS)

Pan, Yu-cun; Zhang, Huai-xin

2013-03-01

A numerical study on the acoustic radiation of a propeller interacting with non-uniform inflow has been conducted. Real geometry of a marine propeller DTMB 4118 is used in the calculation, and sliding mesh technique is adopted to deal with the rotational motion of the propeller. The performance of the DES (Detached Eddy Simulation) approach at capturing the unsteady forces and moments on the propeller is compared with experiment. Far-field sound radiation is predicted by the formation 1A developed by Farassat, an integral solution of FW-H (Ffowcs Williams-Hawkings) equation in time domain. The sound pressure and directivity patterns of the propeller operating in two specific velocity distributions are discussed.

A digital matched filter for reverse time chaos

NASA Astrophysics Data System (ADS)

Bailey, J. Phillip; Beal, Aubrey N.; Dean, Robert N.; Hamilton, Michael C.

2016-07-01

The use of reverse time chaos allows the realization of hardware chaotic systems that can operate at speeds equivalent to existing state of the art while requiring significantly less complex circuitry. Matched filter decoding is possible for the reverse time system since it exhibits a closed form solution formed partially by a linear basis pulse. Coefficients have been calculated and are used to realize the matched filter digitally as a finite impulse response filter. Numerical simulations confirm that this correctly implements a matched filter that can be used for detection of the chaotic signal. In addition, the direct form of the filter has been implemented in hardware description language and demonstrates performance in agreement with numerical results.

The use of multigrid techniques in the solution of the Elrod algorithm for a dynamically loaded journal bearing. M.S. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Woods, Claudia M.

1988-01-01

A numerical solution to a theoretical model of vapor cavitation in a dynamically loaded journal bearing is developed, utilizing a multigrid iterative technique. The code is compared with a presently existing direct solution in terms of computational time and accuracy. The model is based on the Elrod algorithm, a control volume approach to the Reynolds equation which mimics the Jakobssen-Floberg and Olsson cavitation theory. Besides accounting for a moving cavitation boundary and conservation of mass at the boundary, it also conserves mass within the cavitated region via liquid striations. The mixed nature of the equations (elliptic in the full film zone and nonelliptic in the cavitated zone) coupled with the dynamic aspects of the problem create interesting difficulties for the present solution approach. Emphasis is placed on the methods found to eliminate solution instabilities. Excellent results are obtained for both accuracy and reduction of computational time.

Periodic waves in fiber Bragg gratings

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

Chow, K. W.; Merhasin, Ilya M.; Malomed, Boris A.

2008-02-15

We construct two families of exact periodic solutions to the standard model of fiber Bragg grating (FBG) with Kerr nonlinearity. The solutions are named ''sn'' and ''cn'' waves, according to the elliptic functions used in their analytical representation. The sn wave exists only inside the FBG's spectral bandgap, while waves of the cn type may only exist at negative frequencies ({omega}<0), both inside and outside the bandgap. In the long-wave limit, the sn and cn families recover, respectively, the ordinary gap solitons, and (unstable) antidark and dark solitons. Stability of the periodic solutions is checked by direct numerical simulations and,more » in the case of the sn family, also through the calculation of instability growth rates for small perturbations. Although, rigorously speaking, all periodic solutions are unstable, a subfamily of practically stable sn waves, with a sufficiently large spatial period and {omega}>0, is identified. However, the sn waves with {omega}<0, as well as all cn solutions, are strongly unstable.« less

Supersonic Flow of Chemically Reacting Gas-Particle Mixtures. Volume 2: RAMP - A Computer Code for Analysis of Chemically Reacting Gas-Particle Flows

NASA Technical Reports Server (NTRS)

Penny, M. M.; Smith, S. D.; Anderson, P. G.; Sulyma, P. R.; Pearson, M. L.

1976-01-01

A computer program written in conjunction with the numerical solution of the flow of chemically reacting gas-particle mixtures was documented. The solution to the set of governing equations was obtained by utilizing the method of characteristics. The equations cast in characteristic form were shown to be formally the same for ideal, frozen, chemical equilibrium and chemical non-equilibrium reacting gas mixtures. The characteristic directions for the gas-particle system are found to be the conventional gas Mach lines, the gas streamlines and the particle streamlines. The basic mesh construction for the flow solution is along streamlines and normals to the streamlines for axisymmetric or two-dimensional flow. The analysis gives detailed information of the supersonic flow and provides for a continuous solution of the nozzle and exhaust plume flow fields. Boundary conditions for the flow solution are either the nozzle wall or the exhaust plume boundary.

The kinked interface crack

NASA Astrophysics Data System (ADS)

Heitzer, Joerg

1992-05-01

Two methods for the numerical solution of the integral equation describing the kinked interface crack, one proposed by Erdogan et al. (1973) and the other by Theokaris and Iokimidis (1979), are examined. The method of Erdogan et al. is then used to solve the equation in order to determine the kinking angle of the interface crack. Results are presented for two material combinations, aluminum/epoxy and glass/ceramic, under uniaxial tension in the direction normal to the interface.

Spectral methods in general relativity and large Randall-Sundrum II black holes

NASA Astrophysics Data System (ADS)

Abdolrahimi, Shohreh; Cattoën, Céline; Page, Don N.; \\\\; Yaghoobpour-Tari, Shima

2013-06-01

Using a novel numerical spectral method, we have found solutions for large static Randall-Sundrum II (RSII) black holes by perturbing a numerical AdS5-CFT4 solution to the Einstein equation with a negative cosmological constant Λ that is asymptotically conformal to the Schwarzschild metric. We used a numerical spectral method independent of the Ricci-DeTurck-flow method used by Figueras, Lucietti, and Wiseman for a similar numerical solution. We have compared our black-hole solution to the one Figueras and Wiseman have derived by perturbing their numerical AdS5-CFT4 solution, showing that our solution agrees closely with theirs. We have obtained a closed-form approximation to the metric of the black hole on the brane. We have also deduced the new results that to first order in 1/(-ΛM2), the Hawking temperature and entropy of an RSII static black hole have the same values as the Schwarzschild metric with the same mass, but the horizon area is increased by about 4.7/(-Λ).

Pumping Test Determination of Unsaturated Aquifer Properties

NASA Astrophysics Data System (ADS)

Mishra, P. K.; Neuman, S. P.

2008-12-01

Tartakovsky and Neuman [2007] presented a new analytical solution for flow to a partially penetrating well pumping at a constant rate from a compressible unconfined aquifer considering the unsaturated zone. In their solution three-dimensional, axially symmetric unsaturated flow is described by a linearized version of Richards' equation in which both hydraulic conductivity and water content vary exponentially with incremental capillary pressure head relative to its air entry value, the latter defining the interface between the saturated and unsaturated zones. Both exponential functions are characterized by a common exponent k having the dimension of inverse length, or equivalently a dimensionless exponent kd=kb where b is initial saturated thickness. The authors used their solution to analyze drawdown data from a pumping test conducted by Moench et al. [2001] in a Glacial Outwash Deposit at Cape Cod, Massachusetts. Their analysis yielded estimates of horizontal and vertical saturated hydraulic conductivities, specific storage, specific yield and k . Recognizing that hydraulic conductivity and water content seldom vary identically with incremental capillary pressure head, as assumed by Tartakovsky and Neuman [2007], we note that k is at best an effective rather than a directly measurable soil parameter. We therefore ask to what extent does interpretation of a pumping test based on the Tartakovsky-Neuman solution allow estimating aquifer unsaturated parameters as described by more common constitutive water retention and relative hydraulic conductivity models such as those of Brooks and Corey [1964] or van Genuchten [1980] and Mualem [1976a]? We address this question by showing how may be used to estimate the capillary air entry pressure head k and the parameters of such constitutive models directly, without a need for inverse unsaturated numerical simulations of the kind described by Moench [2003]. To assess the validity of such direct estimates we use maximum likelihood- based model selection criteria to compare the abilities of numerical models based on the STOMP code to reproduce observed drawdowns during the test when saturated and unsaturated aquifer parameters are estimated either in the above manner or by means of the inverse code PEST.

SoftWAXS: a computational tool for modeling wide-angle X-ray solution scattering from biomolecules.

PubMed

Bardhan, Jaydeep; Park, Sanghyun; Makowski, Lee

2009-10-01

This paper describes a computational approach to estimating wide-angle X-ray solution scattering (WAXS) from proteins, which has been implemented in a computer program called SoftWAXS. The accuracy and efficiency of SoftWAXS are analyzed for analytically solvable model problems as well as for proteins. Key features of the approach include a numerical procedure for performing the required spherical averaging and explicit representation of the solute-solvent boundary and the surface of the hydration layer. These features allow the Fourier transform of the excluded volume and hydration layer to be computed directly and with high accuracy. This approach will allow future investigation of different treatments of the electron density in the hydration shell. Numerical results illustrate the differences between this approach to modeling the excluded volume and a widely used model that treats the excluded-volume function as a sum of Gaussians representing the individual atomic excluded volumes. Comparison of the results obtained here with those from explicit-solvent molecular dynamics clarifies shortcomings inherent to the representation of solvent as a time-averaged electron-density profile. In addition, an assessment is made of how the calculated scattering patterns depend on input parameters such as the solute-atom radii, the width of the hydration shell and the hydration-layer contrast. These results suggest that obtaining predictive calculations of high-resolution WAXS patterns may require sophisticated treatments of solvent.

Uncertainty propagation in orbital mechanics via tensor decomposition

NASA Astrophysics Data System (ADS)

Sun, Yifei; Kumar, Mrinal

2016-03-01

Uncertainty forecasting in orbital mechanics is an essential but difficult task, primarily because the underlying Fokker-Planck equation (FPE) is defined on a relatively high dimensional (6-D) state-space and is driven by the nonlinear perturbed Keplerian dynamics. In addition, an enormously large solution domain is required for numerical solution of this FPE (e.g. encompassing the entire orbit in the x-y-z subspace), of which the state probability density function (pdf) occupies a tiny fraction at any given time. This coupling of large size, high dimensionality and nonlinearity makes for a formidable computational task, and has caused the FPE for orbital uncertainty propagation to remain an unsolved problem. To the best of the authors' knowledge, this paper presents the first successful direct solution of the FPE for perturbed Keplerian mechanics. To tackle the dimensionality issue, the time-varying state pdf is approximated in the CANDECOMP/PARAFAC decomposition tensor form where all the six spatial dimensions as well as the time dimension are separated from one other. The pdf approximation for all times is obtained simultaneously via the alternating least squares algorithm. Chebyshev spectral differentiation is employed for discretization on account of its spectral ("super-fast") convergence rate. To facilitate the tensor decomposition and control the solution domain size, system dynamics is expressed using spherical coordinates in a noninertial reference frame. Numerical results obtained on a regular personal computer are compared with Monte Carlo simulations.

Multiresolution representation and numerical algorithms: A brief review

NASA Technical Reports Server (NTRS)

Harten, Amiram

1994-01-01

In this paper we review recent developments in techniques to represent data in terms of its local scale components. These techniques enable us to obtain data compression by eliminating scale-coefficients which are sufficiently small. This capability for data compression can be used to reduce the cost of many numerical solution algorithms by either applying it to the numerical solution operator in order to get an approximate sparse representation, or by applying it to the numerical solution itself in order to reduce the number of quantities that need to be computed.

Constructing exact symmetric informationally complete measurements from numerical solutions

NASA Astrophysics Data System (ADS)

Appleby, Marcus; Chien, Tuan-Yow; Flammia, Steven; Waldron, Shayne

2018-04-01

Recently, several intriguing conjectures have been proposed connecting symmetric informationally complete quantum measurements (SIC POVMs, or SICs) and algebraic number theory. These conjectures relate the SICs to their minimal defining algebraic number field. Testing or sharpening these conjectures requires that the SICs are expressed exactly, rather than as numerical approximations. While many exact solutions of SICs have been constructed previously using Gröbner bases, this method has probably been taken as far as is possible with current computer technology (except in special cases where there are additional symmetries). Here, we describe a method for converting high-precision numerical solutions into exact ones using an integer relation algorithm in conjunction with the Galois symmetries of an SIC. Using this method, we have calculated 69 new exact solutions, including nine new dimensions, where previously only numerical solutions were known—which more than triples the number of known exact solutions. In some cases, the solutions require number fields with degrees as high as 12 288. We use these solutions to confirm that they obey the number-theoretic conjectures, and address two questions suggested by the previous work.

Assessment of numerical methods for the solution of fluid dynamics equations for nonlinear resonance systems

NASA Technical Reports Server (NTRS)

Przekwas, A. J.; Yang, H. Q.

1989-01-01

The capability of accurate nonlinear flow analysis of resonance systems is essential in many problems, including combustion instability. Classical numerical schemes are either too diffusive or too dispersive especially for transient problems. In the last few years, significant progress has been made in the numerical methods for flows with shocks. The objective was to assess advanced shock capturing schemes on transient flows. Several numerical schemes were tested including TVD, MUSCL, ENO, FCT, and Riemann Solver Godunov type schemes. A systematic assessment was performed on scalar transport, Burgers' and gas dynamic problems. Several shock capturing schemes are compared on fast transient resonant pipe flow problems. A system of 1-D nonlinear hyperbolic gas dynamics equations is solved to predict propagation of finite amplitude waves, the wave steepening, formation, propagation, and reflection of shocks for several hundred wave cycles. It is shown that high accuracy schemes can be used for direct, exact nonlinear analysis of combustion instability problems, preserving high harmonic energy content for long periods of time.

Data mining techniques for scientific computing: Application to asymptotic paraxial approximations to model ultrarelativistic particles

NASA Astrophysics Data System (ADS)

Assous, Franck; Chaskalovic, Joël

2011-06-01

We propose a new approach that consists in using data mining techniques for scientific computing. Indeed, data mining has proved to be efficient in other contexts which deal with huge data like in biology, medicine, marketing, advertising and communications. Our aim, here, is to deal with the important problem of the exploitation of the results produced by any numerical method. Indeed, more and more data are created today by numerical simulations. Thus, it seems necessary to look at efficient tools to analyze them. In this work, we focus our presentation to a test case dedicated to an asymptotic paraxial approximation to model ultrarelativistic particles. Our method directly deals with numerical results of simulations and try to understand what each order of the asymptotic expansion brings to the simulation results over what could be obtained by other lower-order or less accurate means. This new heuristic approach offers new potential applications to treat numerical solutions to mathematical models.

Dipole excitation of surface plasmon on a conducting sheet: Finite element approximation and validation

NASA Astrophysics Data System (ADS)

Maier, Matthias; Margetis, Dionisios; Luskin, Mitchell

2017-06-01

We formulate and validate a finite element approach to the propagation of a slowly decaying electromagnetic wave, called surface plasmon-polariton, excited along a conducting sheet, e.g., a single-layer graphene sheet, by an electric Hertzian dipole. By using a suitably rescaled form of time-harmonic Maxwell's equations, we derive a variational formulation that enables a direct numerical treatment of the associated class of boundary value problems by appropriate curl-conforming finite elements. The conducting sheet is modeled as an idealized hypersurface with an effective electric conductivity. The requisite weak discontinuity for the tangential magnetic field across the hypersurface can be incorporated naturally into the variational formulation. We carry out numerical simulations for an infinite sheet with constant isotropic conductivity embedded in two spatial dimensions; and validate our numerics against the closed-form exact solution obtained by the Fourier transform in the tangential coordinate. Numerical aspects of our treatment such as an absorbing perfectly matched layer, as well as local refinement and a posteriori error control are discussed.

A higher order numerical method for time fractional partial differential equations with nonsmooth data

NASA Astrophysics Data System (ADS)

Xing, Yanyuan; Yan, Yubin

2018-03-01

Gao et al. [11] (2014) introduced a numerical scheme to approximate the Caputo fractional derivative with the convergence rate O (k 3 - α), 0 < α < 1 by directly approximating the integer-order derivative with some finite difference quotients in the definition of the Caputo fractional derivative, see also Lv and Xu [20] (2016), where k is the time step size. Under the assumption that the solution of the time fractional partial differential equation is sufficiently smooth, Lv and Xu [20] (2016) proved by using energy method that the corresponding numerical method for solving time fractional partial differential equation has the convergence rate O (k 3 - α), 0 < α < 1 uniformly with respect to the time variable t. However, in general the solution of the time fractional partial differential equation has low regularity and in this case the numerical method fails to have the convergence rate O (k 3 - α), 0 < α < 1 uniformly with respect to the time variable t. In this paper, we first obtain a similar approximation scheme to the Riemann-Liouville fractional derivative with the convergence rate O (k 3 - α), 0 < α < 1 as in Gao et al. [11] (2014) by approximating the Hadamard finite-part integral with the piecewise quadratic interpolation polynomials. Based on this scheme, we introduce a time discretization scheme to approximate the time fractional partial differential equation and show by using Laplace transform methods that the time discretization scheme has the convergence rate O (k 3 - α), 0 < α < 1 for any fixed tn > 0 for smooth and nonsmooth data in both homogeneous and inhomogeneous cases. Numerical examples are given to show that the theoretical results are consistent with the numerical results.

Analytical and numerical solution for wave reflection from a porous wave absorber

NASA Astrophysics Data System (ADS)

Magdalena, Ikha; Roque, Marian P.

2018-03-01

In this paper, wave reflection from a porous wave absorber is investigated theoretically and numerically. The equations that we used are based on shallow water type model. Modification of motion inside the absorber is by including linearized friction term in momentum equation and introducing a filtered velocity. Here, an analytical solution for wave reflection coefficient from a porous wave absorber over a flat bottom is derived. Numerically, we solve the equations using the finite volume method on a staggered grid. To validate our numerical model, comparison of the numerical reflection coefficient is made against the analytical solution. Further, we implement our numerical scheme to study the evolution of surface waves pass through a porous absorber over varied bottom topography.

Numerical Modeling of HgCdTe Solidification: Effects of Phase Diagram, Double-Diffusion Convection and Microgravity Level

NASA Technical Reports Server (NTRS)

Bune, Andris V.; Gillies, Donald C.; Lehoczky, Sandor L.

1997-01-01

Melt convection, along with species diffusion and segregation on the solidification interface are the primary factors responsible for species redistribution during HgCdTe crystal growth from the melt. As no direct information about convection velocity is available, numerical modeling is a logical approach to estimate convection. Furthermore influence of microgravity level, double-diffusion and material properties should be taken into account. In the present study, HgCdTe is considered as a binary alloy with melting temperature available from a phase diagram. The numerical model of convection and solidification of binary alloy is based on the general equations of heat and mass transfer in two-dimensional region. Mathematical modeling of binary alloy solidification is still a challenging numericial problem. A Rigorous mathematical approach to this problem is available only when convection is not considered at all. The proposed numerical model was developed using the finite element code FIDAP. In the present study, the numerical model is used to consider thermal, solutal convection and a double diffusion source of mass transport.

A GENERAL MASS-CONSERVATIVE NUMERICAL SOLUTION FOR THE UNSATURATED FLOW EQUATION

EPA Science Inventory

Numerical approximations based on different forms of the governing partial differential equation can lead to significantly different results for unsaturated flow problems. Numerical solution based on the standard h-based form of Richards equation generally yields poor results, ch...

Flow and Heat Transfer Analysis of an Eyring-Powell Fluid in a Pipe

NASA Astrophysics Data System (ADS)

Ali, N.; Nazeer, F.; Nazeer, Mubbashar

2018-02-01

The steady non-isothermal flow of an Eyring-Powell fluid in a pipe is investigated using both perturbation and numerical methods. The results are presented for two viscosity models, namely the Reynolds model and the Vogel model. The shooting method is employed to compute the numerical solution. Criteria for validity of perturbation solution are developed. When these criteria are met, it is shown that the perturbation solution is in good agreement with the numerical solution. The influence of various emerging parameters on the velocity and temperature field is also shown.

Numerical Generation of Dense Plume Fingers in Unsaturated Homogeneous Porous Media

NASA Astrophysics Data System (ADS)

Cremer, C.; Graf, T.

2012-04-01

In nature, the migration of dense plumes typically results in the formation of vertical plume fingers. Flow direction in fingers is downwards, which is counterbalanced by upwards flow of less dense fluid between fingers. In heterogeneous media, heterogeneity itself is known to trigger the formation of fingers. In homogeneous media, however, fingers are also created even if all grains had the same diameter. The reason is that pore-scale heterogeneity leading to different flow velocities also exists in homogeneous media due to two effects: (i) Grains of identical size may randomly arrange differently, e.g. forming tetrahedrons, hexahedrons or octahedrons. Each arrangement creates pores of varying diameter, thus resulting in different average flow velocities. (ii) Random variations of solute concentration lead to varying buoyancy effects, thus also resulting in different velocities. As a continuation of previously made efforts to incorporate pore-scale heterogeneity into fully saturated soil such that dense fingers are realistically generated (Cremer and Graf, EGU Assembly, 2011), the current paper extends the research scope from saturated to unsaturated soil. Perturbation methods are evaluated by numerically re-simulating a laboratory-scale experiment of plume transport in homogeneous unsaturated sand (Simmons et al., Transp. Porous Media, 2002). The following 5 methods are being discussed: (i) homogeneous sand, (ii) initial perturbation of solute concentration, (iii) spatially random, time-constant perturbation of solute source, (iv) spatially and temporally random noise of simulated solute concentration, and (v) random K-field that introduces physically insignificant but numerically significant heterogeneity. Results demonstrate that, as opposed to saturated flow, perturbing the solute source will not result in plume fingering. This is because the location of the perturbed source (domain top) and the location of finger generation (groundwater surface) do not coincide. Alternatively, similar to saturated flow, applying either a random concentration noise (iv) or a random K-field (v) generates realistic plume fingering. Future work will focus on the generation mechanisms of plume finger splitting.

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.

On the Angular Variation of Solar Reflectance of Snow

NASA Technical Reports Server (NTRS)

Chang, A. T. C.; Choudhury, B. J.

1979-01-01

Spectral and integrated solar reflectance of nonhomogeneous snowpacks were derived assuming surface reflection of direct radiation and subsurface multiple scattering. For surface reflection, a bidirectional reflectance distribution function derived for an isotropic Gaussian faceted surface was considered and for subsurface multiple scattering, an approximate solution of the radiative transfer equation was studied. Solar radiation incident on the snowpack was decomposed into direct and atmospherically scattered radiation. Spectral attenuation coefficients of ozone, carbon dioxide, water vapor, aerosol and molecular scattering were included in the calculation of incident solar radiation. Illustrative numerical results were given for a case of North American winter atmospheric conditions. The calculated dependence of spectrally integrated directional reflectance (or albedo) on solar elevation was in qualitative agreement with available observations.

Transonic airfoil analysis and design in nonuniform flow

NASA Technical Reports Server (NTRS)

Chang, J. F.; Lan, C. E.

1986-01-01

A nonuniform transonic airfoil code is developed for applications in analysis, inverse design and direct optimization involving an airfoil immersed in propfan slipstream. Problems concerning the numerical stability, convergence, divergence and solution oscillations are discussed. The code is validated by comparing with some known results in incompressible flow. A parametric investigation indicates that the airfoil lift-drag ratio can be increased by decreasing the thickness ratio. A better performance can be achieved if the airfoil is located below the slipstream center. Airfoil characteristics designed by the inverse method and a direct optimization are compared. The airfoil designed with the method of direct optimization exhibits better characteristics and achieves a gain of 22 percent in lift-drag ratio with a reduction of 4 percent in thickness.

Computational reacting gas dynamics

NASA Technical Reports Server (NTRS)

Lam, S. H.

1993-01-01

In the study of high speed flows at high altitudes, such as that encountered by re-entry spacecrafts, the interaction of chemical reactions and other non-equilibrium processes in the flow field with the gas dynamics is crucial. Generally speaking, problems of this level of complexity must resort to numerical methods for solutions, using sophisticated computational fluid dynamics (CFD) codes. The difficulties introduced by reacting gas dynamics can be classified into three distinct headings: (1) the usually inadequate knowledge of the reaction rate coefficients in the non-equilibrium reaction system; (2) the vastly larger number of unknowns involved in the computation and the expected stiffness of the equations; and (3) the interpretation of the detailed reacting CFD numerical results. The research performed accepts the premise that reacting flows of practical interest in the future will in general be too complex or 'untractable' for traditional analytical developments. The power of modern computers must be exploited. However, instead of focusing solely on the construction of numerical solutions of full-model equations, attention is also directed to the 'derivation' of the simplified model from the given full-model. In other words, the present research aims to utilize computations to do tasks which have traditionally been done by skilled theoreticians: to reduce an originally complex full-model system into an approximate but otherwise equivalent simplified model system. The tacit assumption is that once the appropriate simplified model is derived, the interpretation of the detailed numerical reacting CFD numerical results will become much easier. The approach of the research is called computational singular perturbation (CSP).

Existence and numerical simulation of periodic traveling wave solutions to the Casimir equation for the Ito system

NASA Astrophysics Data System (ADS)

Abbasbandy, S.; Van Gorder, R. A.; Hajiketabi, M.; Mesrizadeh, M.

2015-10-01

We consider traveling wave solutions to the Casimir equation for the Ito system (a two-field extension of the KdV equation). These traveling waves are governed by a nonlinear initial value problem with an interesting nonlinearity (which actually amplifies in magnitude as the size of the solution becomes small). The nonlinear problem is parameterized by two initial constant values, and we demonstrate that the existence of solutions is strongly tied to these parameter values. For our interests, we are concerned with positive, bounded, periodic wave solutions. We are able to classify parameter regimes which admit such solutions in full generality, thereby obtaining a nice existence result. Using the existence result, we are then able to numerically simulate the positive, bounded, periodic solutions. We elect to employ a group preserving scheme in order to numerically study these solutions, and an outline of this approach is provided. The numerical simulations serve to illustrate the properties of these solutions predicted analytically through the existence result. Physically, these results demonstrate the existence of a type of space-periodic structure in the Casimir equation for the Ito model, which propagates as a traveling wave.

Constrained multibody system dynamics: An automated approach

NASA Technical Reports Server (NTRS)

Kamman, J. W.; Huston, R. L.

1982-01-01

The governing equations for constrained multibody systems are formulated in a manner suitable for their automated, numerical development and solution. The closed loop problem of multibody chain systems is addressed. The governing equations are developed by modifying dynamical equations obtained from Lagrange's form of d'Alembert's principle. The modifications is based upon a solution of the constraint equations obtained through a zero eigenvalues theorem, is a contraction of the dynamical equations. For a system with n-generalized coordinates and m-constraint equations, the coefficients in the constraint equations may be viewed as constraint vectors in n-dimensional space. In this setting the system itself is free to move in the n-m directions which are orthogonal to the constraint vectors.

Combined AIE/EBE/GMRES approach to incompressible flows. [Adaptive Implicit-Explicit/Grouped Element-by-Element/Generalized Minimum Residuals

NASA Technical Reports Server (NTRS)

Liou, J.; Tezduyar, T. E.

1990-01-01

Adaptive implicit-explicit (AIE), grouped element-by-element (GEBE), and generalized minimum residuals (GMRES) solution techniques for incompressible flows are combined. In this approach, the GEBE and GMRES iteration methods are employed to solve the equation systems resulting from the implicitly treated elements, and therefore no direct solution effort is involved. The benchmarking results demonstrate that this approach can substantially reduce the CPU time and memory requirements in large-scale flow problems. Although the description of the concepts and the numerical demonstration are based on the incompressible flows, the approach presented here is applicable to larger class of problems in computational mechanics.

Shape sensing using multi-core fiber optic cable and parametric curve solutions.

PubMed

Moore, Jason P; Rogge, Matthew D

2012-01-30

The shape of a multi-core optical fiber is calculated by numerically solving a set of Frenet-Serret equations describing the path of the fiber in three dimensions. Included in the Frenet-Serret equations are curvature and bending direction functions derived from distributed fiber Bragg grating strain measurements in each core. The method offers advantages over prior art in that it determines complex three-dimensional fiber shape as a continuous parametric solution rather than an integrated series of discrete planar bends. Results and error analysis of the method using a tri-core optical fiber is presented. Maximum error expressed as a percentage of fiber length was found to be 7.2%.

Effective photon mass and exact translating quantum relativistic structures

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

Haas, Fernando, E-mail: fernando.haas@ufrgs.br; Manrique, Marcos Antonio Albarracin, E-mail: sagret10@hotmail.com

2016-04-15

Using a variation of the celebrated Volkov solution, the Klein-Gordon equation for a charged particle is reduced to a set of ordinary differential equations, exactly solvable in specific cases. The new quantum relativistic structures can reveal a localization in the radial direction perpendicular to the wave packet propagation, thanks to a non-vanishing scalar potential. The external electromagnetic field, the particle current density, and the charge density are determined. The stability analysis of the solutions is performed by means of numerical simulations. The results are useful for the description of a charged quantum test particle in the relativistic regime, provided spinmore » effects are not decisive.« less

A users guide for A344: A program using a finite difference method to analyze transonic flow over oscillating airfoils

NASA Technical Reports Server (NTRS)

Weatherill, W. H.; Ehlers, F. E.

1979-01-01

The design and usage of a pilot program for calculating the pressure distributions over harmonically oscillating airfoils in transonic flow are described. The procedure used is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equations for small disturbances. The steady velocity potential which must be obtained from some other program, was required for input. The unsteady equation, as solved, is linear with spatially varying coefficients. Since sinusoidal motion was assumed, time was not a variable. The numerical solution was obtained through a finite difference formulation and either a line relaxation or an out of core direct solution method.

The solution of a model problem of the atmospheric entry of a small meteoroid

NASA Astrophysics Data System (ADS)

Zalogin, G. N.; Kusov, A. L.

2016-03-01

Direct simulation Monte Carlo modeling (DSMC) is used to solve the problem of the entry into the Earth's atmosphere of a small meteoroid. The main aspects of the physical theory of meteors, such as mass loss (ablation) and effects of aerodynamic and thermal shielding, are considered based on the numerical solution of the model problem of the atmospheric entry of an iron meteoroid. The DSMC makes it possible to obtain insight into the structure of the disturbed area around the meteoroid (coma) and trace its evolution depending on entry velocity and height (Knudsen number) in a transitional flow regime where calculation methods used for free molecular and continuum regimes are inapplicable.

Exospheric perturbations by radiation pressure. 2: Solution for orbits in the ecliptic plane

NASA Technical Reports Server (NTRS)

Chamberlain, J. W.

1980-01-01

The instantaneous rates of change for the orbital elements eccentricity, longitude of perigee from the Sun, and longitude from the Sun of the ascending node are integrated simultaneously for the case of the inclination i = 0. The results confirm the validity of using mean rates when the orbits are tightly bound to the planet and serve as examples to be reproduced by the complicated numerical solutions required for arbitrary inclination. Strongly bound hydrogen atoms escaping from Earth due to radiation pressure do not seem a likely cause of the geotail extending in the anti-sun direction. Instead, radiation pressure will cause those particles' orbits to deteriorate into the Earth's atmosphere.

Homoclinic orbits in three-dimensional Shilnikov-type chaotic systems

NASA Astrophysics Data System (ADS)

Feng, Jing-Jing; Zhang, Qi-Chang; Wang, Wei; Hao, Shu-Ying

2013-09-01

In this paper, the Padé approximant and analytic solution in the neighborhood of the initial value are introduced into the process of constructing the Shilnikov type homoclinic trajectories in three-dimensional nonlinear dynamical systems. The PID controller system with quadratic and cubic nonlinearities, the simplified solar-wind-driven-magnetosphere-ionosphere system, and the human DNA sequence system are considered. With the aid of presenting a new condition, the solutions of solving the boundary-value problems which are formulated for the trajectory and evaluating the initial amplitude values become available. At the same time, the value of the bifurcation parameter is obtained directly, which is almost consistent with the numerical result.

Numerical solution of a spatio-temporal gender-structured model for hantavirus infection in rodents.

PubMed

Bürger, Raimund; Chowell, Gerardo; Gavilán, Elvis; Mulet, Pep; Villada, Luis M

2018-02-01

In this article we describe the transmission dynamics of hantavirus in rodents using a spatio-temporal susceptible-exposed-infective-recovered (SEIR) compartmental model that distinguishes between male and female subpopulations [L.J.S. Allen, R.K. McCormack and C.B. Jonsson, Bull. Math. Biol. 68 (2006), 511--524]. Both subpopulations are assumed to differ in their movement with respect to local variations in the densities of their own and the opposite gender group. Three alternative models for the movement of the male individuals are examined. In some cases the movement is not only directed by the gradient of a density (as in the standard diffusive case), but also by a non-local convolution of density values as proposed, in another context, in [R.M. Colombo and E. Rossi, Commun. Math. Sci., 13 (2015), 369--400]. An efficient numerical method for the resulting convection-diffusion-reaction system of partial differential equations is proposed. This method involves techniques of weighted essentially non-oscillatory (WENO) reconstructions in combination with implicit-explicit Runge-Kutta (IMEX-RK) methods for time stepping. The numerical results demonstrate significant differences in the spatio-temporal behavior predicted by the different models, which suggest future research directions.

Modulated heat pulse propagation and partial transport barriers in chaotic magnetic fields

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

Castillo-Negrete, Diego del; Blazevski, Daniel

2016-04-15

Direct numerical simulations of the time dependent parallel heat transport equation modeling heat pulses driven by power modulation in three-dimensional chaotic magnetic fields are presented. The numerical method is based on the Fourier formulation of a Lagrangian-Green's function method that provides an accurate and efficient technique for the solution of the parallel heat transport equation in the presence of harmonic power modulation. The numerical results presented provide conclusive evidence that even in the absence of magnetic flux surfaces, chaotic magnetic field configurations with intermediate levels of stochasticity exhibit transport barriers to modulated heat pulse propagation. In particular, high-order islands andmore » remnants of destroyed flux surfaces (Cantori) act as partial barriers that slow down or even stop the propagation of heat waves at places where the magnetic field connection length exhibits a strong gradient. Results on modulated heat pulse propagation in fully stochastic fields and across magnetic islands are also presented. In qualitative agreement with recent experiments in large helical device and DIII-D, it is shown that the elliptic (O) and hyperbolic (X) points of magnetic islands have a direct impact on the spatio-temporal dependence of the amplitude of modulated heat pulses.« less

On the analytic and numeric optimisation of airplane trajectories under real atmospheric conditions

NASA Astrophysics Data System (ADS)

Gonzalo, J.; Domínguez, D.; López, D.

2014-12-01

From the beginning of aviation era, economic constraints have forced operators to continuously improve the planning of the flights. The revenue is proportional to the cost per flight and the airspace occupancy. Many methods, the first started in the middle of last century, have explore analytical, numerical and artificial intelligence resources to reach the optimal flight planning. In parallel, advances in meteorology and communications allow an almost real-time knowledge of the atmospheric conditions and a reliable, error-bounded forecast for the near future. Thus, apart from weather risks to be avoided, airplanes can dynamically adapt their trajectories to minimise their costs. International regulators are aware about these capabilities, so it is reasonable to envisage some changes to allow this dynamic planning negotiation to soon become operational. Moreover, current unmanned airplanes, very popular and often small, suffer the impact of winds and other weather conditions in form of dramatic changes in their performance. The present paper reviews analytic and numeric solutions for typical trajectory planning problems. Analytic methods are those trying to solve the problem using the Pontryagin principle, where influence parameters are added to state variables to form a split condition differential equation problem. The system can be solved numerically -indirect optimisation- or using parameterised functions -direct optimisation-. On the other hand, numerical methods are based on Bellman's dynamic programming (or Dijkstra algorithms), where the fact that two optimal trajectories can be concatenated to form a new optimal one if the joint point is demonstrated to belong to the final optimal solution. There is no a-priori conditions for the best method. Traditionally, analytic has been more employed for continuous problems whereas numeric for discrete ones. In the current problem, airplane behaviour is defined by continuous equations, while wind fields are given in a discrete grid at certain time intervals. The research demonstrates advantages and disadvantages of each method as well as performance figures of the solutions found for typical flight conditions under static and dynamic atmospheres. This provides significant parameters to be used in the selection of solvers for optimal trajectories.

Experimental investigation of the stability boundary for double-diffusive finger convection in a Hele-Shaw cell

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

Cooper, Clay A.; Glass, Robert J.; Tyler, Scott W.

OAK - B135 We apply high resolution, full field light transmission techniques to study the onset and development of convection in simulated porous media (Hele-Shaw cells) and fractures. The light transmission technique allows quantitative measurement of the solute concentration fields in time thus allowing direct measurements of the mass flux of components. Experiments are first designed to test theoretical stability relations as a function of the solute concentrations, solute diffusivities and the medium's permeability. Structural evolution and convective transport as a function of dimensionless control parameters is then determined across the full range of parameter space. We also consider themore » application of lattice gas automata techniques to numerically model the onset and development of convection. (Gary Drew notified on 3/25/03 of copyrighted Material)« less

Collisional breakup in a quantum system of three charged particles

PubMed

Rescigno; Baertschy; Isaacs; McCurdy

1999-12-24

Since the invention of quantum mechanics, even the simplest example of the collisional breakup of a system of charged particles, e(-) + H --> H(+) + e(-) + e(-) (where e(-) is an electron and H is hydrogen), has resisted solution and is now one of the last unsolved fundamental problems in atomic physics. A complete solution requires calculation of the energies and directions for a final state in which all three particles are moving away from each other. Even with supercomputers, the correct mathematical description of this state has proved difficult to apply. A framework for solving ionization problems in many areas of chemistry and physics is finally provided by a mathematical transformation of the Schrodinger equation that makes the final state tractable, providing the key to a numerical solution of this problem that reveals its full dynamics.

Application of Newton's method to the postbuckling of rings under pressure loadings

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.

1989-01-01

The postbuckling response of circular rings (or long cylinders) is examined. The rings are subjected to four types of external pressure loadings; each type of pressure is defined by its magnitude and direction at points on the buckled ring. Newton's method is applied to the nonlinear differential equations of the exact inextensional theory for the ring problem. A zeroth approximation for the solution of the nonlinear equations, based on the mode shape corresponding to the first buckling pressure, is derived in closed form for each of the four types of pressure. The zeroth approximation is used to start the iteration cycle in Newton's method to compute numerical solutions of the nonlinear equations. The zeroth approximations for the postbuckling pressure-deflection curves are compared with the converged solutions from Newton's method and with similar results reported in the literature.

Ellipsoidal terrain correction based on multi-cylindrical equal-area map projection of the reference ellipsoid

NASA Astrophysics Data System (ADS)

Ardalan, A. A.; Safari, A.

2004-09-01

An operational algorithm for computation of terrain correction (or local gravity field modeling) based on application of closed-form solution of the Newton integral in terms of Cartesian coordinates in multi-cylindrical equal-area map projection of the reference ellipsoid is presented. Multi-cylindrical equal-area map projection of the reference ellipsoid has been derived and is described in detail for the first time. Ellipsoidal mass elements with various sizes on the surface of the reference ellipsoid are selected and the gravitational potential and vector of gravitational intensity (i.e. gravitational acceleration) of the mass elements are computed via numerical solution of the Newton integral in terms of geodetic coordinates {λ,ϕ,h}. Four base- edge points of the ellipsoidal mass elements are transformed into a multi-cylindrical equal-area map projection surface to build Cartesian mass elements by associating the height of the corresponding ellipsoidal mass elements to the transformed area elements. Using the closed-form solution of the Newton integral in terms of Cartesian coordinates, the gravitational potential and vector of gravitational intensity of the transformed Cartesian mass elements are computed and compared with those of the numerical solution of the Newton integral for the ellipsoidal mass elements in terms of geodetic coordinates. Numerical tests indicate that the difference between the two computations, i.e. numerical solution of the Newton integral for ellipsoidal mass elements in terms of geodetic coordinates and closed-form solution of the Newton integral in terms of Cartesian coordinates, in a multi-cylindrical equal-area map projection, is less than 1.6×10-8 m2/s2 for a mass element with a cross section area of 10×10 m and a height of 10,000 m. For a mass element with a cross section area of 1×1 km and a height of 10,000 m the difference is less than 1.5×10-4m2/s2. Since 1.5× 10-4 m2/s2 is equivalent to 1.5×10-5m in the vertical direction, it can be concluded that a method for terrain correction (or local gravity field modeling) based on closed-form solution of the Newton integral in terms of Cartesian coordinates of a multi-cylindrical equal-area map projection of the reference ellipsoid has been developed which has the accuracy of terrain correction (or local gravity field modeling) based on the Newton integral in terms of ellipsoidal coordinates.

Analyzing the effects of instillation volume on intravesical delivery using biphasic solute transport in a deformable geometry.

PubMed

Smith, Sean G; Griffith, Boyce E; Zaharoff, David A

2018-04-05

Ailments of the bladder are often treated via intravesical delivery-direct application of therapeutic into the bladder through a catheter. This technique is employed hundreds of thousands of times every year, but protocol development has largely been limited to empirical determination. Furthermore, the numerical analyses of intravesical delivery performed to date have been restricted to static geometries and have not accounted for bladder deformation. This study uses a finite element analysis approach with biphasic solute transport to investigate several parameters pertinent to intravesical delivery including solute concentration, solute transport properties and instillation volume. The volume of instillation was found to have a substantial impact on the exposure of solute to the deeper muscle layers of the bladder, which are typically more difficult to reach. Indeed, increasing the instillation volume from 50-100 ml raised the muscle solute exposure as a percentage of overall bladder exposure from 60-70% with higher levels achieved for larger instillation volumes. Similar increases were not seen for changes in solute concentration or solute transport properties. These results indicate the role that instillation volume may play in targeting particular layers of the bladder during an intravesical delivery.

Measurement and calculation of forces in a magnetic journal bearing actuator

NASA Technical Reports Server (NTRS)

Knight, Josiah; Mccaul, Edward; Xia, Zule

1991-01-01

Numerical calculations and experimental measurements of forces from an actuator of the type used in active magnetic journal bearings are presented. The calculations are based on solution of the scalar magnetic potential field in and near the gap regions. The predicted forces from single magnet with steady current are compared with experimental measurements in the same geometry. The measured forces are smaller than calculated ones in the principal direction but are larger than calculated in the normal direction. This combination of results indicate that material and spatial effects other than saturation play roles in determining the force available from an actuator.

Drag reduction by a linear viscosity profile.

PubMed

De Angelis, Elisabetta; Casciola, Carlo M; L'vov, Victor S; Pomyalov, Anna; Procaccia, Itamar; Tiberkevich, Vasil

2004-11-01

Drag reduction by polymers in turbulent flows raises an apparent contradiction: the stretching of the polymers must increase the viscosity, so why is the drag reduced? A recent theory proposed that drag reduction, in agreement with experiments, is consistent with the effective viscosity growing linearly with the distance from the wall. With this self-consistent solution the reduction in the Reynolds stress overwhelms the increase in viscous drag. In this Rapid Communication we show, using direct numerical simulations, that a linear viscosity profile indeed reduces the drag in agreement with the theory and in close correspondence with direct simulations of the FENE-P model at the same flow conditions.

Permeability of model porous medium formed by random discs

NASA Astrophysics Data System (ADS)

Gubaidullin, A. A.; Gubkin, A. S.; Igoshin, D. E.; Ignatev, P. A.

2018-03-01

Two-dimension model of the porous medium with skeleton of randomly located overlapping discs is proposed. The geometry and computational grid are built in open package Salome. Flow of Newtonian liquid in longitudinal and transverse directions is calculated and its flow rate is defined. The numerical solution of the Navier-Stokes equations for a given pressure drop at the boundaries of the area is realized in the open package OpenFOAM. Calculated value of flow rate is used for defining of permeability coefficient on the base of Darcy law. For evaluating of representativeness of computational domain the permeability coefficients in longitudinal and transverse directions are compered.

Geophysical monitoring of solute transport in dual-domain environments through laboratory experiments, field-scale solute tracer tests, and numerical simulation

NASA Astrophysics Data System (ADS)

Swanson, Ryan David

The advection-dispersion equation (ADE) fails to describe non-Fickian solute transport breakthrough curves (BTCs) in saturated porous media in both laboratory and field experiments, necessitating the use of other models. The dual-domain mass transfer (DDMT) model partitions the total porosity into mobile and less-mobile domains with an exchange of mass between the two domains, and this model can reproduce better fits to BTCs in many systems than ADE-based models. However, direct experimental estimation of DDMT model parameters remains elusive and model parameters are often calculated a posteriori by an optimization procedure. Here, we investigate the use of geophysical tools (direct-current resistivity, nuclear magnetic resonance, and complex conductivity) to estimate these model parameters directly. We use two different samples of the zeolite clinoptilolite, a material shown to demonstrate solute mass transfer due to a significant internal porosity, and provide the first evidence that direct-current electrical methods can track solute movement into and out of a less-mobile pore space in controlled laboratory experiments. We quantify the effects of assuming single-rate DDMT for multirate mass transfer systems. We analyze pore structures using material characterization methods (mercury porosimetry, scanning electron microscopy, and X-ray computer tomography), and compare these observations to geophysical measurements. Nuclear magnetic resonance in conjunction with direct-current resistivity measurements can constrain mobile and less-mobile porosities, but complex conductivity may have little value in relation to mass transfer despite the hypothesis that mass transfer and complex conductivity lengths scales are related. Finally, we conduct a geoelectrical monitored tracer test at the Macrodispersion Experiment (MADE) site in Columbus, MS. We relate hydraulic and electrical conductivity measurements to generate a 3D hydraulic conductivity field, and compare to hydraulic conductivity fields estimated through ordinary kriging and sequential Gaussian simulation. Time-lapse electrical measurements are used to verify or dismiss aspects of breakthrough curves for different hydraulic conductivity fields. Our results quantify the potential for geophysical measurements to infer on single-rate DDMT parameters, show site-specific relations between hydraulic and electrical conductivity, and track solute exchange into and out of less-mobile domains.

Realistic natural atmospheric phenomena and weather effects for interactive virtual environments

NASA Astrophysics Data System (ADS)

McLoughlin, Leigh

Clouds and the weather are important aspects of any natural outdoor scene, but existing dynamic techniques within computer graphics only offer the simplest of cloud representations. The problem that this work looks to address is how to provide a means of simulating clouds and weather features such as precipitation, that are suitable for virtual environments. Techniques for cloud simulation are available within the area of meteorology, but numerical weather prediction systems are computationally expensive, give more numerical accuracy than we require for graphics and are restricted to the laws of physics. Within computer graphics, we often need to direct and adjust physical features or to bend reality to meet artistic goals, which is a key difference between the subjects of computer graphics and physical science. Pure physically-based simulations, however, evolve their solutions according to pre-set rules and are notoriously difficult to control. The challenge then is for the solution to be computationally lightweight and able to be directed in some measure while at the same time producing believable results. This work presents a lightweight physically-based cloud simulation scheme that simulates the dynamic properties of cloud formation and weather effects. The system simulates water vapour, cloud water, cloud ice, rain, snow and hail. The water model incorporates control parameters and the cloud model uses an arbitrary vertical temperature profile, with a tool described to allow the user to define this. The result of this work is that clouds can now be simulated in near real-time complete with precipitation. The temperature profile and tool then provide a means of directing the resulting formation..

Active Control of Flow Separation Over an Airfoil

NASA Technical Reports Server (NTRS)

Ravindran, S. S.

1999-01-01

Designing an aircraft without conventional control surfaces is of interest to aerospace community. In this direction, smart actuator devices such as synthetic jets have been proposed to provide aircraft maneuverability instead of control surfaces. In this article, a numerical study is performed to investigate the effects of unsteady suction and blowing on airfoils. The unsteady suction and blowing is introduced at the leading edge of the airfoil in the form of tangential jet. Numerical solutions are obtained using Reynolds-Averaged viscous compressible Navier-Stokes equations. Unsteady suction and blowing is investigated as a means of separation control to obtain lift on airfoils. The effect of blowing coefficients on lift and drag is investigated. The numerical simulations are compared with experiments from the Tel-Aviv University (TAU). These results indicate that unsteady suction and blowing can be used as a means of separation control to generate lift on airfoils.

Simulation of light propagation in the thin-film waveguide lens

NASA Astrophysics Data System (ADS)

Malykh, M. D.; Divakov, D. V.; Sevastianov, L. A.; Sevastianov, A. L.

2018-04-01

In this paper we investigate the solution of the problem of modeling the propagation of electromagnetic radiation in three-dimensional integrated optical structures, such as waveguide lenses. When propagating through three-dimensional waveguide structures the waveguide modes can be hybridized, so the mathematical model of their propagation must take into account the connection of TE- and TM-mode components. Therefore, an adequate consideration of hybridization of the waveguide modes is possible only in vector formulation of the problem. An example of three-dimensional structure that hybridizes waveguide modes is the Luneburg waveguide lens, which also has focusing properties. If the waveguide lens has a radius of the order of several tens of wavelengths, its variable thickness at distances of the order of several wavelengths is almost constant. Assuming in this case that the electromagnetic field also varies slowly in the direction perpendicular to the direction of propagation, one can introduce a small parameter characterizing this slow varying and decompose the solution in powers of the small parameter. In this approach, in the zeroth approximation, scalar diffraction problems are obtained, the solution of which is less resource-consuming than the solution of vector problems. The calculated first-order corrections of smallness describe the connection of TE- and TM-modes, so the solutions obtained are weakly-hybridized modes. The formulation of problems and methods for their numerical solution in this paper are based on the authors' research on waveguide diffraction on a lens in a scalar formulation.

A simulation study of homogeneous ice nucleation in supercooled salty water

NASA Astrophysics Data System (ADS)

Soria, Guiomar D.; Espinosa, Jorge R.; Ramirez, Jorge; Valeriani, Chantal; Vega, Carlos; Sanz, Eduardo

2018-06-01

We use computer simulations to investigate the effect of salt on homogeneous ice nucleation. The melting point of the employed solution model was obtained both by direct coexistence simulations and by thermodynamic integration from previous calculations of the water chemical potential. Using a seeding approach, in which we simulate ice seeds embedded in a supercooled aqueous solution, we compute the nucleation rate as a function of temperature for a 1.85 NaCl mol per water kilogram solution at 1 bar. To improve the accuracy and reliability of our calculations, we combine seeding with the direct computation of the ice-solution interfacial free energy at coexistence using the Mold Integration method. We compare the results with previous simulation work on pure water to understand the effect caused by the solute. The model captures the experimental trend that the nucleation rate at a given supercooling decreases when adding salt. Despite the fact that the thermodynamic driving force for ice nucleation is higher for salty water for a given supercooling, the nucleation rate slows down with salt due to a significant increase of the ice-fluid interfacial free energy. The salty water model predicts an ice nucleation rate that is in good agreement with experimental measurements, bringing confidence in the predictive ability of the model. We expect that the combination of state-of-the-art simulation methods here employed to study ice nucleation from solution will be of much use in forthcoming numerical investigations of crystallization in mixtures.

A simulation study of homogeneous ice nucleation in supercooled salty water.

PubMed

Soria, Guiomar D; Espinosa, Jorge R; Ramirez, Jorge; Valeriani, Chantal; Vega, Carlos; Sanz, Eduardo

2018-06-14

We use computer simulations to investigate the effect of salt on homogeneous ice nucleation. The melting point of the employed solution model was obtained both by direct coexistence simulations and by thermodynamic integration from previous calculations of the water chemical potential. Using a seeding approach, in which we simulate ice seeds embedded in a supercooled aqueous solution, we compute the nucleation rate as a function of temperature for a 1.85 NaCl mol per water kilogram solution at 1 bar. To improve the accuracy and reliability of our calculations, we combine seeding with the direct computation of the ice-solution interfacial free energy at coexistence using the Mold Integration method. We compare the results with previous simulation work on pure water to understand the effect caused by the solute. The model captures the experimental trend that the nucleation rate at a given supercooling decreases when adding salt. Despite the fact that the thermodynamic driving force for ice nucleation is higher for salty water for a given supercooling, the nucleation rate slows down with salt due to a significant increase of the ice-fluid interfacial free energy. The salty water model predicts an ice nucleation rate that is in good agreement with experimental measurements, bringing confidence in the predictive ability of the model. We expect that the combination of state-of-the-art simulation methods here employed to study ice nucleation from solution will be of much use in forthcoming numerical investigations of crystallization in mixtures.

Numerically solving the relativistic Grad-Shafranov equation in Kerr spacetimes: numerical techniques

NASA Astrophysics Data System (ADS)

Mahlmann, J. F.; Cerdá-Durán, P.; Aloy, M. A.

2018-07-01

The study of the electrodynamics of static, axisymmetric, and force-free Kerr magnetospheres relies vastly on solutions of the so-called relativistic Grad-Shafranov equation (GSE). Different numerical approaches to the solution of the GSE have been introduced in the literature, but none of them has been fully assessed from the numerical point of view in terms of efficiency and quality of the solutions found. We present a generalization of these algorithms and give a detailed background on the algorithmic implementation. We assess the numerical stability of the implemented algorithms and quantify the convergence of the presented methodology for the most established set-ups (split-monopole, paraboloidal, BH disc, uniform).

Numerically solving the relativistic Grad-Shafranov equation in Kerr spacetimes: Numerical techniques

NASA Astrophysics Data System (ADS)

Mahlmann, J. F.; Cerdá-Durán, P.; Aloy, M. A.

2018-04-01

The study of the electrodynamics of static, axisymmetric and force-free Kerr magnetospheres relies vastly on solutions of the so called relativistic Grad-Shafranov equation (GSE). Different numerical approaches to the solution of the GSE have been introduced in the literature, but none of them has been fully assessed from the numerical point of view in terms of efficiency and quality of the solutions found. We present a generalization of these algorithms and give detailed background on the algorithmic implementation. We assess the numerical stability of the implemented algorithms and quantify the convergence of the presented methodology for the most established setups (split-monopole, paraboloidal, BH-disk, uniform).

A numerical method for osmotic water flow and solute diffusion with deformable membrane boundaries in two spatial dimension

NASA Astrophysics Data System (ADS)

Yao, Lingxing; Mori, Yoichiro

2017-12-01

Osmotic forces and solute diffusion are increasingly seen as playing a fundamental role in cell movement. Here, we present a numerical method that allows for studying the interplay between diffusive, osmotic and mechanical effects. An osmotically active solute obeys a advection-diffusion equation in a region demarcated by a deformable membrane. The interfacial membrane allows transmembrane water flow which is determined by osmotic and mechanical pressure differences across the membrane. The numerical method is based on an immersed boundary method for fluid-structure interaction and a Cartesian grid embedded boundary method for the solute. We demonstrate our numerical algorithm with the test case of an osmotic engine, a recently proposed mechanism for cell propulsion.

Bidirectional reaction steps in metabolic networks: I. Modeling and simulation of carbon isotope labeling experiments.

PubMed

Wiechert, W; de Graaf, A A

1997-07-05

The extension of metabolite balancing with carbon labeling experiments, as described by Marx et al. (Biotechnol. Bioeng. 49: 11-29), results in a much more detailed stationary metabolic flux analysis. As opposed to basic metabolite flux balancing alone, this method enables both flux directions of bidirectional reaction steps to be quantitated. However, the mathematical treatment of carbon labeling systems is much more complicated, because it requires the solution of numerous balance equations that are bilinear with respect to fluxes and fractional labeling. In this study, a universal modeling framework is presented for describing the metabolite and carbon atom flux in a metabolic network. Bidirectional reaction steps are extensively treated and their impact on the system's labeling state is investigated. Various kinds of modeling assumptions, as usually made for metabolic fluxes, are expressed by linear constraint equations. A numerical algorithm for the solution of the resulting linear constrained set of nonlinear equations is developed. The numerical stability problems caused by large bidirectional fluxes are solved by a specially developed transformation method. Finally, the simulation of carbon labeling experiments is facilitated by a flexible software tool for network synthesis. An illustrative simulation study on flux identifiability from available flux and labeling measurements in the cyclic pentose phosphate pathway of a recombinant strain of Zymomonas mobilis concludes this contribution.

An optimization-based approach for solving a time-harmonic multiphysical wave problem with higher-order schemes

NASA Astrophysics Data System (ADS)

Mönkölä, Sanna

2013-06-01

This study considers developing numerical solution techniques for the computer simulations of time-harmonic fluid-structure interaction between acoustic and elastic waves. The focus is on the efficiency of an iterative solution method based on a controllability approach and spectral elements. We concentrate on the model, in which the acoustic waves in the fluid domain are modeled by using the velocity potential and the elastic waves in the structure domain are modeled by using displacement. Traditionally, the complex-valued time-harmonic equations are used for solving the time-harmonic problems. Instead of that, we focus on finding periodic solutions without solving the time-harmonic problems directly. The time-dependent equations can be simulated with respect to time until a time-harmonic solution is reached, but the approach suffers from poor convergence. To overcome this challenge, we follow the approach first suggested and developed for the acoustic wave equations by Bristeau, Glowinski, and Périaux. Thus, we accelerate the convergence rate by employing a controllability method. The problem is formulated as a least-squares optimization problem, which is solved with the conjugate gradient (CG) algorithm. Computation of the gradient of the functional is done directly for the discretized problem. A graph-based multigrid method is used for preconditioning the CG algorithm.

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.

Second-order numerical methods for multi-term fractional differential equations: Smooth and non-smooth solutions

NASA Astrophysics Data System (ADS)

Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em

2017-12-01

Starting with the asymptotic expansion of the error equation of the shifted Gr\\"{u}nwald--Letnikov formula, we derive a new modified weighted shifted Gr\\"{u}nwald--Letnikov (WSGL) formula by introducing appropriate correction terms. We then apply one special case of the modified WSGL formula to solve multi-term fractional ordinary and partial differential equations, and we prove the linear stability and second-order convergence for both smooth and non-smooth solutions. We show theoretically and numerically that numerical solutions up to certain accuracy can be obtained with only a few correction terms. Moreover, the correction terms can be tuned according to the fractional derivative orders without explicitly knowing the analytical solutions. Numerical simulations verify the theoretical results and demonstrate that the new formula leads to better performance compared to other known numerical approximations with similar resolution.

Multiple stationary solutions of an irradiated slab

NASA Astrophysics Data System (ADS)

Taylor, P. D.; Feltham, D. L.

2005-04-01

A mathematical model describing the heat budget of an irradiated medium is introduced. The one-dimensional form of the equations and boundary conditions are presented and analysed. Heat transport at one face of the slab occurs by absorption (and reflection) of an incoming beam of short-wave radiation with a fraction of this radiation penetrating into the body of the slab, a diffusive heat flux in the slab and a prescribed incoming heat flux term. The other face of the slab is immersed in its own melt and is considered to be a free surface. Here, temperature continuity is prescribed and evolution of the surface is determined by a Stefan condition. These boundary conditions are flexible enough to describe a range of situations such as a laser shining on an opaque medium, or the natural environment of polar sea ice or lake ice. A two-stream radiation model is used which replaces the simple Beer's law of radiation attenuation frequently used for semi-infinite domains. The stationary solutions of the governing equations are sought and it is found that there exists two possible stationary solutions for a given set of boundary conditions and a range of parameter choices. It is found that the existence of two stationary solutions is a direct result of the model of radiation absorption, due to its effect on the albedo of the medium. A linear stability analysis and numerical calculations indicate that where two stationary solutions exist, the solution corresponding to a larger thickness is always stable and the solution corresponding to a smaller thickness is unstable. Numerical simulations reveal that when there are two solutions, if the slab is thinner than the smaller stationary thickness it will melt completely, whereas if the slab is thicker than the smaller stationary thickness it will evolve toward the larger stationary thickness. These results indicate that other mechanisms (e.g. wave-induced agglomeration of crystals) are necessary to grow a slab from zero initial thickness in the parameter regime that yields two stationary solutions.

Analysis of control system responses for aircraft stability and efficient numerical techniques for real-time simulations

NASA Astrophysics Data System (ADS)

Stroe, Gabriela; Andrei, Irina-Carmen; Frunzulica, Florin

2017-01-01

The objectives of this paper are the study and the implementation of both aerodynamic and propulsion models, as linear interpolations using look-up tables in a database. The aerodynamic and propulsion dependencies on state and control variable have been described by analytic polynomial models. Some simplifying hypotheses were made in the development of the nonlinear aircraft simulations. The choice of a certain technique to use depends on the desired accuracy of the solution and the computational effort to be expended. Each nonlinear simulation includes the full nonlinear dynamics of the bare airframe, with a scaled direct connection from pilot inputs to control surface deflections to provide adequate pilot control. The engine power dynamic response was modeled with an additional state equation as first order lag in the actual power level response to commanded power level was computed as a function of throttle position. The number of control inputs and engine power states varied depending on the number of control surfaces and aircraft engines. The set of coupled, nonlinear, first-order ordinary differential equations that comprise the simulation model can be represented by the vector differential equation. A linear time-invariant (LTI) system representing aircraft dynamics for small perturbations about a reference trim condition is given by the state and output equations present. The gradients are obtained numerically by perturbing each state and control input independently and recording the changes in the trimmed state and output equations. This is done using the numerical technique of central finite differences, including the perturbations of the state and control variables. For a reference trim condition of straight and level flight, linearization results in two decoupled sets of linear, constant-coefficient differential equations for longitudinal and lateral / directional motion. The linearization is valid for small perturbations about the reference trim condition. Experimental aerodynamic and thrust data are used to model the applied aerodynamic and propulsion forces and moments for arbitrary states and controls. There is no closed form solution to such problems, so the equations must be solved using numerical integration. Techniques for solving this initial value problem for ordinary differential equations are employed to obtain approximate solutions at discrete points along the aircraft state trajectory.

Evolution of the single-mode Rayleigh-Taylor instability under the influence of time-dependent accelerations

NASA Astrophysics Data System (ADS)

Ramaprabhu, P.; Karkhanis, V.; Banerjee, R.; Varshochi, H.; Khan, M.; Lawrie, A. G. W.

2016-01-01

From nonlinear models and direct numerical simulations we report on several findings of relevance to the single-mode Rayleigh-Taylor (RT) instability driven by time-varying acceleration histories. The incompressible, direct numerical simulations (DNSs) were performed in two (2D) and three dimensions (3D), and at a range of density ratios of the fluid combinations (characterized by the Atwood number). We investigated several acceleration histories, including acceleration profiles of the general form g (t ) ˜tn , with n ≥0 and acceleration histories reminiscent of the linear electric motor experiments. For the 2D flow, results from numerical simulations compare well with a 2D potential flow model and solutions to a drag-buoyancy model reported as part of this work. When the simulations are extended to three dimensions, bubble and spike growth rates are in agreement with the so-called level 2 and level 3 models of Mikaelian [K. O. Mikaelian, Phys. Rev. E 79, 065303(R) (2009), 10.1103/PhysRevE.79.065303], and with corresponding 3D drag-buoyancy model solutions derived in this article. Our generalization of the RT problem to study variable g (t ) affords us the opportunity to investigate the appropriate scaling for bubble and spike amplitudes under these conditions. We consider two candidates, the displacement Z and width s2, but find the appropriate scaling is dependent on the density ratios between the fluids—at low density ratios, bubble and spike amplitudes are explained by both s2 and Z , while at large density differences the displacement collapses the spike data. Finally, for all the acceleration profiles studied here, spikes enter a free-fall regime at lower Atwood numbers than predicted by all the models.

Prospect of Using Numerical Dynamo Model for Prediction of Geomagnetic Secular Variation

NASA Technical Reports Server (NTRS)

Kuang, Weijia; Tangborn, Andrew

2003-01-01

Modeling of the Earth's core has reached a level of maturity to where the incorporation of observations into the simulations through data assimilation has become feasible. Data assimilation is a method by which observations of a system are combined with a model output (or forecast) to obtain a best guess of the state of the system, called the analysis. The analysis is then used as an initial condition for the next forecast. By doing assimilation, not only we shall be able to predict partially secular variation of the core field, we could also use observations to further our understanding of dynamical states in the Earth's core. One of the first steps in the development of an assimilation system is a comparison between the observations and the model solution. The highly turbulent nature of core dynamics, along with the absence of any regular external forcing and constraint (which occurs in atmospheric dynamics, for example) means that short time comparisons (approx. 1000 years) cannot be made between model and observations. In order to make sensible comparisons, a direct insertion assimilation method has been implemented. In this approach, magnetic field observations at the Earth's surface have been substituted into the numerical model, such that the ratio of the multiple components and the dipole component from observation is adjusted at the core-mantle boundary and extended to the interior of the core, while the total magnetic energy remains unchanged. This adjusted magnetic field is then used as the initial field for a new simulation. In this way, a time tugged simulation is created which can then be compared directly with observations. We present numerical solutions with and without data insertion and discuss their implications for the development of a more rigorous assimilation system.

Variational methods for direct/inverse problems of atmospheric dynamics and chemistry

NASA Astrophysics Data System (ADS)

Penenko, Vladimir; Penenko, Alexey; Tsvetova, Elena

2013-04-01

We present a variational approach for solving direct and inverse problems of atmospheric hydrodynamics and chemistry. It is important that the accurate matching of numerical schemes has to be provided in the chain of objects: direct/adjoint problems - sensitivity relations - inverse problems, including assimilation of all available measurement data. To solve the problems we have developed a new enhanced set of cost-effective algorithms. The matched description of the multi-scale processes is provided by a specific choice of the variational principle functionals for the whole set of integrated models. Then all functionals of variational principle are approximated in space and time by splitting and decomposition methods. Such approach allows us to separately consider, for example, the space-time problems of atmospheric chemistry in the frames of decomposition schemes for the integral identity sum analogs of the variational principle at each time step and in each of 3D finite-volumes. To enhance the realization efficiency, the set of chemical reactions is divided on the subsets related to the operators of production and destruction. Then the idea of the Euler's integrating factors is applied in the frames of the local adjoint problem technique [1]-[3]. The analytical solutions of such adjoint problems play the role of integrating factors for differential equations describing atmospheric chemistry. With their help, the system of differential equations is transformed to the equivalent system of integral equations. As a result we avoid the construction and inversion of preconditioning operators containing the Jacobi matrixes which arise in traditional implicit schemes for ODE solution. This is the main advantage of our schemes. At the same time step but on the different stages of the "global" splitting scheme, the system of atmospheric dynamic equations is solved. For convection - diffusion equations for all state functions in the integrated models we have developed the monotone and stable discrete-analytical numerical schemes [1]-[3] conserving the positivity of the chemical substance concentrations and possessing the properties of energy and mass balance that are postulated in the general variational principle for integrated models. All algorithms for solution of transport, diffusion and transformation problems are direct (without iterations). The work is partially supported by the Programs No 4 of Presidium RAS and No 3 of Mathematical Department of RAS, by RFBR project 11-01-00187 and Integrating projects of SD RAS No 8 and 35. Our studies are in the line with the goals of COST Action ES1004. References Penenko V., Tsvetova E. Discrete-analytical methods for the implementation of variational principles in environmental applications// Journal of computational and applied mathematics, 2009, v. 226, 319-330. Penenko A.V. Discrete-analytic schemes for solving an inverse coefficient heat conduction problem in a layered medium with gradient methods// Numerical Analysis and Applications, 2012, V. 5, pp 326-341. V. Penenko, E. Tsvetova. Variational methods for constructing the monotone approximations for atmospheric chemistry models //Numerical Analysis and Applications, 2013 (in press).

Numerical techniques for the solution of the compressible Navier-Stokes equations and implementation of turbulence models. [separated turbulent boundary layer flow problems

NASA Technical Reports Server (NTRS)

Baldwin, B. S.; Maccormack, R. W.; Deiwert, G. S.

1975-01-01

The time-splitting explicit numerical method of MacCormack is applied to separated turbulent boundary layer flow problems. Modifications of this basic method are developed to counter difficulties associated with complicated geometry and severe numerical resolution requirements of turbulence model equations. The accuracy of solutions is investigated by comparison with exact solutions for several simple cases. Procedures are developed for modifying the basic method to improve the accuracy. Numerical solutions of high-Reynolds-number separated flows over an airfoil and shock-separated flows over a flat plate are obtained. A simple mixing length model of turbulence is used for the transonic flow past an airfoil. A nonorthogonal mesh of arbitrary configuration facilitates the description of the flow field. For the simpler geometry associated with the flat plate, a rectangular mesh is used, and solutions are obtained based on a two-equation differential model of turbulence.

Bäcklund transformation, analytic soliton solutions and numerical simulation for a (2+1)-dimensional complex Ginzburg-Landau equation in a nonlinear fiber

NASA Astrophysics Data System (ADS)

Yu, Ming-Xiao; Tian, Bo; Chai, Jun; Yin, Hui-Min; Du, Zhong

2017-10-01

In this paper, we investigate a nonlinear fiber described by a (2+1)-dimensional complex Ginzburg-Landau equation with the chromatic dispersion, optical filtering, nonlinear and linear gain. Bäcklund transformation in the bilinear form is constructed. With the modified bilinear method, analytic soliton solutions are obtained. For the soliton, the amplitude can decrease or increase when the absolute value of the nonlinear or linear gain is enlarged, and the width can be compressed or amplified when the absolute value of the chromatic dispersion or optical filtering is enhanced. We study the stability of the numerical solutions numerically by applying the increasing amplitude, embedding the white noise and adding the Gaussian pulse to the initial values based on the analytic solutions, which shows that the numerical solutions are stable, not influenced by the finite initial perturbations.

Numerical modeling of the radiative transfer in a turbid medium using the synthetic iteration.

PubMed

Budak, Vladimir P; Kaloshin, Gennady A; Shagalov, Oleg V; Zheltov, Victor S

2015-07-27

In this paper we propose the fast, but the accurate algorithm for numerical modeling of light fields in the turbid media slab. For the numerical solution of the radiative transfer equation (RTE) it is required its discretization based on the elimination of the solution anisotropic part and the replacement of the scattering integral by a finite sum. The solution regular part is determined numerically. A good choice of the method of the solution anisotropic part elimination determines the high convergence of the algorithm in the mean square metric. The method of synthetic iterations can be used to improve the convergence in the uniform metric. A significant increase in the solution accuracy with the use of synthetic iterations allows applying the two-stream approximation for the regular part determination. This approach permits to generalize the proposed method in the case of an arbitrary 3D geometry of the medium.

Direct Numerical Simulation of Pebble Bed Flows: Database Development and Investigation of Low-Frequency Temporal Instabilities

DOE PAGES

Fick, Lambert H.; Merzari, Elia; Hassan, Yassin A.

2017-02-20

Computational analyses of fluid flow through packed pebble bed domains using the Reynolds-averaged NavierStokes framework have had limited success in the past. Because of a lack of high-fidelity experimental or computational data, optimization of Reynolds-averaged closure models for these geometries has not been extensively developed. In the present study, direct numerical simulation was employed to develop a high-fidelity database that can be used for optimizing Reynolds-averaged closure models for pebble bed flows. A face-centered cubic domain with periodic boundaries was used. Flow was simulated at a Reynolds number of 9308 and cross-verified by using available quasi-DNS data. During the simulations,more » low-frequency instability modes were observed that affected the stationary solution. Furthermore, these instabilities were investigated by using the method of proper orthogonal decomposition, and a correlation was found between the time-dependent asymmetry of the averaged velocity profile data and the behavior of the highest energy eigenmodes.« less

Krylov Deferred Correction Accelerated Method of Lines Transpose for Parabolic Problems

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

Jia, Jun; Jingfang, Huang

2008-01-01

In this paper, a new class of numerical methods for the accurate and efficient solutions of parabolic partial differential equations is presented. Unlike traditional method of lines (MoL), the new {\\bf \\it Krylov deferred correction (KDC) accelerated method of lines transpose (MoL^T)} first discretizes the temporal direction using Gaussian type nodes and spectral integration, and symbolically applies low-order time marching schemes to form a preconditioned elliptic system, which is then solved iteratively using Newton-Krylov techniques such as Newton-GMRES or Newton-BiCGStab method. Each function evaluation in the Newton-Krylov method is simply one low-order time-stepping approximation of the error by solving amore » decoupled system using available fast elliptic equation solvers. Preliminary numerical experiments show that the KDC accelerated MoL^T technique is unconditionally stable, can be spectrally accurate in both temporal and spatial directions, and allows optimal time-step sizes in long-time simulations.« less

Direct Numerical Simulation of Pebble Bed Flows: Database Development and Investigation of Low-Frequency Temporal Instabilities

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

Fick, Lambert H.; Merzari, Elia; Hassan, Yassin A.

Computational analyses of fluid flow through packed pebble bed domains using the Reynolds-averaged NavierStokes framework have had limited success in the past. Because of a lack of high-fidelity experimental or computational data, optimization of Reynolds-averaged closure models for these geometries has not been extensively developed. In the present study, direct numerical simulation was employed to develop a high-fidelity database that can be used for optimizing Reynolds-averaged closure models for pebble bed flows. A face-centered cubic domain with periodic boundaries was used. Flow was simulated at a Reynolds number of 9308 and cross-verified by using available quasi-DNS data. During the simulations,more » low-frequency instability modes were observed that affected the stationary solution. Furthermore, these instabilities were investigated by using the method of proper orthogonal decomposition, and a correlation was found between the time-dependent asymmetry of the averaged velocity profile data and the behavior of the highest energy eigenmodes.« less

Semi-analytical solution for flow in a leaky unconfined aquifer toward a partially penetrating pumping well

NASA Astrophysics Data System (ADS)

Malama, Bwalya; Kuhlman, Kristopher L.; Barrash, Warren

2008-07-01

SummaryA semi-analytical solution is presented for the problem of flow in a system consisting of unconfined and confined aquifers, separated by an aquitard. The unconfined aquifer is pumped continuously at a constant rate from a well of infinitesimal radius that partially penetrates its saturated thickness. The solution is termed semi-analytical because the exact solution obtained in double Laplace-Hankel transform space is inverted numerically. The solution presented here is more general than similar solutions obtained for confined aquifer flow as we do not adopt the assumption of unidirectional flow in the confined aquifer (typically assumed to be horizontal) and the aquitard (typically assumed to be vertical). Model predicted results show significant departure from the solution that does not take into account the effect of leakage even for cases where aquitard hydraulic conductivities are two orders of magnitude smaller than those of the aquifers. The results show low sensitivity to changes in radial hydraulic conductivities for aquitards that are two or more orders of magnitude smaller than those of the aquifers, in conformity to findings of earlier workers that radial flow in aquitards may be neglected under such conditions. Hence, for cases were aquitard hydraulic conductivities are two or more orders of magnitude smaller than aquifer conductivities, the simpler models that restrict flow to the radial direction in aquifers and to the vertical direction in aquitards may be sufficient. However, the model developed here can be used to model flow in aquifer-aquitard systems where radial flow is significant in aquitards.

Efficient implementation of three-dimensional reference interaction site model self-consistent-field method: Application to solvatochromic shift calculations

NASA Astrophysics Data System (ADS)

Minezawa, Noriyuki; Kato, Shigeki

2007-02-01

The authors present an implementation of the three-dimensional reference interaction site model self-consistent-field (3D-RISM-SCF) method. First, they introduce a robust and efficient algorithm for solving the 3D-RISM equation. The algorithm is a hybrid of the Newton-Raphson and Picard methods. The Jacobian matrix is analytically expressed in a computationally useful form. Second, they discuss the solute-solvent electrostatic interaction. For the solute to solvent route, the electrostatic potential (ESP) map on a 3D grid is constructed directly from the electron density. The charge fitting procedure is not required to determine the ESP. For the solvent to solute route, the ESP acting on the solute molecule is derived from the solvent charge distribution obtained by solving the 3D-RISM equation. Matrix elements of the solute-solvent interaction are evaluated by the direct numerical integration. A remarkable reduction in the computational time is observed in both routes. Finally, the authors implement the first derivatives of the free energy with respect to the solute nuclear coordinates. They apply the present method to "solute" water and formaldehyde in aqueous solvent using the simple point charge model, and the results are compared with those from other methods: the six-dimensional molecular Ornstein-Zernike SCF, the one-dimensional site-site RISM-SCF, and the polarizable continuum model. The authors also calculate the solvatochromic shifts of acetone, benzonitrile, and nitrobenzene using the present method and compare them with the experimental and other theoretical results.

Efficient implementation of three-dimensional reference interaction site model self-consistent-field method: application to solvatochromic shift calculations.

PubMed

Minezawa, Noriyuki; Kato, Shigeki

2007-02-07

The authors present an implementation of the three-dimensional reference interaction site model self-consistent-field (3D-RISM-SCF) method. First, they introduce a robust and efficient algorithm for solving the 3D-RISM equation. The algorithm is a hybrid of the Newton-Raphson and Picard methods. The Jacobian matrix is analytically expressed in a computationally useful form. Second, they discuss the solute-solvent electrostatic interaction. For the solute to solvent route, the electrostatic potential (ESP) map on a 3D grid is constructed directly from the electron density. The charge fitting procedure is not required to determine the ESP. For the solvent to solute route, the ESP acting on the solute molecule is derived from the solvent charge distribution obtained by solving the 3D-RISM equation. Matrix elements of the solute-solvent interaction are evaluated by the direct numerical integration. A remarkable reduction in the computational time is observed in both routes. Finally, the authors implement the first derivatives of the free energy with respect to the solute nuclear coordinates. They apply the present method to "solute" water and formaldehyde in aqueous solvent using the simple point charge model, and the results are compared with those from other methods: the six-dimensional molecular Ornstein-Zernike SCF, the one-dimensional site-site RISM-SCF, and the polarizable continuum model. The authors also calculate the solvatochromic shifts of acetone, benzonitrile, and nitrobenzene using the present method and compare them with the experimental and other theoretical results.

An improved conjugate gradient scheme to the solution of least squares SVM.

PubMed

Chu, Wei; Ong, Chong Jin; Keerthi, S Sathiya

2005-03-01

The least square support vector machines (LS-SVM) formulation corresponds to the solution of a linear system of equations. Several approaches to its numerical solutions have been proposed in the literature. In this letter, we propose an improved method to the numerical solution of LS-SVM and show that the problem can be solved using one reduced system of linear equations. Compared with the existing algorithm for LS-SVM, the approach used in this letter is about twice as efficient. Numerical results using the proposed method are provided for comparisons with other existing algorithms.

Numerical Solution of the Electron Transport Equation in the Upper Atmosphere

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

Woods, Mark Christopher; Holmes, Mark; Sailor, William C

A new approach for solving the electron transport equation in the upper atmosphere is derived. The problem is a very stiff boundary value problem, and to obtain an accurate numerical solution, matrix factorizations are used to decouple the fast and slow modes. A stable finite difference method is applied to each mode. This solver is applied to a simplifieed problem for which an exact solution exists using various versions of the boundary conditions that might arise in a natural auroral display. The numerical and exact solutions are found to agree with each other to at least two significant digits.

Design of underwater robot lines based on a hybrid automatic optimization strategy

NASA Astrophysics Data System (ADS)

Lyu, Wenjing; Luo, Weilin

2014-09-01

In this paper, a hybrid automatic optimization strategy is proposed for the design of underwater robot lines. Isight is introduced as an integration platform. The construction of this platform is based on the user programming and several commercial software including UG6.0, GAMBIT2.4.6 and FLUENT12.0. An intelligent parameter optimization method, the particle swarm optimization, is incorporated into the platform. To verify the strategy proposed, a simulation is conducted on the underwater robot model 5470, which originates from the DTRC SUBOFF project. With the automatic optimization platform, the minimal resistance is taken as the optimization goal; the wet surface area as the constraint condition; the length of the fore-body, maximum body radius and after-body's minimum radius as the design variables. With the CFD calculation, the RANS equations and the standard turbulence model are used for direct numerical simulation. By analyses of the simulation results, it is concluded that the platform is of high efficiency and feasibility. Through the platform, a variety of schemes for the design of the lines are generated and the optimal solution is achieved. The combination of the intelligent optimization algorithm and the numerical simulation ensures a global optimal solution and improves the efficiency of the searching solutions.

DRBEM solution of the acid-mediated tumour invasion model with time-dependent carrying capacities

NASA Astrophysics Data System (ADS)

Meral, Gülnihal

2017-07-01

It is known that the pH level of the extracellular tumour environment directly effects the progression of the tumour. In this study, the mathematical model for the acid-mediated tumour cell invasion consisting of a system of nonlinear reaction diffusion equations describing the interaction between the density of the tumour cells, normal cells and the concentration of ? protons produced by the tumour cells is solved numerically using the combined application of dual reciprocity boundary element method (DRBEM) and finite difference method. The space derivatives in the model are discretised by DRBEM using the fundamental solution of Laplace equation considering the time derivative and the nonlinearities as the nonhomogenity. The resulting systems of ordinary differential equations after the application of DRBEM are then discretised using forward difference. Because of the highly nonlinear character of the model, there arises difficulties in solving the model especially for two-dimensions and the boundary-only nature of DRBEM discretisation gives the advantage of having solutions with a lower computational cost. The proposed method is tested with different kinds of carrying capacities which also depend on time. The results of the numerical simulations are compared among each case and seen to confirm the expected behaviour of the model.

Fractional dynamics pharmacokinetics–pharmacodynamic models

PubMed Central

2010-01-01

While an increasing number of fractional order integrals and differential equations applications have been reported in the physics, signal processing, engineering and bioengineering literatures, little attention has been paid to this class of models in the pharmacokinetics–pharmacodynamic (PKPD) literature. One of the reasons is computational: while the analytical solution of fractional differential equations is available in special cases, it this turns out that even the simplest PKPD models that can be constructed using fractional calculus do not allow an analytical solution. In this paper, we first introduce new families of PKPD models incorporating fractional order integrals and differential equations, and, second, exemplify and investigate their qualitative behavior. The families represent extensions of frequently used PK link and PD direct and indirect action models, using the tools of fractional calculus. In addition the PD models can be a function of a variable, the active drug, which can smoothly transition from concentration to exposure, to hyper-exposure, according to a fractional integral transformation. To investigate the behavior of the models we propose, we implement numerical algorithms for fractional integration and for the numerical solution of a system of fractional differential equations. For simplicity, in our investigation we concentrate on the pharmacodynamic side of the models, assuming standard (integer order) pharmacokinetics. PMID:20455076

Simulation of solute transport across low-permeability barrier walls

USGS Publications Warehouse

Harte, P.T.; Konikow, Leonard F.; Hornberger, G.Z.

2006-01-01

Low-permeability, non-reactive barrier walls are often used to contain contaminants in an aquifer. Rates of solute transport through such barriers are typically many orders of magnitude slower than rates through the aquifer. Nevertheless, the success of remedial actions may be sensitive to these low rates of transport. Two numerical simulation methods for representing low-permeability barriers in a finite-difference groundwater-flow and transport model were tested. In the first method, the hydraulic properties of the barrier were represented directly on grid cells and in the second method, the intercell hydraulic-conductance values were adjusted to approximate the reduction in horizontal flow, allowing use of a coarser and computationally efficient grid. The alternative methods were tested and evaluated on the basis of hypothetical test problems and a field case involving tetrachloroethylene (PCE) contamination at a Superfund site in New Hampshire. For all cases, advective transport across the barrier was negligible, but preexisting numerical approaches to calculate dispersion yielded dispersive fluxes that were greater than expected. A transport model (MODFLOW-GWT) was modified to (1) allow different dispersive and diffusive properties to be assigned to the barrier than the adjacent aquifer and (2) more accurately calculate dispersion from concentration gradients and solute fluxes near barriers. The new approach yields reasonable and accurate concentrations for the test cases. ?? 2006.

On the homogenization of the acoustic wave propagation in perforated ducts of finite length for an inviscid and a viscous model.

PubMed

Semin, Adrien; Schmidt, Kersten

2018-02-01

The direct numerical simulation of the acoustic wave propagation in multiperforated absorbers with hundreds or thousands of tiny openings would result in a huge number of basis functions to resolve the microstructure. One is, however, primarily interested in effective and so homogenized transmission and absorption properties and how they are influenced by microstructure and its endpoints. For this, we introduce the surface homogenization that asymptotically decomposes the solution in a macroscopic part, a boundary layer corrector close to the interface and a near-field part close to its ends. The effective transmission and absorption properties are expressed by transmission conditions for the macroscopic solution on an infinitely thin interface and corner conditions at its endpoints to ensure the correct singular behaviour, which are intrinsic to the microstructure. We study and give details on the computation of the effective parameters for an inviscid and a viscous model and show their dependence on geometrical properties of the microstructure for the example of Helmholtz equation. Numerical experiments indicate that with the obtained macroscopic solution representation one can achieve an high accuracy for low and high porosities as well as for viscous boundary conditions while using only a small number of basis functions.

Modeling Kelvin Wave Cascades in Superfluid Helium

NASA Astrophysics Data System (ADS)

Boffetta, G.; Celani, A.; Dezzani, D.; Laurie, J.; Nazarenko, S.

2009-09-01

We study two different types of simplified models for Kelvin wave turbulence on quantized vortex lines in superfluids near zero temperature. Our first model is obtained from a truncated expansion of the Local Induction Approximation (Truncated-LIA) and it is shown to possess the same scalings and the essential behaviour as the full Biot-Savart model, being much simpler than the later and, therefore, more amenable to theoretical and numerical investigations. The Truncated-LIA model supports six-wave interactions and dual cascades, which are clearly demonstrated via the direct numerical simulation of this model in the present paper. In particular, our simulations confirm presence of the weak turbulence regime and the theoretically predicted spectra for the direct energy cascade and the inverse wave action cascade. The second type of model we study, the Differential Approximation Model (DAM), takes a further drastic simplification by assuming locality of interactions in k-space via using a differential closure that preserves the main scalings of the Kelvin wave dynamics. DAMs are even more amenable to study and they form a useful tool by providing simple analytical solutions in the cases when extra physical effects are present, e.g. forcing by reconnections, friction dissipation and phonon radiation. We study these models numerically and test their theoretical predictions, in particular the formation of the stationary spectra, and closeness of numerics for the higher-order DAM to the analytical predictions for the lower-order DAM.

Investigation of Hill's optical turbulence model by means of direct numerical simulation.

PubMed

Muschinski, Andreas; de Bruyn Kops, Stephen M

2015-12-01

For almost four decades, Hill's "Model 4" [J. Fluid Mech. 88, 541 (1978) has played a central role in research and technology of optical turbulence. Based on Batchelor's generalized Obukhov-Corrsin theory of scalar turbulence, Hill's model predicts the dimensionless function h(κl(0), Pr) that appears in Tatarskii's well-known equation for the 3D refractive-index spectrum in the case of homogeneous and isotropic turbulence, Φn(κ)=0.033C2(n)κ(-11/3) h(κl(0), Pr). Here we investigate Hill's model by comparing numerical solutions of Hill's differential equation with scalar spectra estimated from direct numerical simulation (DNS) output data. Our DNS solves the Navier-Stokes equation for the 3D velocity field and the transport equation for the scalar field on a numerical grid containing 4096(3) grid points. Two independent DNS runs are analyzed: one with the Prandtl number Pr=0.7 and a second run with Pr=1.0 . We find very good agreement between h(κl(0), Pr) estimated from the DNS output data and h(κl(0), Pr) predicted by the Hill model. We find that the height of the Hill bump is 1.79 Pr(1/3), implying that there is no bump if Pr<0.17 . Both the DNS and the Hill model predict that the viscous-diffusive "tail" of h(κl(0), Pr) is exponential, not Gaussian.

Complete Numerical Solution of the Diffusion Equation of Random Genetic Drift

PubMed Central

Zhao, Lei; Yue, Xingye; Waxman, David

2013-01-01

A numerical method is presented to solve the diffusion equation for the random genetic drift that occurs at a single unlinked locus with two alleles. The method was designed to conserve probability, and the resulting numerical solution represents a probability distribution whose total probability is unity. We describe solutions of the diffusion equation whose total probability is unity as complete. Thus the numerical method introduced in this work produces complete solutions, and such solutions have the property that whenever fixation and loss can occur, they are automatically included within the solution. This feature demonstrates that the diffusion approximation can describe not only internal allele frequencies, but also the boundary frequencies zero and one. The numerical approach presented here constitutes a single inclusive framework from which to perform calculations for random genetic drift. It has a straightforward implementation, allowing it to be applied to a wide variety of problems, including those with time-dependent parameters, such as changing population sizes. As tests and illustrations of the numerical method, it is used to determine: (i) the probability density and time-dependent probability of fixation for a neutral locus in a population of constant size; (ii) the probability of fixation in the presence of selection; and (iii) the probability of fixation in the presence of selection and demographic change, the latter in the form of a changing population size. PMID:23749318

Numerical Simulation of the Fluid-Structure Interaction of a Surface Effect Ship Bow Seal

NASA Astrophysics Data System (ADS)

Bloxom, Andrew L.

Numerical simulations of fluid-structure interaction (FSI) problems were performed in an effort to verify and validate a commercially available FSI tool. This tool uses an iterative partitioned coupling scheme between CD-adapco's STAR-CCM+ finite volume fluid solver and Simulia's Abaqus finite element structural solver to simulate the FSI response of a system. Preliminary verification and validation work (V&V) was carried out to understand the numerical behavior of the codes individually and together as a FSI tool. Verification and Validation work that was completed included code order verification of the respective fluid and structural solvers with Couette-Poiseuille flow and Euler-Bernoulli beam theory. These results confirmed the 2 nd order accuracy of the spatial discretizations used. Following that, a mixture of solution verifications and model calibrations was performed with the inclusion of the physics models implemented in the solution of the FSI problems. Solution verifications were completed for fluid and structural stand-alone models as well as for the coupled FSI solutions. These results re-confirmed the spatial order of accuracy but for more complex flows and physics models as well as the order of accuracy of the temporal discretizations. In lieu of a good material definition, model calibration is performed to reproduce the experimental results. This work used model calibration for both instances of hyperelastic materials which were presented in the literature as validation cases because these materials were defined as linear elastic. Calibrated, three dimensional models of the bow seal on the University of Michigan bow seal test platform showed the ability to reproduce the experimental results qualitatively through averaging of the forces and seal displacements. These simulations represent the only current 3D results for this case. One significant result of this study is the ability to visualize the flow around the seal and to directly measure the seal resistances at varying cushion pressures, seal immersions, forward speeds, and different seal materials. SES design analysis could greatly benefit from the inclusion of flexible seals in simulations, and this work is a positive step in that direction. In future work, the inclusion of more complex seal geometries and contact will further enhance the capability of this tool.

Staggered solution procedures for multibody dynamics simulation

NASA Technical Reports Server (NTRS)

Park, K. C.; Chiou, J. C.; Downer, J. D.

1990-01-01

The numerical solution procedure for multibody dynamics (MBD) systems is termed a staggered MBD solution procedure that solves the generalized coordinates in a separate module from that for the constraint force. This requires a reformulation of the constraint conditions so that the constraint forces can also be integrated in time. A major advantage of such a partitioned solution procedure is that additional analysis capabilities such as active controller and design optimization modules can be easily interfaced without embedding them into a monolithic program. After introducing the basic equations of motion for MBD system in the second section, Section 3 briefly reviews some constraint handling techniques and introduces the staggered stabilized technique for the solution of the constraint forces as independent variables. The numerical direct time integration of the equations of motion is described in Section 4. As accurate damping treatment is important for the dynamics of space structures, we have employed the central difference method and the mid-point form of the trapezoidal rule since they engender no numerical damping. This is in contrast to the current practice in dynamic simulations of ground vehicles by employing a set of backward difference formulas. First, the equations of motion are partitioned according to the translational and the rotational coordinates. This sets the stage for an efficient treatment of the rotational motions via the singularity-free Euler parameters. The resulting partitioned equations of motion are then integrated via a two-stage explicit stabilized algorithm for updating both the translational coordinates and angular velocities. Once the angular velocities are obtained, the angular orientations are updated via the mid-point implicit formula employing the Euler parameters. When the two algorithms, namely, the two-stage explicit algorithm for the generalized coordinates and the implicit staggered procedure for the constraint Lagrange multipliers, are brought together in a staggered manner, they constitute a staggered explicit-implicit procedure which is summarized in Section 5. Section 6 presents some example problems and discussions concerning several salient features of the staggered MBD solution procedure are offered in Section 7.

The discrete adjoint method for parameter identification in multibody system dynamics.

PubMed

Lauß, Thomas; Oberpeilsteiner, Stefan; Steiner, Wolfgang; Nachbagauer, Karin

2018-01-01

The adjoint method is an elegant approach for the computation of the gradient of a cost function to identify a set of parameters. An additional set of differential equations has to be solved to compute the adjoint variables, which are further used for the gradient computation. However, the accuracy of the numerical solution of the adjoint differential equation has a great impact on the gradient. Hence, an alternative approach is the discrete adjoint method , where the adjoint differential equations are replaced by algebraic equations. Therefore, a finite difference scheme is constructed for the adjoint system directly from the numerical time integration method. The method provides the exact gradient of the discretized cost function subjected to the discretized equations of motion.

A digital matched filter for reverse time chaos

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

Bailey, J. Phillip, E-mail: mchamilton@auburn.edu; Beal, Aubrey N.; Dean, Robert N.

2016-07-15

The use of reverse time chaos allows the realization of hardware chaotic systems that can operate at speeds equivalent to existing state of the art while requiring significantly less complex circuitry. Matched filter decoding is possible for the reverse time system since it exhibits a closed form solution formed partially by a linear basis pulse. Coefficients have been calculated and are used to realize the matched filter digitally as a finite impulse response filter. Numerical simulations confirm that this correctly implements a matched filter that can be used for detection of the chaotic signal. In addition, the direct form ofmore » the filter has been implemented in hardware description language and demonstrates performance in agreement with numerical results.« less

A numerical algorithm for optimal feedback gains in high dimensional linear quadratic regulator problems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Ito, K.

1991-01-01

A hybrid method for computing the feedback gains in linear quadratic regulator problem is proposed. The method, which combines use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite-dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantages of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed, and numerical evidence of the efficacy of these ideas is presented.

Analysis of free turbulent shear flows by numerical methods

NASA Technical Reports Server (NTRS)

Korst, H. H.; Chow, W. L.; Hurt, R. F.; White, R. A.; Addy, A. L.

1973-01-01

Studies are described in which the effort was essentially directed to classes of problems where the phenomenologically interpreted effective transport coefficients could be absorbed by, and subsequently extracted from (by comparison with experimental data), appropriate coordinate transformations. The transformed system of differential equations could then be solved without further specifications or assumptions by numerical integration procedures. An attempt was made to delineate different regimes for which specific eddy viscosity models could be formulated. In particular, this would account for the carryover of turbulence from attached boundary layers, the transitory adjustment, and the asymptotic behavior of initially disturbed mixing regions. Such models were subsequently used in seeking solutions for the prescribed two-dimensional test cases, yielding a better insight into overall aspects of the exchange mechanisms.

Numerical investigation of separated nozzle flows

NASA Technical Reports Server (NTRS)

Chen, C. L.; Chakravarthy, S. R.; Hung, C. M.

1994-01-01

A numerical study of axisymmetric overexpanded nozzle is presented. The flow structure of the startup and throttle-down processes are examined. During the impulsive startup process, observed flow features include the Mach disk, separation shock, Mach stem, vortex core, contact surface, slip stream, initial shock front, and shocklet. Also the movement of the Mach disk is not monotonical in the downstream direction. For a range of pressure ratios, hysteresis phenomenon occurs; different solutions were obtained depending on different processes. Three types of flow structures were observed. The location of separation point and the lower end turning point of hysteresis are closely predicted. A high peak of pressure is associated with the nozzle flow reattachment. The reversed vortical structure and affects engine performance.

A numerical algorithm for optimal feedback gains in high dimensional LQR problems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Ito, K.

1986-01-01

A hybrid method for computing the feedback gains in linear quadratic regulator problems is proposed. The method, which combines the use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated so as to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantage of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed and numerical evidence of the efficacy of our ideas presented.

Beam shaping of laser diode radiation by waveguides with arbitrary cladding geometry written with fs-laser radiation.

PubMed

Beckmann, Dennis; Schnitzler, Daniel; Schaefer, Dagmar; Gottmann, Jens; Kelbassa, Ingomar

2011-12-05

Waveguides with arbitrary cross sections are written in the volume of Al(2)O(3)-crystals using tightly focused femtosecond laser radiation. Utilizing a scanning system with large numerical aperture, complex cladding geometries are realized with a precision around 0.5 µm and a scanning speed up to 100 mm/s. Individual beam and mode shaping of laser diode radiation is demonstrated by varying the design of the waveguide cladding. The influence of the writing parameters on the waveguide properties are investigated resulting in a numerical aperture of the waveguides in the range of 0.1. This direct laser writing technique enables optical devices which could possibly replace bulky beam shaping setups with an integrated solution.

Large-Scale 3D Printing: The Way Forward

NASA Astrophysics Data System (ADS)

Jassmi, Hamad Al; Najjar, Fady Al; Ismail Mourad, Abdel-Hamid

2018-03-01

Research on small-scale 3D printing has rapidly evolved, where numerous industrial products have been tested and successfully applied. Nonetheless, research on large-scale 3D printing, directed to large-scale applications such as construction and automotive manufacturing, yet demands a great a great deal of efforts. Large-scale 3D printing is considered an interdisciplinary topic and requires establishing a blended knowledge base from numerous research fields including structural engineering, materials science, mechatronics, software engineering, artificial intelligence and architectural engineering. This review article summarizes key topics of relevance to new research trends on large-scale 3D printing, particularly pertaining (1) technological solutions of additive construction (i.e. the 3D printers themselves), (2) materials science challenges, and (3) new design opportunities.

A Hermite WENO reconstruction for fourth order temporal accurate schemes based on the GRP solver for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Du, Zhifang; Li, Jiequan

2018-02-01

This paper develops a new fifth order accurate Hermite WENO (HWENO) reconstruction method for hyperbolic conservation schemes in the framework of the two-stage fourth order accurate temporal discretization in Li and Du (2016) [13]. Instead of computing the first moment of the solution additionally in the conventional HWENO or DG approach, we can directly take the interface values, which are already available in the numerical flux construction using the generalized Riemann problem (GRP) solver, to approximate the first moment. The resulting scheme is fourth order temporal accurate by only invoking the HWENO reconstruction twice so that it becomes more compact. Numerical experiments show that such compactness makes significant impact on the resolution of nonlinear waves.

Unsteady three-dimensional marginal separation caused by surface-mounted obstacles and/or local suction

NASA Astrophysics Data System (ADS)

Braun, Stefan; Kluwick, Alfred

2004-09-01

Earlier investigations of steady two-dimensional marginally separated laminar boundary layers have shown that the non-dimensional wall shear (or equivalently the negative non-dimensional perturbation displacement thickness) is governed by a nonlinear integro-differential equation. This equation contains a single controlling parameter Gamma characterizing, for example, the angle of attack of a slender airfoil and has the important property that (real) solutions exist up to a critical value Gamma_c of Gamma only. Here we investigate three-dimensional unsteady perturbations of an incompressible steady two-dimensional marginally separated laminar boundary layer with special emphasis on the flow behaviour near Gamma_c. Specifically, it is shown that the integro differential equation which governs these disturbances if Gamma_c {-} Gamma {=} O(1) reduces to a nonlinear partial differential equation known as the Fisher equation as Gamma approaches the critical value Gamma_c. This in turn leads to a significant simplification of the problem allowing, among other things, a systematic study of devices used in boundary-layer control and an analytical investigation of the conditions leading to the formation of finite-time singularities which have been observed in earlier numerical studies of unsteady two-dimensional and three-dimensional flows in the vicinity of a line of symmetry. Also, it is found that it is possible to construct exact solutions which describe waves of constant form travelling in the spanwise direction. These waves may contain singularities which can be interpreted as vortex sheets. The existence of these solutions strongly suggests that solutions of the Fisher equation which lead to finite-time blow-up may be extended beyond the blow-up time, thereby generating moving singularities which can be interpreted as vortical structures qualitatively similar to those emerging in direct numerical simulations of near critical (i.e. transitional) laminar separation bubbles. This is supported by asymptotic analysis.

Finite element method formulation in polar coordinates for transient heat conduction problems

NASA Astrophysics Data System (ADS)

Duda, Piotr

2016-04-01

The aim of this paper is the formulation of the finite element method in polar coordinates to solve transient heat conduction problems. It is hard to find in the literature a formulation of the finite element method (FEM) in polar or cylindrical coordinates for the solution of heat transfer problems. This document shows how to apply the most often used boundary conditions. The global equation system is solved by the Crank-Nicolson method. The proposed algorithm is verified in three numerical tests. In the first example, the obtained transient temperature distribution is compared with the temperature obtained from the presented analytical solution. In the second numerical example, the variable boundary condition is assumed. In the last numerical example the component with the shape different than cylindrical is used. All examples show that the introduction of the polar coordinate system gives better results than in the Cartesian coordinate system. The finite element method formulation in polar coordinates is valuable since it provides a higher accuracy of the calculations without compacting the mesh in cylindrical or similar to tubular components. The proposed method can be applied for circular elements such as boiler drums, outlet headers, flux tubes. This algorithm can be useful during the solution of inverse problems, which do not allow for high density grid. This method can calculate the temperature distribution in the bodies of different properties in the circumferential and the radial direction. The presented algorithm can be developed for other coordinate systems. The examples demonstrate a good accuracy and stability of the proposed method.

CSM solutions of rotating blade dynamics using integrating matrices

NASA Technical Reports Server (NTRS)

Lakin, William D.

1992-01-01

The dynamic behavior of flexible rotating beams continues to receive considerable research attention as it constitutes a fundamental problem in applied mechanics. Further, beams comprise parts of many rotating structures of engineering significance. A topic of particular interest at the present time involves the development of techniques for obtaining the behavior in both space and time of a rotor acted upon by a simple airload loading. Most current work on problems of this type use solution techniques based on normal modes. It is certainly true that normal modes cannot be disregarded, as knowledge of natural blade frequencies is always important. However, the present work has considered a computational structural mechanics (CSM) approach to rotor blade dynamics problems in which the physical properties of the rotor blade provide input for a direct numerical solution of the relevant boundary-and-initial-value problem. Analysis of the dynamics of a given rotor system may require solution of the governing equations over a long time interval corresponding to many revolutions of the loaded flexible blade. For this reason, most of the common techniques in computational mechanics, which treat the space-time behavior concurrently, cannot be applied to the rotor dynamics problem without a large expenditure of computational resources. By contrast, the integrating matrix technique of computational mechanics has the ability to consistently incorporate boundary conditions and 'remove' dependence on a space variable. For problems involving both space and time, this feature of the integrating matrix approach thus can generate a 'splitting' which forms the basis of an efficient CSM method for numerical solution of rotor dynamics problems.

Implicit unified gas-kinetic scheme for steady state solutions in all flow regimes

NASA Astrophysics Data System (ADS)

Zhu, Yajun; Zhong, Chengwen; Xu, Kun

2016-06-01

This paper presents an implicit unified gas-kinetic scheme (UGKS) for non-equilibrium steady state flow computation. The UGKS is a direct modeling method for flow simulation in all regimes with the updates of both macroscopic flow variables and microscopic gas distribution function. By solving the macroscopic equations implicitly, a predicted equilibrium state can be obtained first through iterations. With the newly predicted equilibrium state, the evolution equation of the gas distribution function and the corresponding collision term can be discretized in a fully implicit way for fast convergence through iterations as well. The lower-upper symmetric Gauss-Seidel (LU-SGS) factorization method is implemented to solve both macroscopic and microscopic equations, which improves the efficiency of the scheme. Since the UGKS is a direct modeling method and its physical solution depends on the mesh resolution and the local time step, a physical time step needs to be fixed before using an implicit iterative technique with a pseudo-time marching step. Therefore, the physical time step in the current implicit scheme is determined by the same way as that in the explicit UGKS for capturing the physical solution in all flow regimes, but the convergence to a steady state speeds up through the adoption of a numerical time step with large CFL number. Many numerical test cases in different flow regimes from low speed to hypersonic ones, such as the Couette flow, cavity flow, and the flow passing over a cylinder, are computed to validate the current implicit method. The overall efficiency of the implicit UGKS can be improved by one or two orders of magnitude in comparison with the explicit one.

Accuracy and efficiency considerations for wide-angle wavefield extrapolators and scattering operators

NASA Astrophysics Data System (ADS)

Thomson, C. J.

2005-10-01

Several observations are made concerning the numerical implementation of wide-angle one-way wave equations, using for illustration scalar waves obeying the Helmholtz equation in two space dimensions. This simple case permits clear identification of a sequence of physically motivated approximations of use when the mathematically exact pseudo-differential operator (PSDO) one-way method is applied. As intuition suggests, these approximations largely depend on the medium gradients in the direction transverse to the main propagation direction. A key point is that narrow-angle approximations are to be avoided in the interests of accuracy. Another key consideration stems from the fact that the so-called `standard-ordering' PSDO indicates how lateral interpolation of the velocity structure can significantly reduce computational costs associated with the Fourier or plane-wave synthesis lying at the heart of the calculations. A third important point is that the PSDO theory shows what approximations are necessary in order to generate an exponential one-way propagator for the laterally varying case, representing the intuitive extension of classical integral-transform solutions for a laterally homogeneous medium. This exponential propagator permits larger forward stepsizes. Numerical comparisons with Helmholtz (i.e. full) wave-equation finite-difference solutions are presented for various canonical problems. These include propagation along an interfacial gradient, the effects of a compact inclusion and the formation of extended transmitted and backscattered wave trains by model roughness. The ideas extend to the 3-D, generally anisotropic case and to multiple scattering by invariant embedding. It is concluded that the method is very competitive, striking a new balance between simplifying approximations and computational labour. Complicated wave-scattering effects are retained without the need for expensive global solutions, providing a robust and flexible modelling tool.

Application of the Fokker-Planck molecular mixing model to turbulent scalar mixing using moment methods

NASA Astrophysics Data System (ADS)

Madadi-Kandjani, E.; Fox, R. O.; Passalacqua, A.

2017-06-01

An extended quadrature method of moments using the β kernel density function (β -EQMOM) is used to approximate solutions to the evolution equation for univariate and bivariate composition probability distribution functions (PDFs) of a passive scalar for binary and ternary mixing. The key element of interest is the molecular mixing term, which is described using the Fokker-Planck (FP) molecular mixing model. The direct numerical simulations (DNSs) of Eswaran and Pope ["Direct numerical simulations of the turbulent mixing of a passive scalar," Phys. Fluids 31, 506 (1988)] and the amplitude mapping closure (AMC) of Pope ["Mapping closures for turbulent mixing and reaction," Theor. Comput. Fluid Dyn. 2, 255 (1991)] are taken as reference solutions to establish the accuracy of the FP model in the case of binary mixing. The DNSs of Juneja and Pope ["A DNS study of turbulent mixing of two passive scalars," Phys. Fluids 8, 2161 (1996)] are used to validate the results obtained for ternary mixing. Simulations are performed with both the conditional scalar dissipation rate (CSDR) proposed by Fox [Computational Methods for Turbulent Reacting Flows (Cambridge University Press, 2003)] and the CSDR from AMC, with the scalar dissipation rate provided as input and obtained from the DNS. Using scalar moments up to fourth order, the ability of the FP model to capture the evolution of the shape of the PDF, important in turbulent mixing problems, is demonstrated. Compared to the widely used assumed β -PDF model [S. S. Girimaji, "Assumed β-pdf model for turbulent mixing: Validation and extension to multiple scalar mixing," Combust. Sci. Technol. 78, 177 (1991)], the β -EQMOM solution to the FP model more accurately describes the initial mixing process with a relatively small increase in computational cost.

A low-rank control variate for multilevel Monte Carlo simulation of high-dimensional uncertain systems

NASA Astrophysics Data System (ADS)

Fairbanks, Hillary R.; Doostan, Alireza; Ketelsen, Christian; Iaccarino, Gianluca

2017-07-01

Multilevel Monte Carlo (MLMC) is a recently proposed variation of Monte Carlo (MC) simulation that achieves variance reduction by simulating the governing equations on a series of spatial (or temporal) grids with increasing resolution. Instead of directly employing the fine grid solutions, MLMC estimates the expectation of the quantity of interest from the coarsest grid solutions as well as differences between each two consecutive grid solutions. When the differences corresponding to finer grids become smaller, hence less variable, fewer MC realizations of finer grid solutions are needed to compute the difference expectations, thus leading to a reduction in the overall work. This paper presents an extension of MLMC, referred to as multilevel control variates (MLCV), where a low-rank approximation to the solution on each grid, obtained primarily based on coarser grid solutions, is used as a control variate for estimating the expectations involved in MLMC. Cost estimates as well as numerical examples are presented to demonstrate the advantage of this new MLCV approach over the standard MLMC when the solution of interest admits a low-rank approximation and the cost of simulating finer grids grows fast.

Direct Coexistence Methods to Determine the Solubility of Salts in Water from Numerical Simulations. Test Case NaCl.

PubMed

Manzanilla-Granados, Héctor M; Saint-Martín, Humberto; Fuentes-Azcatl, Raúl; Alejandre, José

2015-07-02

The solubility of NaCl, an equilibrium between a saturated solution of ions and a solid with a crystalline structure, was obtained from molecular dynamics simulations using the SPC/E and TIP4P-Ew water models. Four initial setups on supersaturated systems were tested on sodium chloride (NaCl) solutions to determine the equilibrium conditions and computational performance: (1) an ionic solution confined between two crystal plates of periodic NaCl, (2) a solution with all the ions initially distributed randomly, (3) a nanocrystal immersed in pure water, and (4) a nanocrystal immersed in an ionic solution. In some cases, the equilibration of the system can take several microseconds. The results from this work showed that the solubility of NaCl was the same, within simulation error, for the four setups, and in agreement with previously reported values from simulations with the setup (1). The system of a nanocrystal immersed in supersaturated solution was found to equilibrate faster than others. In agreement with laser-Doppler droplet measurements, at equilibrium with the solution the crystals in all the setups had a slight positive charge.

Documentation for the MODFLOW 6 framework

USGS Publications Warehouse

Hughes, Joseph D.; Langevin, Christian D.; Banta, Edward R.

2017-08-10

MODFLOW is a popular open-source groundwater flow model distributed by the U.S. Geological Survey. Growing interest in surface and groundwater interactions, local refinement with nested and unstructured grids, karst groundwater flow, solute transport, and saltwater intrusion, has led to the development of numerous MODFLOW versions. Often times, there are incompatibilities between these different MODFLOW versions. The report describes a new MODFLOW framework called MODFLOW 6 that is designed to support multiple models and multiple types of models. The framework is written in Fortran using a modular object-oriented design. The primary framework components include the simulation (or main program), Timing Module, Solutions, Models, Exchanges, and Utilities. The first version of the framework focuses on numerical solutions, numerical models, and numerical exchanges. This focus on numerical models allows multiple numerical models to be tightly coupled at the matrix level.

Numerical Study of Periodic Traveling Wave Solutions for the Predator-Prey Model with Landscape Features

NASA Astrophysics Data System (ADS)

Yun, Ana; Shin, Jaemin; Li, Yibao; Lee, Seunggyu; Kim, Junseok

We numerically investigate periodic traveling wave solutions for a diffusive predator-prey system with landscape features. The landscape features are modeled through the homogeneous Dirichlet boundary condition which is imposed at the edge of the obstacle domain. To effectively treat the Dirichlet boundary condition, we employ a robust and accurate numerical technique by using a boundary control function. We also propose a robust algorithm for calculating the numerical periodicity of the traveling wave solution. In numerical experiments, we show that periodic traveling waves which move out and away from the obstacle are effectively generated. We explain the formation of the traveling waves by comparing the wavelengths. The spatial asynchrony has been shown in quantitative detail for various obstacles. Furthermore, we apply our numerical technique to the complicated real landscape features.

Klein–Gordon equation in curved space-time

NASA Astrophysics Data System (ADS)

Lehn, R. D.; Chabysheva, S. S.; Hiller, J. R.

2018-07-01

We report the methods and results of a computational physics project on the solution of the relativistic Klein–Gordon equation for a light particle gravitationally bound to a heavy central mass. The gravitational interaction is prescribed by the metric of a spherically symmetric space-time. Metrics are considered for an impenetrable sphere, a soft sphere of uniform density, and a soft sphere with a linear transition from constant to zero density; in each case the radius of the central mass is chosen to be sufficient to avoid any event horizon. The solutions are obtained numerically and compared with nonrelativistic Coulomb-type solutions, both directly and in perturbation theory, to study the general-relativistic corrections to the quantum solutions for a 1/r potential. The density profile with a linear transition is chosen to avoid singularities in the wave equation that can be caused by a discontinuous derivative of the density. This project should be of interest to instructors and students of computational physics at the graduate and advanced undergraduate levels.

Numerical inverse method predicting acoustic spinning modes radiated by a ducted fan from free-field test data.

PubMed

Lewy, Serge

2008-07-01

Spinning modes generated by a ducted turbofan at a given frequency determine the acoustic free-field directivity. An inverse method starting from measured directivity patterns is interesting in providing information on the noise sources without requiring tedious spinning-mode experimental analyses. According to a previous article, equations are based on analytical modal splitting inside a cylindrical duct and on a Rayleigh or a Kirchhoff integral on the duct exit cross section to get far-field directivity. Equations are equal in number to free-field measurement locations and the unknowns are the propagating mode amplitudes (there are generally more unknowns than equations). A MATLAB procedure has been implemented by using either the pseudoinverse function or the backslash operator. A constraint comes from the fact that squared modal amplitudes must be positive which involves an iterative least squares fitting. Numerical simulations are discussed along with several examples based on tests performed by Rolls-Royce in the framework of a European project. It is assessed that computation is very fast and it well fits the measured directivities, but the solution depends on the method and is not unique. This means that the initial set of modes should be chosen according to any known physical property of the acoustic sources.

Wavelet and adaptive methods for time dependent problems and applications in aerosol dynamics

NASA Astrophysics Data System (ADS)

Guo, Qiang

Time dependent partial differential equations (PDEs) are widely used as mathematical models of environmental problems. Aerosols are now clearly identified as an important factor in many environmental aspects of climate and radiative forcing processes, as well as in the health effects of air quality. The mathematical models for the aerosol dynamics with respect to size distribution are nonlinear partial differential and integral equations, which describe processes of condensation, coagulation and deposition. Simulating the general aerosol dynamic equations on time, particle size and space exhibits serious difficulties because the size dimension ranges from a few nanometer to several micrometer while the spatial dimension is usually described with kilometers. Therefore, it is an important and challenging task to develop efficient techniques for solving time dependent dynamic equations. In this thesis, we develop and analyze efficient wavelet and adaptive methods for the time dependent dynamic equations on particle size and further apply them to the spatial aerosol dynamic systems. Wavelet Galerkin method is proposed to solve the aerosol dynamic equations on time and particle size due to the fact that aerosol distribution changes strongly along size direction and the wavelet technique can solve it very efficiently. Daubechies' wavelets are considered in the study due to the fact that they possess useful properties like orthogonality, compact support, exact representation of polynomials to a certain degree. Another problem encountered in the solution of the aerosol dynamic equations results from the hyperbolic form due to the condensation growth term. We propose a new characteristic-based fully adaptive multiresolution numerical scheme for solving the aerosol dynamic equation, which combines the attractive advantages of adaptive multiresolution technique and the characteristics method. On the aspect of theoretical analysis, the global existence and uniqueness of solutions of continuous time wavelet numerical methods for the nonlinear aerosol dynamics are proved by using Schauder's fixed point theorem and the variational technique. Optimal error estimates are derived for both continuous and discrete time wavelet Galerkin schemes. We further derive reliable and efficient a posteriori error estimate which is based on stable multiresolution wavelet bases and an adaptive space-time algorithm for efficient solution of linear parabolic differential equations. The adaptive space refinement strategies based on the locality of corresponding multiresolution processes are proved to converge. At last, we develop efficient numerical methods by combining the wavelet methods proposed in previous parts and the splitting technique to solve the spatial aerosol dynamic equations. Wavelet methods along the particle size direction and the upstream finite difference method along the spatial direction are alternately used in each time interval. Numerical experiments are taken to show the effectiveness of our developed methods.

Impact adding bifurcation in an autonomous hybrid dynamical model of church bell

NASA Astrophysics Data System (ADS)

Brzeski, P.; Chong, A. S. E.; Wiercigroch, M.; Perlikowski, P.

2018-05-01

In this paper we present the bifurcation analysis of the yoke-bell-clapper system which corresponds to the biggest bell "Serce Lodzi" mounted in the Cathedral Basilica of St Stanislaus Kostka, Lodz, Poland. The mathematical model of the system considered in this work has been derived and verified based on measurements of dynamics of the real bell. We perform numerical analysis both by direct numerical integration and path-following method using toolbox ABESPOL (Chong, 2016). By introducing the active yoke the position of the bell-clapper system with respect to the yoke axis of rotation can be easily changed and it can be used to probe the system dynamics. We found a wide variety of periodic and non-periodic solutions, and examined the ranges of coexistence of solutions and transitions between them via different types of bifurcations. Finally, a new type of bifurcation induced by a grazing event - an "impact adding bifurcation" has been proposed. When it occurs, the number of impacts between the bell and the clapper is increasing while the period of the system's motion stays the same.

Collisionless kinetic theory of oblique tearing instabilities

DOE PAGES

Baalrud, S. D.; Bhattacharjee, A.; Daughton, W.

2018-02-15

The linear dispersion relation for collisionless kinetic tearing instabilities is calculated for the Harris equilibrium. In contrast to the conventional 2D geometry, which considers only modes at the center of the current sheet, modes can span the current sheet in 3D. Modes at each resonant surface have a unique angle with respect to the guide field direction. Both kinetic simulations and numerical eigenmode solutions of the linearized Vlasov-Maxwell equations have recently revealed that standard analytic theories vastly overestimate the growth rate of oblique modes. In this paper, we find that this stabilization is associated with the density-gradient-driven diamagnetic drift. Themore » analytic theories miss this drift stabilization because the inner tearing layer broadens at oblique angles sufficiently far that the assumption of scale separation between the inner and outer regions of boundary-layer theory breaks down. The dispersion relation obtained by numerically solving a single second order differential equation is found to approximately capture the drift stabilization predicted by solutions of the full integro-differential eigenvalue problem. Finally, a simple analytic estimate for the stability criterion is provided.« less

Two-relaxation-time lattice Boltzmann method for the anisotropic dispersive Henry problem

NASA Astrophysics Data System (ADS)

Servan-Camas, Borja; Tsai, Frank T.-C.

2010-02-01

This study develops a lattice Boltzmann method (LBM) with a two-relaxation-time collision operator (TRT) to cope with anisotropic heterogeneous hydraulic conductivity and anisotropic velocity-dependent hydrodynamic dispersion in the saltwater intrusion problem. The directional-speed-of-sound technique is further developed to address anisotropic hydraulic conductivity and dispersion tensors. Forcing terms are introduced in the LBM to correct numerical errors that arise during the recovery procedure and to describe the sink/source terms in the flow and transport equations. In order to facilitate the LBM implementation, the forcing terms are combined with the equilibrium distribution functions (EDFs) to create pseudo-EDFs. This study performs linear stability analysis and derives LBM stability domains to solve the anisotropic advection-dispersion equation. The stability domains are used to select the time step at which the lattice Boltzmann method provides stable solutions to the numerical examples. The LBM was implemented for the anisotropic dispersive Henry problem with high ratios of longitudinal to transverse dispersivities, and the results compared well to the solutions in the work of Abarca et al. (2007).