The applications of high-order, compact finite difference methods in shock calculations are discussed. The main concern is to define a local mean which will serve as a reference for introducing a local nonlinear limiting to control spurious numerical oscillations while maintaining the formal accuracy of the scheme. For scalar conservation laws, the resulting schemes can be proven total-variation stable in one space dimension and maximum-norm stable in multiple space dimensions. Numerical...

Topics: NASA Technical Reports Server (NTRS), BURGER EQUATION, FINITE DIFFERENCE THEORY, MATHEMATICAL...

In this article, we make a few remarks on the role that attractors and inertial manifolds play in fluid mechanics problems. We then describe the role of incremental unknowns for approximating attractors and inertial manifolds when finite difference multigrid discretizations are used. The relation with direct numerical simulation and large eddy simulation is also mentioned.

Topics: NASA Technical Reports Server (NTRS), BURGER EQUATION, FINITE DIFFERENCE THEORY, MULTIGRID METHODS,...

A stabilization problem for Burgers' equation is considered. Using linearization, various controllers are constructed which minimize certain weighted energy functionals. These controllers produce the desired degree of stability for the closed-loop nonlinear system. A numerical scheme for computing the feedback gain functional is developed and several numerical experiments are performed to show the theoretical results.

Topics: NASA Technical Reports Server (NTRS), BURGER EQUATION, CONTROLLERS, FEEDBACK CONTROL,...

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...

Topics: NASA Technical Reports Server (NTRS), NONLINEARITY, AEROACOUSTICS, SOUND PROPAGATION, NONLINEAR...

Forward Euler's explicit, finite-difference formula of extrapolation, is used as a predictor and a convex formula as a corrector to integrate differential equations numerically. An application has been made to Burger's equation.

Topics: NASA Technical Reports Server (NTRS), BURGER EQUATION, DIFFERENTIAL EQUATIONS, EXTRAPOLATION,...

We consider a viscous incompressible fluid flow driven between two parallel plates by a constant pressure gradient. The flow is at a finite Reynolds number, with an 0(l) disturbance in the form of a traveling wave. A phase equation approach is used to discuss the evolution of slowly varying fully nonlinear two dimensional wavetrains. We consider uniform wavetrains in detail, showing that the development of a wavenumber perturbation is governed by Burgers equation in most cases. The wavenumber...

Topics: NASA Technical Reports Server (NTRS), BURGER EQUATION, CHANNEL FLOW, INCOMPRESSIBLE FLUIDS,...

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385

May 31, 2011
05/11

by
NON

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The NASA Glenn Research Center (GRC) is developing and demonstrating communications and network technologies that are helping to enable the near-Earth space Internet. GRC envisions several service categories. The first of these categories is direct data distribution or D3 (pronounced ''D-cubed''). Commercially provided D3 will make it possible to download a data set from a spacecraft, like the International Space Station. as easily as one can extract a file from a remote server today, using a...

Topics: BOUNDARY CONDITIONS, VARIABILITY, BURGER EQUATION, MATHEMATICAL MODELS, UNCERTAIN SYSTEMS, ERROR...

The existing 2-D alpha-mu scheme and alpha-epsilon scheme based on the method of space-time conservation element and solution element, which were constructed for solving the linear 2-D unsteady advection-diffusion equation and unsteady advection equation, respectively, are tested. Also, the alpha-epsilon scheme is modified to become the V-E scheme for solving the nonlinear 2-D inviscid Burgers equation. Numerical solutions of six test problems are presented in comparison with their exact...

Topics: NASA Technical Reports Server (NTRS), ADVECTION, COMPUTATIONAL FLUID DYNAMICS, CONSERVATION...

This paper addresses the critical need for the development of intelligent or assisting software tools for the scientist who is working in the initial problem formulation and mathematical model representation stage of research. In particular, examples of that representation in fluid dynamics and instability theory are discussed. The creation of a mathematical model that is ready for application of certain solution strategies requires extensive symbolic manipulation of the original mathematical...

Topics: NASA Technical Reports Server (NTRS), MATHEMATICAL MODELS, NUMERICAL ANALYSIS, COMPUTATIONAL FLUID...

This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as...

Topics: NASA Technical Reports Server (NTRS), NONLINEAR SYSTEMS, NAVIER-STOKES EQUATION, COMPUTATIONAL...

A motivation is given for studying Burgers flow and a solution technique is outlined which works equally well for Oseen or Burgers flow past a circular cylinder. The separation behind the cylinder, the drag experienced by the cylinder, and asymptotic behavior far from the cylinder are described. It is shown that the predictions of Burgers flow near the cylinder provide a substantial improvement over those of Oseen flow. Finally, the equations of motion for Burgers flow past an ellipse are...

Topics: NASA Technical Reports Server (NTRS), BURGER EQUATION, ELLIPTICAL CYLINDERS, EQUATIONS OF MOTION,...

Wavelet bases are used to generate spaces of approximation for the resolution of bidimensional elliptic and parabolic problems. Under some specific hypotheses relating the properties of the wavelets to the order of the involved operators, it is shown that an approximate solution can be built. This approximation is then stable and converges towards the exact solution. It is designed such that fast algorithms involving biorthogonal multi resolution analyses can be used to resolve the...

Topics: NASA Technical Reports Server (NTRS), PARTIAL DIFFERENTIAL EQUATIONS, INTEGRAL TRANSFORMATIONS,...

A triangle based total variation diminishing (TVD) scheme for the numerical approximation of hyperbolic conservation laws in two space dimensions is constructed. The novelty of the scheme lies in the nature of the preprocessing of the cell averaged data, which is accomplished via a nearest neighbor linear interpolation followed by a slope limiting procedures. Two such limiting procedures are suggested. The resulting method is considerably more simple than other triangle based non-oscillatory...

Topics: NASA Technical Reports Server (NTRS), ADVECTION, APPROXIMATION, TRIANGLES, TVD SCHEMES, BURGER...

The Burgers equation with a small viscosity term, initial and periodic boundary conditions is resolved using a spatial approximation constructed from an orthonormal basis of wavelets. The algorithm is directly derived from the notions of multiresolution analysis and tree algorithms. Before the numerical algorithm is described these notions are first recalled. The method uses extensively the localization properties of the wavelets in the physical and Fourier spaces. Moreover, the authors take...

Topics: NASA Technical Reports Server (NTRS), BOUNDARY CONDITIONS, BURGER EQUATION, COEFFICIENTS, DEGREES...

The cubic spline collocation procedure for the numerical solution of partial differential equations was reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy for a nonuniform mesh and overall fourth-order accuracy for a uniform mesh. Application of the technique was made to the Burger's equation, to the flow around a...

Topics: NASA Technical Reports Server (NTRS), NUMERICAL ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, SPLINE...

Uniform high order spectral methods to solve multi-dimensional Euler equations for gas dynamics are discussed. Uniform high order spectral approximations with spectral accuracy in smooth regions of solutions are constructed by introducing the idea of the Essentially Non-Oscillatory (ENO) polynomial interpolations into the spectral methods. The authors present numerical results for the inviscid Burgers' equation, and for the one dimensional Euler equations including the interactions between a...

Topics: NASA Technical Reports Server (NTRS), BURGER EQUATION, DETONATION WAVES, DIFFERENTIAL EQUATIONS,...

A method for active fluid flow control based on control theory is discussed. Dynamic programming and fixed point successive approximations are used to accommodate the nonlinear control problem. The long-term goal of this project is to establish an effective method applicable to complex flows such as turbulence and jets. However, in this report, the method is applied to stochastic Burgers equation as an intermediate step towards this goal. Numerical results are compared with those obtained by...

Topics: NASA Technical Reports Server (NTRS), ACTIVE CONTROL, BURGER EQUATION, COMPUTATIONAL FLUID...

The problem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems was considered. Concentration was on a system with unbounded input and output operators governed by Burgers' equation. A linearized model was used to compute low-order-finite-dimensional control laws by minimizing certain energy functionals. Then these laws were applied to the nonlinear model. Standard approaches to this problem employ model/controller reduction...

Topics: NASA Technical Reports Server (NTRS), BURGER EQUATION, COMPENSATORS, CONTROL THEORY, DISTRIBUTED...

The purpose of this paper is to present asymptotically stable open boundary conditions for the numerical approximation of the compressible Navier-Stokes equations in three spatial dimensions. The treatment uses the conservation form of the Navier-Stokes equations and utilizes linearization and localization at the boundaries based on these variables. The proposed boundary conditions are applied through a penalty procedure, thus ensuring correct behavior of the scheme as the Reynolds number tends...

Topics: NASA Technical Reports Server (NTRS), ASYMPTOTIC PROPERTIES, BOUNDARY CONDITIONS, CIRCULAR...

The Kuramoto-Sivashinsky equation arises in a variety of applications, among which are modeling reaction diffusion systems, flame propagation and viscous flow problems. It is considered here, as a prototype to the larger class of generalized Burgers equations: those consist of a quadratic nonlinearity and an arbitrary linear parabolic part. It is shown that such equations are well posed, thus admitting a unique smooth solution, continuously dependent on its initial data. As an attractive...

Topics: NASA Technical Reports Server (NTRS), BURGER EQUATION, EXISTENCE, NONLINEAR EQUATIONS, UNIQUENESS,...

Stable and accurate interface conditions are derived for the linear advection-diffusion equation. The conditions are functionally independent of the spatial order of accuracy and rely only on the form of the discrete operator. We focus on high-order finite-difference operators that satisfy the summation-by-parts (SBP) property. We prove that stability is a natural consequence of the SBP operators used in conjunction with the new boundary conditions. In addition, we show that the interface...

Topics: NASA Technical Reports Server (NTRS), FINITE DIFFERENCE THEORY, NUMERICAL STABILITY, LINEAR...

Test problems are used to examine the performance of several one-dimensional numerical schemes based on the space-time conservation and solution element (CE/SE) method. Investigated in this paper are the CE/SE schemes constructed previously for solving the linear unsteady advection-diffusion equation and the schemes derived here for solving the nonlinear viscous and inviscid Burgers equations. In comparison with the numerical solutions obtained using several traditional finite-difference...

Topics: NASA Technical Reports Server (NTRS), CONSERVATION, INVISCID FLOW, NONLINEARITY, SPACE-TIME...

The evolution of weak disturbances in inert binary mixtures is determined for the one-dimensional piston problem. The interaction of the dissipative and nonlinear mechanisms is described by Burgers' equation. The binary mixture diffusion mechanisms enter as an additive term in an effective diffusivity. Results for the impulsive motion of a piston moving into an ambient medium and the sinusoidally oscillating piston are used to illustrate the results and elucidate the incorrect behavior...

Topics: NASA Technical Reports Server (NTRS), BINARY MIXTURES, PERTURBATION THEORY, PISTONS, BURGER...

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205

May 31, 2011
05/11

by
deGroh, H. C.; Li, K.; Li, B. Q

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A 2-D finite element model is presented for the melt growth of single crystals in a microgravity environment with a superimposed DC magnetic field. The model is developed based on the deforming finite element methodology and is capable of predicting the phenomena of the steady and transient convective flows, heat transfer, solute distribution, and solid-liquid interface morphology associated with the melt growth of single crystals in microgravity with and without an applied magnetic field....

Topics: COLLOCATION, FUNCTIONS (MATHEMATICS), RUNGE-KUTTA METHOD, PARTIAL DIFFERENTIAL EQUATIONS,...

A cubic spline approximation is presented which is suited for many fluid-mechanics problems. This procedure provides a high degree of accuracy, even with a nonuniform mesh, and leads to an accurate treatment of derivative boundary conditions. The truncation errors and stability limitations of several implicit and explicit integration schemes are presented. For two-dimensional flows, a spline-alternating-direction-implicit method is evaluated. The spline procedure is assessed, and results are...

Topics: NASA Technical Reports Server (NTRS), CAVITATION FLOW, FLUID MECHANICS, SPLINE FUNCTIONS, BURGER...

The previously obtained second-order-accurate partial implicitization numerical technique used in the solution of fluid dynamic problems was modified with little complication to achieve fourth-order accuracy. The Von Neumann stability analysis demonstrated the unconditional linear stability of the technique. The order of the truncation error was deduced from the Taylor series expansions of the linearized difference equations and was verified by numerical solutions to Burger's equation. For...

Topics: NASA Technical Reports Server (NTRS), BURGER EQUATION, DIFFERENCE EQUATIONS, FLUID DYNAMICS,...

When one considers the effect in the physical space, Daubechies-based wavelet methods are equivalent to finite difference methods with grid refinement in regions of the domain where small scale structure exists. Adding a wavelet basis function at a given scale and location where one has a correspondingly large wavelet coefficient is, essentially, equivalent to adding a grid point, or two, at the same location and at a grid density which corresponds to the wavelet scale. This paper introduces a...

Topics: NASA Technical Reports Server (NTRS), COMPUTATIONAL GRIDS, CONSERVATION LAWS, FINITE DIFFERENCE...

Wavelet bases are used to generate spaces of approximation for the resolution of bidimensional elliptic and parabolic problems. Under some specific hypotheses relating the properties of the wavelets to the order of the involved operators, it is shown that an approximate solution can be built. This approximation is then stable and converges towards the exact solution. It is designed such that fast algorithms involving biorthogonal multi resolution analyses can be used to resolve the...

Topics: NASA Technical Reports Server (NTRS), WAVELET ANALYSIS, ALGORITHMS, BURGER EQUATION, OPERATORS...

The upwind differencing first order schemes of Godunov, Engquist-Osher and Roe are discussed on the basis of the inviscid Burgers equations. The differences between the schemes are interpreted as differences between the approximate Riemann solutions on which their numerical flux functions are based. Special attention is given to the proper formulation of these schemes when a source term is present. Second order two step schemes, based on the numerical flux functions of the first order schemes...

Topics: NASA Technical Reports Server (NTRS), BURGER EQUATION, DIFFERENCES, INTEGRAL EQUATIONS, INVISCID...

Topics covered include: Low-dispersion scheme for nonlinear acoustic waves in nonuniform flow; Computation of acoustic scattering by a low-dispersion scheme; Algorithmic extension of low-dispersion scheme and modeling effects for acoustic wave simulation; The accuracy of shock capturing in two spatial dimensions; Using high-order methods on lower-order geometries; and Computational considerations for the simulation of discontinuous flows.

Topics: NASA Technical Reports Server (NTRS), AEROACOUSTICS, ACOUSTIC SCATTERING, SOUND WAVES, WAVE...

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of...

Topics: NASA Technical Reports Server (NTRS), BURGER EQUATION, COMPUTATIONAL GRIDS, CONDUCTIVE HEAT...

Fourth order difference approximations of initial-boundary value problems for hyperbolic partial differential equations are considered. We use the method of lines approach with both explicit and compact implicit difference operators in space. The explicit operator satisfies an energy estimate leading to strict stability. For the implicit operator we develop boundary conditions and give a complete proof of strong stability using the Laplace transform technique. We also present numerical...

Topics: NASA Technical Reports Server (NTRS), BOUNDARY CONDITIONS, BOUNDARY VALUE PROBLEMS, BURGER...

General interface coupling conditions are presented for multi-domain collocation methods, which satisfy the summation-by-parts (SBP) spatial discretization convention. The combined interior/interface operators are proven to be L2 stable, pointwise stable, and conservative, while maintaining the underlying accuracy of the interior SBP operator. The new interface conditions resemble (and were motivated by) those used in the discontinuous Galerkin finite element community, and maintain many of the...

Topics: NASA Technical Reports Server (NTRS), FINITE DIFFERENCE THEORY, SIMULATION, DISCRETIZATION...

This paper presents a novel approach to design of the supersonic aircraft outer mold line (OML) by optimizing the A-weighted loudness of sonic boom signature predicted on the ground. The optimization process uses the sensitivity information obtained by coupling the discrete adjoint formulations for the augmented Burgers Equation and Computational Fluid Dynamics (CFD) equations. This coupled formulation links the loudness of the ground boom signature to the aircraft geometry thus allowing...

Topics: NASA Technical Reports Server (NTRS), SONIC BOOMS, SUPERSONIC AIRCRAFT, AIRCRAFT DESIGN, SHAPE...

For Courant numbers larger than one and cell Reynolds numbers larger than two, oscillations and in some cases instabilities are typically found with implicit numerical solutions of the fluid dynamics equations. This behavior has sometimes been associated with the loss of diagonal dominance of the coefficient matrix. It is shown that these problems can be related to the choice of the spatial differences, with the resulting instability related to aliasing or nonlinear interaction. Appropriate...

Topics: NASA Technical Reports Server (NTRS), APPLICATIONS OF MATHEMATICS, FLUID DYNAMICS, SMOOTHING,...

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

Topics: NASA Technical Reports Server (NTRS), CAUCHY PROBLEM, CONSERVATION LAWS, FINITE DIFFERENCE THEORY,...

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360

Jul 26, 2010
07/10

by
Higginbotham, Scott A.; Davis, J. Bradle

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A debris/ice/TPS assessment and photographic analysis was conducted for the Space Shuttle Mission STS-38. Debris inspection of the flight elements and launch pad were performed before and after launch. Ice/frost conditions on the external tank were assessed by the use of computer programs, nomographs, and infrared scanner data during cryogenic loading of the vehicle followed by on-pad visual inspection. High speed photography was analyzed after launch to identify ice/debris sources and evaluate...

Topics: BOUNDARY CONDITIONS, VISCOSITY, BURGER EQUATION, COEFFICIENTS, DEGREES OF FREEDOM, LINEAR...

The solution of partial differential equations (PDEs) with Walsh functions offers new opportunities to simulate many challenging problems in mathematical physics. The approach was developed to better simulate hypersonic flows with shocks on unstructured grids. It is unique in that integrals and derivatives are computed using simple matrix multiplication of series representations of functions without the need for divided differences. The product of any two Walsh functions is another Walsh...

Topics: NASA Technical Reports Server (NTRS), WALSH FUNCTION, USER MANUALS (COMPUTER PROGRAMS), PARTIAL...

Richards' equation, which models the flow of liquid through unsaturated porous media, is highly nonlinear and difficult to solve. Step gradients in the field variables require the use of fine grids and small time step sizes. The numerical instabilities caused by the nonlinearities often require the use of iterative methods such as Picard or Newton interation. These difficulties result in large CPU requirements in solving Richards equation. With this in mind, adaptive and multigrid methods are...

Topics: NASA Technical Reports Server (NTRS), ALGORITHMS, COMPUTATIONAL FLUID DYNAMICS, COMPUTATIONAL...

A procedure is presented for utilizing a bi-grid stability analysis as a practical tool for predicting multigrid performance in a range of numerical methods for solving Euler and Navier-Stokes equations. Model problems based on the convection, diffusion and Burger's equation are used to illustrate the superiority of the bi-grid analysis as a predictive tool for multigrid performance in comparison to the smoothing factor derived from conventional von Neumann analysis. For the Euler equations,...

Topics: NASA Technical Reports Server (NTRS), COMPUTATIONAL FLUID DYNAMICS, COMPUTATIONAL GRIDS,...

The well-known analytical solution of Burgers' equation is extended to curvilinear coordinate systems in three dimensions by a method that is much simpler and more suitable to practical applications than that previously used. The results obtained are applied to incompressible flow with cylindrical symmetry, and also to the decay of an initially linearly increasing wind.

Topics: NASA Technical Reports Server (NTRS), BURGER EQUATION, ANALYSIS (MATHEMATICS), SPHERICAL...

Consider the initial boundary value problem for Burgers' equation. It is shown that its solutions converge, in time, to a unique steady state. The speed of the convergence depends on the boundary conditions and can be exponentially slow. Methods to speed up the rate of convergence are also discussed.

Topics: NASA Technical Reports Server (NTRS), BOUNDARY VALUE PROBLEMS, BURGER EQUATION, CONVERGENCE,...

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...

Topics: NASA Technical Reports Server (NTRS), AEROACOUSTICS, SOUND PROPAGATION, NONLINEARITY, AEROSPACE...

The compact form of the discontinuous Galerkin method allows for a detailed local analysis of the method in the neighborhood of the shock for a non-linear model problem. Insight gained from the analysis leads to new flux formulas that are stable and that preserve the compactness of the method. Although developed for a model equation, the flux formulas are applicable to systems such as the Euler equations. This article presents the analysis for methods with a degree up to 5. The analysis is...

Topics: NASA Technical Reports Server (NTRS), SHOCK, BURGER EQUATION, NONLINEARITY, GALERKIN METHOD,...

Research on high intensity (finite amplitude) acoustic waves shows that nonlinear distortion effects generally result in a shift of energy to higher frequencies. The higher intensities associated with supersonic jets would therefore indicate that high frequency enhancement of the spectrum should occur, resulting in the differences observed between subsonic and supersonic jets. A 10,000 acoustic watt source installed in an anechoic chamber generates sound levels such that acoustic shocks are...

Topics: NASA Technical Reports Server (NTRS), FAR FIELDS, JET AIRCRAFT NOISE, NOISE PROPAGATION, SUPERSONIC...

The spectrum, energy transfer, and spectral interactions in steady Burgers turbulence are studied using numerically generated data. The velocity field is initially random and the turbulence is maintained steady by forcing the amplitude of a band of low wavenumbers to be invariant in time, while permitting the phase to change as dictated by the equation. The spectrum, as expected, is very different from that of Navier-Stokes turbulence. It is demonstrated that the far range of the spectrum...

Topics: NASA Technical Reports Server (NTRS), BURGER EQUATION, ENERGY TRANSFER, INTERACTIONAL AERODYNAMICS,...

This paper presents an approach to shape an aircraft to equivalent area based objectives using the discrete adjoint approach. Equivalent areas can be obtained either using reversed augmented Burgers equation or direct conversion of off-body pressures into equivalent area. Formal coupling with CFD allows computation of sensitivities of equivalent area objectives with respect to aircraft shape parameters. The exactness of the adjoint sensitivities is verified against derivatives obtained using...

Topics: NASA Technical Reports Server (NTRS), AIRCRAFT DESIGN, BURGER EQUATION, COMPUTATIONAL FLUID...

We present a two-dimensional, well-balanced, central-upwind scheme for approximating solutions of the shallow water equations in the presence of a stationary bottom topography on triangular meshes. Our starting point is the recent central scheme of Kurganov and Petrova (KP) for approximating solutions of conservation laws on triangular meshes. In order to extend this scheme from systems of conservation laws to systems of balance laws one has to find an appropriate discretization of the source...

Topics: NASA Technical Reports Server (NTRS), UNSTRUCTURED GRIDS (MATHEMATICS), SHALLOW WATER, TOPOGRAPHY,...

An adaptive spectral method was developed for the efficient solution of time dependent partial differential equations. Adaptive mesh strategies that include resolution refinement and coarsening by three different methods are illustrated on solutions to the 1-D viscous Burger equation and the 2-D Navier-Stokes equations for driven flow in a cavity. Sharp gradients, singularities, and regions of poor resolution are resolved optimally as they develop in time using error estimators which indicate...

Topics: NASA Technical Reports Server (NTRS), ADAPTIVE CONTROL, CAVITY FLOW, COMPUTATIONAL FLUID DYNAMICS,...

Semi-analytic reconstruction uses the analytic solution to a second-order, steady, ordinary differential equation (ODE) to simultaneously evaluate the convective and diffusive flux at all interfaces of a finite volume formulation. The second-order ODE is itself a linearized approximation to the governing first- and second- order partial differential equation conservation laws. Thus, semi-analytic reconstruction defines a family of formulations for finite volume interface fluxes using analytic...

Topics: NASA Technical Reports Server (NTRS), FINITE VOLUME METHOD, DIFFERENTIAL EQUATIONS, ANALYSIS...