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At least 613 records · Page 34
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Well-balanced treatment of gravity in astrophysical fluid dynamics simulations at low Mach numbers

We report accurate simulations of flows in stellar interiors are crucial to improving our understanding of stellar structure and evolution. Because the typically slow flows are merely tiny perturbations on top of a close balance between gravity and the pressure gradient, such simulations place heavy demands on numerical hydrodynamics schemes. We demonstrate how discretization errors on grids of reasonable size can lead to spurious flows orders of magnitude faster than the physical flow. Well-balanced numerical schemes can deal with this problem. Three such schemes were applied in the implicit, finite-volume SEVEN-LEAGUE HYDRO code in combination with a low-Mach-number numerical flux function. We compare how the schemes perform in four numerical experiments addressing some of the challenges imposed by typical problems in stellar hydrodynamics. We find that the α-β and deviation well-balancing methods can accurately maintain hydrostatic solutions provided that gravitational potential energy is included in the total energy balance. They accurately conserve minuscule entropy fluctuations advected in an isentropic stratification, which enables the methods to reproduce the expected scaling of convective flow speed with the heating rate. The deviation method also substantially increases accuracy of maintaining stationary orbital motions in a Keplerian disk on long timescales. The Cargo–LeRoux method fares substantially worse in our tests, although its simplicity may still offer some merits in certain situations. Overall, we find the well-balanced treatment of gravity in combination with low Mach number flux functions essential to reproducing correct physical solutions to challenging stellar slow-flow problems on affordable collocated grids.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1987

Reynolds stress closure in jet flows using wave models

Numerical methods were developed that will form the computational part of the turbulence closure scheme. A wave model was developed for the two-dimensional shear layer. This configuration is being used as a test case for the closure schemes. Various numerical schemes were examined to give efficient solutions of the Rayleigh equation for this geometry. These include both spectral and finite difference methods. Secondly, numerical methods are under development to solve the non-separable Rayleigh equation. This solution is required for the closure scheme in more complex geometries. A model problem was used to assist in the algorithm development. Two-dimensional spectral methods and a hybrid spectral/finite difference technique were developed. An analytic solution of the Rayleigh equation for a basic elliptic flow was obtained. This will be used to verify the stability codes developed for arbitrary geometries. Other numerical methods for solving the Rayleigh equation based on the boundary element technique were also examined. These solutions are forming the basis of a model for the shock structure in jets of arbitrary geometry.

Morris, P. J.↗
NASA NTRS1988

Reynold stress closure in jet flows using wave models

Research program efforts have continued to concentrate on the development of the numerical methods that will form the computational part of the turbulence closure scheme. Studies have continued on the wave model for the two dimensional shear layer. This configuration is being used as a test case for the closure schemes. Several numerical schemes for the solution of the non-separable Rayleigh equation were developed. This solution is required for the closure scheme in more complex geometries. The most efficient method found is a Hybrid scheme that combines both pseudospectral and finite difference techniques. In addition, conformal transformation techniques were developed to transform the arbitrary geometry of the jet to a simple computational domain. The study of the shock structure in arbitrary geometry jets and multiple jets. These developments are described briefly.

Morris, P. J.↗
NASA NTRS2004

Comparisons of Observations with Results from 3D Simulations and Implications for Predictions of Ozone Recovery

Although chemistry and transport models (CTMs) include the same basic elements (photo- chemical mechanism and solver, photolysis scheme, meteorological fields, numerical transport scheme), they produce different results for the future recovery of stratospheric ozone as chlorofluorcarbons decrease. Three simulations will be contrasted: the Global Modeling Initiative (GMI) CTM driven by a single year\'s winds from a general circulation model; the GMI CTM driven by a single year\'s winds from a data assimilation system; the NASA GSFC CTM driven by a winds from a multi-year GCM simulation. CTM results for ozone and other constituents will be compared with each other and with observations from ground-based and satellite platforms to address the following: Does the simulated ozone tendency and its latitude, altitude and seasonal dependence match that derived from observations? Does the balance from analysis of observations? Does the balance among photochemical processes match that expected from observations? Can the differences in prediction for ozone recovery be anticipated from these comparisons?

Douglass, Anne R.↗
NASA NTRS2020

An Overview of the Null-Field Method. II: Convergence and Numerical Stability

In this paper we provide an analysis of the convergence and numerical stability of the null-field method with discrete sources. We show that (i) if the null-field scheme is numerically stable then we can decide whether or not convergence can be achieved; (ii) if the null-field scheme is numerically unstable then we cannot draw any conclusion about the convergence issue; and (iii) the numerical stability is closely related to the property of a tangential system of radiating discrete sources to form a Riesz basis. Our numerical analysis indicates that for prolate spheroids and localized vector spherical wave functions, the null-field scheme is numerically unstable (this system of vector functions does not form a Riesz basis), while for distributed vector spherical wave functions, the numerical instability is not so pronounced (this system of discrete sources almost possesses the property of being a Riesz basis). We also describe an analytical method for computing the surface integrals in the framework of the conventional null-field method with localized vector spherical wave functions which increases the stability of the numerical scheme.

Null-field method↗
NASA NTRS1988

A comparison of ENO and TVD schemes

The numerical performance of a second-order upwind-based TVD scheme is compared with that of a uniform second-order ENO scheme on shock capturing. The cases considered include flows with Mach numbers of 2.9, 5.0, and 10.0. For cases with Mach numbers of 5.0 and 10.0, the computed ENO results are inferior to the corresponding TVD results.

Chang, Shih-Hung↗
NASA NTRS1987

Supercomputing of supersonic flows using upwind relaxation and MacCormack schemes

The performance of two numerical solution schemes, (1) an implicit upwind relaxation with a finite-volume discretization (Thomas and Walters, 1985) and (2) an explicit-implicit MacCormack (1981) scheme with a finite-difference discretization, is compared in two-dimensional simulations of supersonic flow past a flat plate with leading edge, a rearward-facing step, a 10-deg compression corner, a NACA 0012 airfoil at high angle of attack, and a cavity. The algebraic turbulence model, the solution methods, and the boundary conditions and SIMD coding are explained, and the results are presented in tables and graphs and characterized with reference to published experimental data. Scheme (1) is found to converge more rapidly and to give more accurate results than (2) in a wide range of problem types.

Baysal, O.↗
NASA NTRS1990

Upwind Algorithm For Parabolized Navier-Stokes Equations

Supersonic flow about cone calculated accurately. Report presents theoretical basis of computer code solving parabolized Navier-Stokes equations of supersonic and hypersonic flow. For increased accuracy in resolution of details of strong aerodynamic shocks, code incorporates implicit, finite-volume, upwind numerical-integration scheme. Performs well in numerical simulations of flows around simple bodies.

Lawrence, Scott L.↗
NASA NTRS1978

Numerical method for boundary layers with blowing - The exponential box scheme

The paper describes a new numerical scheme based on exponential difference operator concepts combined with Keller's (1968) box scheme approach to produce a stable second-order accurate finite-difference scheme for convection-diffusion problems arising in boundary layer flows in the presence of massive injection through a porous surface. The technique is demonstrated by application to the self-similar boundary layer equations with massive blowing at the surface.

El-Mistikawy, T. M.↗
NASA NTRS1988

A numerical study of ENO and TVD schemes for shock capturing

The numerical performance of a second-order upwind-based total variation diminishing (TVD) scheme and that of a uniform second-order essentially non-oscillatory (ENO) scheme for shock capturing are compared. The TVD scheme used is a modified version of Liou, using the flux-difference splitting (FDS) of Roe and his superbee function as the limiter. The construction of the basic ENO scheme is based on Harten, Engquist, Osher, and Chakravarthy, and the 2-D extensions are obtained by using a Strang-type of fractional-step time-splitting method. Numerical results presented include both steady and unsteady, 1-D and 2-D calculations. All the chosen test problems have exact solutions so that numerical performance can be measured by comparing the computer results to them. For 1-D calculations, the standard shock-tube problems of Sod and Lax are chosen. A very strong shock-tube problem, with the initial density ratio of 400 to 1 and pressure ratio of 500 to 1, is also used to study the behavior of the two schemes. For 2-D calculations, the shock wave reflection problems are adopted for testing. The cases presented in this report include flows with Mach numbers of 2.9, 5.0, and 10.0.

Chang, Shih-Hung↗
NASA NTRS1989

Two-dimensional Euler computations on a triangular mesh using an upwind, finite-volume scheme

A numerical procedure was developed for the finite-volume solution of the Euler equations on unstructured triangular meshes based on a flux-difference split upwind method. Techniques for implementing Roe's (1985) approximate Reimann solver together with the preprocessing MUSCL differencing on unstructured grids are presented. Applications and comparisons with structured grid problems are carried out for a supersonic shock reflection problem, the supersonic flow over a blunt body, the transonic flow over NACA 0012 and RAE 2822 airfoils, and the flow about a double element Karman-Trefftz airfoil.

Whitaker, D. L.↗
DOE OSTI2020

Dimension-free path-integral molecular dynamics without preconditioning

Convergence with respect to imaginary-time discretization (i.e., the number of ring-polymer beads) is an essential part of any path-integral-based molecular dynamics (MD) calculation. However, an unfortunate property of existing non-preconditioned numerical integration schemes for path-integral molecular dynamics—including essentially all existing ring-polymer molecular dynamics (RPMD) and thermostatted RPMD (T-RPMD) methods—is that for a given MD time step, the overlap between the exact ring-polymer Boltzmann–Gibbs distribution and that sampled using MD becomes zero in the infinite-bead limit. This has clear implications for hybrid Metropolis Monte Carlo/MD sampling schemes, and it also causes the divergence with bead number of the primitive path-integral kinetic-energy expectation value when using standard RPMD or T-RPMD. We show that these and other problems can be avoided through the introduction of “dimension-free” numerical integration schemes for which the sampled ring-polymer position distribution has non-zero overlap with the exact distribution in the infinite-bead limit for the case of a harmonic potential. Most notably, we introduce the BCOCB integration scheme, which achieves dimension freedom via a particular symmetric splitting of the integration time step and a novel implementation of the Cayley modification [R. Korol et al., J. Chem. Phys. 151, 124103 (2019)] for the free ring-polymer half-steps. More generally, we show that dimension freedom can be achieved via mollification of the forces from the external physical potential. The dimension-free path-integral numerical integration schemes introduced here yield finite error bounds for a given MD time step, even as the number of beads is taken to infinity; these conclusions are proven for the case of a harmonic potential and borne out numerically for anharmonic systems that include liquid water. The numerical results for BCOCB are particularly striking, allowing for nearly three-fold increases in the stable time step for liquid water with respect to the Bussi–Parrinello (OBABO) and Leimkuhler (BAOAB) integrators, while introducing negligible errors in the calculated statistical properties and absorption spectrum. Importantly, the dimension-free, non-preconditioned integration schemes introduced here preserve ergodicity and global second-order accuracy, and they remain simple, black-box methods that avoid additional computational costs, tunable parameters, or system-specific implementations.

Korol, Roman (ORCID:0000000193076351)↗
NASA NTRS1983

Numerical viscosity and the entropy condition for conservative difference schemes

Consider a scalar, nonlinear conservative difference scheme satisfying the entropy condition. It is shown that difference schemes containing more numerical viscosity will necessarily converge to the unique, physically relevant weak solution of the approximated conservation equation. In particular, entropy satisfying convergence follows for E schemes - those containing more numerical viscosity than Godunov's scheme.

Tadmor, E.↗
NASA NTRS1984

Numerical viscosity and the entropy condition for conservative difference schemes

Consider a scalar, nonlinear conservative difference scheme satisfying the entropy condition. It is shown that difference schemes containing more numerical viscosity will necessarily converge to the unique, physically relevant weak solution of the approximated conservation equation. In particular, entropy satisfying convergence follows for E schemes - those containing more numerical viscosity than Godunov's scheme.

Tadmor, E.↗
NASA NTRS1987

Numerical simulation by TVD schemes of complex shock reflections from airfoils at high angle of attack

The shock-capturing capability of total variation diminishing (TVD) schemes is demonstrated for a more realistic complex shock-diffraction problem for which the experimental data are available. Second-order explicit upwind and symmetric TVD schemes are used to solve the time-dependent Euler equations of gas dynamics for the interaction of a blast wave with an airfoil at high angle-of-attack. The test cases considered are a time-dependent moving curved-shock wave and a contant moving planar-shock wave impinging at an angle-of-attack 30 deg on a NACA 0018 airfoil. Good agreement is obtained between isopycnic contours computed by the TVD schemes and those from experimental interferograms. No drastic difference in flow-field structure is found between the curved- and planar-shock wave cases, except for a difference in density level near the lower surface of the airfoil. Computation for cases with higher shock Mach numbers is also possible. Numerical experiments show that the symmetric TVD scheme is less sensitive to the boundary conditions treatment than the upwind scheme.

Moon, Young J.↗
NASA NTRS1980

Evaluation of several schemes for classification of remotely sensed data

Various numerical analysis schemes for the classification of remotely sensed data are evaluated with respect to their capabilities for crop identification. A per point Gaussian maximum likelihood classifier, per point sum-of-normal-densities classifier, per point linear classifier, per point Gaussian maximum likelihood decision tree classifier and a texture-sensitive per field Gaussian maximum likelihood classifier were applied to seven sets of Landsat MSS data on several crop types and regions. The results of the implementation of the classifiers indicate that, given a representative set of training statistics, the choice of classification algorithm of the differentiation of corn and soybeans from one another and from other crop types made relatively little difference in accuracy, whereas the use of a different training method affected the accuracy significantly. In addition, the linear classifier is found to be the easiest for the analyst to use and to cost least in computer time per classification.

Hixson, M.↗