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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Multitasking for flows about multiple body configurations using the chimera grid scheme

The multitasking of a finite-difference scheme using multiple overset meshes is described. In this chimera, or multiple overset mesh approach, a multiple body configuration is mapped using a major grid about the main component of the configuration, with minor overset meshes used to map each additional component. This type of code is well suited to multitasking. Both steady and unsteady two dimensional computations are run on parallel processors on a CRAY-X/MP 48, usually with one mesh per processor. Flow field results are compared with single processor results to demonstrate the feasibility of running multiple mesh codes on parallel processors and to show the increase in efficiency.

Dougherty, F. C.↗
NASA NTRS1989

Second-order accurate nonoscillatory schemes for scalar conservation laws

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

Huynh, Hung T.↗
NASA NTRS1989

Second-order accurate nonoscillatory schemes for scalar conservation laws

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

Huynh, Hung T.↗
NASA NTRS1997

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

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

Shu, Chi-Wang↗
DOE OSTI2021

High-Fidelity Simulations of Gravity Currents Using a High-Order Finite-Difference Spectral Vanishing Viscosity Approach

This numerical work investigates the potential of a high-order finite-difference spectral vanishing viscosity approach to simulate gravity currents at high Reynolds numbers. The method introduces targeted numerical dissipation at small scales through altering the discretisation of the second derivatives of the viscous terms in the incompressible Navier-Stokes equations to mimic the spectral vanishing viscosity (SVV) operator, originally designed for the regularisation of spectral element method (SEM) solutions of pure advection problems. Using a sixth-order accurate finite-difference scheme, the adoption of the SVV method is straightforward and comes with a negligible additional computational cost. In order to assess the ability of this high-order finite-difference spectral vanishing viscosity approach, we performed large-eddy simulations (LES) of a gravity current in a channelised lock-exchange set-up with our SVV model and with the well-known explicit static and dynamic Smagorinsky sub-grid scale (SGS) models. The obtained data are compared with a direct numerical simulation (DNS) based on more than 800 million mesh nodes, and with experimental measurements. A framework for the energy budget is introduced to investigate the behaviour of the gravity current. First, it is found that the DNS is in good agreement with the experimental data for the evolution of the front location and velocity field as well as for the stirring and mixing inside the gravity current. Secondly, the LES performed with less than 0.4% of the total number of mesh nodes compared to the DNS, can reproduce the main features of the gravity currents, with the SVV model yielding slightly more accurate results. It is also found that the dynamic Smagorinsky model performs better than its static version. For the present study, the static and dynamic Smagorinsky models are 1.8 and 2.5 times more expensive than the SVV model, because the latter does not require the calculation of explicit SGS terms in the Navier-Stokes equations nor spatial filtering operations.

direct numerical simulation↗
NASA NTRS1990

Full numerical simulation of coflowing, axisymmetric jet diffusion flames

The near field of a non-premixed flame in a low speed, coflowing axisymmetric jet is investigated numerically using full simulation. The time-dependent governing equations are solved by a second-order, explicit finite difference scheme and a single-step, finite rate model is used to represent the chemistry. Steady laminar flame results show the correct dependence of flame height on Peclet number and reaction zone thickness on Damkoehler number. Forced simulations reveal a large difference in the instantaneous structure of scalar dissipation fields between nonbuoyant and buoyant cases. In the former, the scalar dissipation marks intense reaction zones, supporting the flamelet concept; however, results suggest that flamelet modeling assumptions need to be reexamined. In the latter, this correspondence breaks down, suggesting that modifications to the flamelet modeling approach are needed in buoyant turbulent diffusion flames.

Mahalingam, S.↗
NASA NTRS1995

Analysis of developing laminar flows in circular pipes using a higher-order finite-difference technique

A higher-order finite-difference technique is developed to calculate the developing-flow field of steady incompressible laminar flows in the entrance regions of circular pipes. Navier-Stokes equations governing the motion of such a flow field are solved by using this new finite-difference scheme. This new technique can increase the accuracy of the finite-difference approximation, while also providing the option of using unevenly spaced clustered nodes for computation such that relatively fine grids can be adopted for regions with large velocity gradients. The velocity profile at the entrance of the pipe is assumed to be uniform for the computation. The velocity distribution and the surface pressure drop of the developing flow then are calculated and compared to existing experimental measurements reported in the literature. Computational results obtained are found to be in good agreement with existing experimental correlations and therefore, the reliability of the new technique has been successfully tested.

Gladden, Herbert J.↗
NASA NTRS1989

Constructing space difference schemes which satisfy a cell entropy inequality

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

Merriam, Marshal L.↗
NASA NTRS1972

Design of the UCLA general circulation model

An edited version is reported of notes distributed at the Summer Workshop on the UCLA General Circulation Model in June 1971. It presents the computational schemes of the UCLA model, along with the mathematical and physical principles on which these schemes are based. Included are the finite difference schemes for the governing fluid-dynamical equations, designed to maintain the important integral constraints and dispersion characteristics of the motion. Also given are the principles of parameterization of cumulus convection by an ensemble of identical clouds. A model of the ground hydrology, involving the liquid, ice and snow states of water, is included. A short summary is given of the scheme for computing solar and infrared radiation transfers through clear and cloudy air.

Arakawa, A.↗
NASA NTRS1989

A high-order Lagrangian-decoupling method for the incompressible Navier-Stokes equations

A high-order Lagrangian-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) Lagrangian variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference schemes for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.

Ho, Lee-Wing↗
NASA NTRS2006

An Accuracy Evaluation of Unstructured Node-Centred Finite Volume Methods

Node-centred edge-based finite volume approximations are very common in computational fluid dynamics since they are assumed to run on structured, unstructured and even on mixed grids. We analyse the accuracy properties of both first and second derivative approximations and conclude that these schemes can not be used on arbitrary grids as is often assumed. For the Euler equations first-order accuracy can be obtained if care is taken when constructing the grid. For the Navier-Stokes equations, the grid restrictions are so severe that these finite volume schemes have little advantage over structured finite difference schemes. Our theoretical results are verified through extensive computations.

Svard, Magnus↗
NASA NTRS1987

Navier-Stokes simulations of blade-vortex interaction using high-order accurate upwind schemes

Conventional, spatially second-order-accurate, finite-difference schemes are much too dissipative for calculations involving vortices that travel large distances (relative to some measure of the size of the vortex). This study presents a fifth-order-accurate upwind-biased scheme that preserves vortex structure for much longer times than existing second-order-accurate central and upwind difference schemes. Vortex calculations demonstrating this aspect of the fifth-order scheme are also presented. The method is then applied to the blade-vortex interaction problem. Results for strong interactions wherein the vortex impinges directly on the airfoil or a shock associated with the airfoil are presented. None of these calculations required any modeling of the shape, size, and trajectory of the interacting vortex.

Rai, Man Mohan↗
NASA NTRS1986

An implicit flux-difference splitting scheme for three-dimensional, incompressible Navier-Stokes solutions to leading edge vortex flows

A new, implicit finite-difference scheme designed to solve the conservative, flux-difference split Navier-Stokes equations is used to compute incompressible vortex flows around delta wings. The completely vectorizable hybrid algorithm is constructed in delta form for steady state solutions independent of the time-step sizes. The scheme combines approximate factorization in crossflow planes with a symmetric planar Gauss-Seidel relaxation in the remaining spatial direction. The governing equations are solved in curvilinear, body-fitted coordinates for treating complex geometries. The computed flow field results are compared with other theoretical and experimental data.

Hartwich, P.-M.↗
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 NTRS1977

An implicit factored scheme for the compressible Navier-Stokes equations

An implicit finite difference scheme is developed for the numerical solution of the compressible Navier-Stokes equations in conservation-law form. The algorithm is second-order-time accurate, noniterative, and spatially factored. In order to obtain an efficient factored algorithm, the spatial cross-derivatives are evaluated explicitly. However, the algorithm is unconditionally stable and, although a three-time-level scheme, requires only two-time-levels of data storage. The algorithm is constructed in a 'delta' form (i.e., increments of the conserved variables and fluxes) that provides a direct derivation of the scheme and leads to an efficient computational algorithm. In addition, the delta form has the advantageous property of a steady-state (if one exists) independent of the size of the time step. Numerical results are presented for a two-dimensional shock boundary-layer interaction problem.

Beam, R. M.↗
NASA NTRS1979

An energy and potential enstrophy conserving scheme for the shallow water equations

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

Arakawa, A.↗
NASA NTRS1988

Total Variation Diminishing (TVD) schemes of uniform accuracy

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

Hartwich, PETER-M.↗