Search NASA⌕ Search

SEARCH · Search NASA

Results for “upwind schemes”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Application of direct solvers to unstructured meshes for the Euler and Navier-Stokes equations using upwind schemes

The application of Newton iteration to inviscid and viscous airfoil calculations on unstructured meshes is examined. A cell-centered finite volume scheme is employed on an unstructured mesh consisting of triangles. Roe's flux difference splitting scheme is used to compute the inviscid fluxes. Higher order accuracy is achieved by an interpolation procedure that makes use of auxiliary gradients. The efficient solution of the sparse linear system of equations which arises upon linearization in time is addressed. Results are presented for inviscid and viscous test cases. The complications which arise due to the introduction of nonlinear limiters are addressed.

Venkatakrishnan, V.↗
NASA NTRS1989

Computation of turbulent flows on a CAST 10 wing using an upwind scheme

Two and three dimensional turbulent calculations around RAE2822, CAST 10 airfoils and a wing side-wall configuration are presented. A finite volume, cell-center method based on flux difference splitting schemes is used to solve the steady state thin-layer Navier-Stokes equations. Comparisons between the performances of different Riemann solvers and reconstruction schemes are also presented. The influence of a side-wall on the symmetry plane of a cylindrical CAST 10 wing is found to be highly sensitive to the turbulence modeling in the vicinity of the wing side-wall juncture.

Marx, Yves P.↗
NASA NTRS1990

Accuracy of upwind schemes applied to the Navier-Stokes equations

A systematic comparison was carried out of the different forms of the van Leer et al. (1987) flux-vector splitting scheme (FVSS) for solving the Navier-Stokes equations with Roe's (1981) implicit flux-difference splitting scheme (FDSS) as applied to a simple viscous configuration. Particular attention is given to the effects of spacial accuracy, grid resolution, and grid stretching on the accuracy of the resulting flow field. It was found that, on coarse highly stretched grids, the FDSS produces more accurate results than the FVSS.

Von Lavante, E.↗
NASA NTRS1994

A genuinely multidimensional upwind scheme and efficient multigrid solver for the compressible Euler equations

We present a new approach towards the construction of a genuinely multidimensional high-resolution scheme for computing steady-state solutions of the Euler equations of gas dynamics. The unique advantage of this approach is that the Gauss-Seidel relaxation is stable when applied directly to the high-resolution discrete equations, thus allowing us to construct a very efficient and simple multigrid steady-state solver. This is the only high-resolution scheme known to us that has this property. The two-dimensional scheme is presented in detail. It is formulated on triangular (structured and unstructured) meshes and can be interpreted as a genuinely two-dimensional extension of the Roe scheme. The quality of the solutions obtained using this scheme and the performance of the multigrid algorithm are illustrated by the numerical experiments. Construction of the three dimensional scheme is outlined briefly as well.

Sidilkover, David↗
NASA NTRS1994

Application of a Third Order Upwind Scheme to Viscous Flow over Clean and Iced Wings

A 3-D compressible Navier-Stokes solver has been developed and applied to 3-D viscous flow over clean and iced wings. This method uses a third order accurate finite volume scheme with flux difference splitting to model the inviscid fluxes, and second order accurate symmetric differences to model the viscous terms. The effects of turbulence are modeled using a Kappa-epsilon model. In the vicinity of the sold walls the kappa and epsilon values are modeled using Gorski's algebraic model. Sampling results are presented for surface pressure distributions, for untapered swept clean and iced wings made of NACA 0012 airfoil sections. The leading edge of these sections is modified using a simulated ice shape. Comparisons with experimental data are given.

Bangalore, A.↗
NASA NTRS2010

Multi-Fluid Block-Adaptive-Tree Solar Wind Roe-Type Upwind Scheme: Magnetospheric Composition and Dynamics During Geomagnetic Storms, Initial Results

The magnetosphere contains a significant amount of ionospheric O{+}, particularly during geomagnetically active times. The presence of ionospheric plasma in the magnetosphere has a notable impact on magnetospheric composition and processes. We present a new multifluid MHD version of the BATS-R-US model of the magnetosphere to track the fate and consequences of ionospheric outflow. The multi-fluid MHD equations are presented as are the novel techniques for overcoming the formidable challenges associated with solving them. Our new model is then applied to the May 4, 1998 and March 31, 2001 geomagnetic storms. The results are juxtaposed with traditional single- fluid MHD and multispecies MHD simulations from a previous study, thereby allowing us to assess the benefits of using a more complex model with additional physics. We find that our multi-fluid MHD model (with outflow) gives comparable results to the multi-species MHD model (with outflow), including a more strongly negative Dst, reduced CPCP, and a drastically improved magnetic field at geosynchronous orbit, as compared to single-fluid MHD with no outflow. Significant differences in composition and magnetic field are found between the multi-species and multi-fluid approach further away from the Earth. We further demonstrate the ability to explore pressure and bulk velocity differences between H{+} and O(+}, which is not possible when utilizing the other techniques considered.

Gkocer, A.↗
NASA NTRS1990

Numerical solution of 3D Navier-Stokes equations with upwind implicit schemes

An upwind MUSCL type implicit scheme for the three-dimensional Navier-Stokes equations is presented. Comparison between different approximate Riemann solvers (Roe and Osher) are performed and the influence of the reconstructions schemes on the accuracy of the solution as well as on the convergence of the method is studied. A new limiter is introduced in order to remove the problems usually associated with non-linear upwind schemes. The implementation of a diagonal upwind implicit operator for the three-dimensional Navier-Stokes equations is also discussed. Finally the turbulence modeling is assessed. Good prediction of separated flows are demonstrated if a non-equilibrium turbulence model is used.

Marx, Yves P.↗
NASA NTRS1985

On symmetric and upwind TVD schemes

A class of explicit and implicit total variation diminishing (TVD) schemes for the compressible Euler and Navier-Stokes equations was developed. They do not generate spurious oscillations across shocks and contact discontinuities. In general, shocks can be captured within 1 to 2 grid points. For the inviscid case, these schemes are divided into upwind TVD schemes and symmetric (nonupwind) TVD schemes. The upwind TVD scheme is based on the second-order TVD scheme. The symmetric TVD scheme is a generalization of Roe's and Davis' TVD Lax-Wendroff scheme. The performance of these schemes on some viscous and inviscid airfoil steady-state calculations is investigated. The symmetric and upwind TVD schemes are compared.

Yee, H. C.↗
NASA NTRS1986

On symmetric and upwind TVD schemes

The performance of the upwind and symmetric total variation diminishing (TVD) schemes in viscous and inviscid airfoil steady-state calculations is considered, and the extension of the implicit second-order-accurate TVD scheme for hyperbolic systems of conservative laws in curvilinear coordinates is discussed. For two-dimensional steady-state applications, schemes are implemented in a conservative noniterative alternating direction implicit form, and results illustrate that the algorithm produces a fairly good solution for an RAE2822 airfoil calculation. The study demonstrates that the symmetric TVD scheme is as accurate as the upwind TVD scheme, while requiring less computational effort than it.

Yee, H. C.↗
NASA NTRS1985

Numerical solution of the two-dimensional Euler equations by second-order upwind difference schemes

Two time-level, five-point explicit and implicit upwind difference schemes based on the characteristic flux difference splitting concept have been developed for the two-dimensional Euler equations. The method is conservative, second-order accurate in time and space, and general coordinate systems are used to treat complex geometries. Nonlinear flux limiters are employed to yield oscillation free sharp shock profiles. Upstream interpolation is used to yield a class of higher-order upwind schemes which closely mimic the locally one-dimensional method of characteristics (with fixed time intervals) through operator splitting. Numerical results have been obtained for a plane shock reflection and for flow over a circular arc in a channel. Characteristics of upwind TVD schemes, as applied to two-dimensional flows with embedded shocks are discussed.

Yang, J. Y.↗
NASA NTRS1992

Investigation of upwind, multigrid, multiblock numerical schemes for three dimensional flows. Volume 1: Runge-Kutta methods for a thin layer Navier-Stokes solver

A state-of-the-art computer code has been developed that incorporates a modified Runge-Kutta time integration scheme, upwind numerical techniques, multigrid acceleration, and multi-block capabilities (RUMM). A three-dimensional thin-layer formulation of the Navier-Stokes equations is employed. For turbulent flow cases, the Baldwin-Lomax algebraic turbulence model is used. Two different upwind techniques are available: van Leer's flux-vector splitting and Roe's flux-difference splitting. Full approximation multi-grid plus implicit residual and corrector smoothing were implemented to enhance the rate of convergence. Multi-block capabilities were developed to provide geometric flexibility. This feature allows the developed computer code to accommodate any grid topology or grid configuration with multiple topologies. The results shown in this dissertation were chosen to validate the computer code and display its geometric flexibility, which is provided by the multi-block structure.

Cannizzaro, Frank E.↗
NASA NTRS2013

Studies of Inviscid Flux Schemes for Acoustics and Turbulence Problems

Five different central difference schemes, based on a conservative differencing form of the Kennedy and Gruber skew-symmetric scheme, were compared with six different upwind schemes based on primitive variable reconstruction and the Roe flux. These eleven schemes were tested on a one-dimensional acoustic standing wave problem, the Taylor-Green vortex problem and a turbulent channel flow problem. The central schemes were generally very accurate and stable, provided the grid stretching rate was kept below 10%. As near-DNS grid resolutions, the results were comparable to reference DNS calculations. At coarser grid resolutions, the need for an LES SGS model became apparent. There was a noticeable improvement moving from CD-2 to CD-4, and higher-order schemes appear to yield clear benefits on coarser grids. The UB-7 and CU-5 upwind schemes also performed very well at near-DNS grid resolutions. The UB-5 upwind scheme does not do as well, but does appear to be suitable for well-resolved DNS. The UF-2 and UB-3 upwind schemes, which have significant dissipation over a wide spectral range, appear to be poorly suited for DNS or LES.

Morris, Chris↗
NASA NTRS1983

A rotationally biased upwind difference scheme for the Euler equations

The upwind difference schemes of Godunov, Osher, Roe and van Leer are able to resolve one dimensional steady shocks for the Euler equations within one or two mesh intervals. Unfortunately, this resolution is lost in two dimensions when the shock crosses the computing grid at an oblique angle. To correct this problem, a numerical scheme was developed which automatically locates the angle at which a shock might be expected to cross the computing grid and then constructs separate finite difference formulas for the flux components normal and tangential to this direction. Numerical results which illustrate the ability of this method to resolve steady oblique shocks are presented.

Davis, S. F.↗
NASA NTRS1984

A rotationally biased upwind difference scheme for the Euler equations

The upwind difference schemes of Godunov, Osher, Roe and van Leer are able to resolve one dimensional steady shocks for the Euler equations within one or two mesh intervals. Unfortunately, this resolution is lost in two dimensions when the shock crosses the computing grid at an oblique angle. To correct this problem, a numerical scheme was developed which automatically locates the angle at which a shock might be expected to cross the computing grid and then constructs separate finite difference formulas for the flux components normal and tangential to this direction. Numerical results which illustrate the ability of this method to resolve steady oblique shocks are presented.

Davis, S. F.↗
NASA NTRS1978

Steady state spurious errors in shock-capturing numerical schemes

The behavior of the steady state spurious error modes of the MacCormack scheme and the upwind scheme of Warming and Beam was obtained from a linearized difference equation for the steady state error. It was shown that the spurious errors can exist either as an eigensolution of the homogeneous part of this difference equation or because of excitation from large discretization errors near oblique shocks. It was found that the upwind scheme does not permit spurious oscillations on the upstream side of shocks. Examples are given for the inviscid Burgers' equation and for one and two dimensional gasdynamic flows.

Karlsen, L. K.↗