SEARCH · Engineering Papers

Results for “conservative 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.

SourceResearch connectionFrom yearThrough year

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

At least 217 records · Page 12

All sources NASA NTRS DOE OSTI

NASA NTRS1992

Low-to-high altitude predictions of three-dimensional ablative reentry flowfields

A new coupled-chemistry PNS scheme has been developed to study 3D hypersonic reentry flows over sphere cones at small angles of attack. A new quasi-steady ablation model for Teflon was used to predict ablative reentry flow fields under laminar, transitional, and turbulent conditions. This solution scheme uses a new two-step solution scheme for solving the species conservation equations under low-altitude conditions. As an example, the scheme is used to study hypersonic flow over a 6-deg sphere-cone configuration at 50 and 125 kft conditions under zero and nonzero angle of attack conditions.

Bhutta, Bilal A.↗

NASA NTRS1972

A two-spacecraft test of a single spacecraft method of estimating shock normals

By assuming the validity of a subset of the Rankine-Hugoniot conservation relations for interplanetary (IP) shocks in an isotropic medium it has been demonstrated, in principle, that improved shock normals can be calculated by using a least-squares technique on combined magnetic field and plasma data from a single spacecraft. The scheme uses those six conservation relations not involving pressure and temperature. This paper deals with a test of the scheme by examining in detail a shock across which the magnetic field changed direction by a small amount (approximately 10 deg). On January 26, 1968 at about 1430 UT this shock was observed by the plasma and magnetic field instruments in Explorers 33 and 35. The spacecraft were 76.6 and 56.9 R sub E sunward of the earth, respectively (and 43.5 R sub E from each other), and therefore well outside the earth's bow shock region, a necessary condition for a valid test.

Lepping, R. P.↗

NASA NTRS1988

High-resolution shock-capturing schemes for inviscid and viscous hypersonic flows

A class of implicit Total Variation Diminishing (TVD) type algorithms suitable for transonic and supersonic multidimensional Euler and Navier-Stokes equations was extended to hypersonic computations. The improved conservative shock-capturing schemes are spatially second- and third-order, and are fully implicit. They can be first- or second-order accurate in time and are suitable for either steady or unsteady calculations. Enhancement of stability and convergence rate for hypersonic flows is discussed. With the proper choice of the temporal discretization and suitable implicit linearization, these schemes are fairly efficient and accurate for very complex two-dimensional hypersonic inviscid and viscous shock interactions. This study is complimented by a variety of steady and unsteady viscous and inviscid hypersonic blunt-body flow computations. Due to the inherent stiffness of viscous flow problems, numerical experiments indicated that the convergence rate is in general slower for viscous flows than for inviscid steady flows.

Yee, H. C.↗

NASA NTRS1990

High-resolution shock-capturing schemes for inviscid and viscous hypersonic flows

Hypersonic computations are presently conducted with an extension of a class of high-resolution implicit TVD algorithms suited to transonic multidimensional Euler and Navier-Stokes equations. These conservative shock-capturing schemes, which are spatially second- and third-order, may be first- and second-order accurate in time and suitable for either steady or unsteady calculations. Attention is given to the enhancement of hypersonic flows' convergence rate and stability; accuracy and efficiency is achieved by these means for very complex two-dimensional hypersonic viscous and inviscid shock interactions.

Yee, H. C.↗

NASA NTRS1985

Finite-volume scheme for transonic potential flow about airfoils and bodies in an arbitrarily-shaped channel

A conservative finite-volume difference scheme is developed for the potential equation to solve transonic flow about airfoils and bodies in an arbitrary channel. The scheme employs a mesh which is a nearly-conformal 'O' mesh about the airfoil and nearly orthogonal at the channel walls. The mesh extends to infinity upstream and downstream, where the mapping is singular. Special procedures are required to treat the singularities at infinity, including computation of the metrics near those points. Channels with exit areas different from inlet areas are solved; a body with a sting mount is an example of such a case.

South, J. C., Jr.↗

NASA NTRSDate not supplied

A New Approach for a Wider Class of Entropy Split Methods for Compressible Gas Dynamics and MHD

The high order entropy split methods of Sjögreen & Yee [1, 2] by entropy splitting of the compressible Euler (inviscid) flux derivatives for a thermally-perfect gas are based on Harten’s entropy function [3, 4, 5]. Their derivation takes advantage of the homogeneity property of Euler flux, symmetrizable Euler flux derivatives and energy-norm stability in conjunction with high order classical spatial central, DRP (dispersion relation-preserving) [6, 7, 8] or Padé (compact) spatial discretizations [9] with summation-by-parts (SBP) operators [10]. Our entropy split methods have been proven entropy conserving and stable [1, 11, 12]. Our proofs do not rely on a two-point numerical flux, but rather only a linear difference operator is required to derive these methods. To extend the entropy split method for the MHD, we used the Godunov symmetrizable non-conservative MHD form [12, 13, 14]. These high order entropy split methods not only preserve certain physical properties of the chosen governing equations but are also known to either improve numerical stability, and/or minimize aliasing errors in long time integration of turbulent flow computations without the aid of added numerical dissipation. In our previous published work, extensive error norm comparison with grid refinement was performed to show the high accuracy performance of these methods. These studies also showed how well the entropy split methods conserve the entropy, momentum and mass, and preserve the kinetic energy for long time integration of the various flows [1, 2, 12, 13, 14]. The objective of the present work is to use a new approach to obtain a wider class of entropy split methods consisting of a two-point numerical flux portion and a non-conservative portion in such a way that the homogeneity property of the compressible Euler flux is not required. For high order classical spatial central, DRP (dispersion relation-preserving) or Padé (compact) spatial discretizations, this new approach can be proven to be entropy conservative with conservative spatial dsicretizations while at the same time allowing a wider class of symmetrizable inviscid flux derivatives. We also use this generalization to derive an entropy split scheme that is entropy conserving for the equations of MHD without the homogeneity property using the Godunov symmetrizable ideal MHD formulation [15].

High Order Physical Preserving Methods↗

NASA NTRS1983

High resolution schemes and the entropy condition

A systematic procedure for constructing semidiscrete, second order accurate, variation diminishing, five point band width, approximations to scalar conservation laws, is presented. These schemes are constructed to also satisfy a single discrete entropy inequality. Thus, in the convex flux case, convergence is proven to be the unique physically correct solution. For hyperbolic systems of conservation laws, this construction is used formally to extend the first author's first order accurate scheme, and show (under some minor technical hypotheses) that limit solutions satisfy an entropy inequality. Results concerning discrete shocks, a maximum principle, and maximal order of accuracy are obtained. Numerical applications are also presented.

Osher, S.↗

NASA NTRS1985

Uniformly high-order accurate non-oscillatory schemes, 1

The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws was begun. These schemes share many desirable properties with total variation diminishing schemes (TVD), but TVD schemes have at most first order accuracy, in the sense of truncation error, at extreme of the solution. A uniformly second order approximation was constucted, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell.

Harten, A.↗

NASA NTRS1983

A new consistent spatial differencing scheme for the transonic full-potential equation

A new spatial differencing scheme for the transonic full-potential equation in conservative form has been developed. This scheme guarantees zero truncation error on any curvilinear mesh for freestream flows in either two- or three-space dimensions. Solutions obtained with this new differencing scheme, away from freestream regions, exhibit greatly improved accuracy, especially for nonsmooth or singular meshes.

Flores, J.↗

NASA NTRS1997

Accurate Monotonicity - Preserving Schemes With Runge-Kutta Time Stepping

A new class of high-order monotonicity-preserving schemes for the numerical solution of conservation laws is presented. The interface value in these schemes is obtained by limiting a higher-order polynominal reconstruction. The limiting is designed to preserve accuracy near extrema and to work well with Runge-Kutta time stepping. Computational efficiency is enhanced by a simple test that determines whether the limiting procedure is needed. For linear advection in one dimension, these schemes are shown as well as the Euler equations also confirm their high accuracy, good shock resolution, and computational efficiency.

Suresh, A.↗

NASA NTRS1980

An alternating-direction-implicit algorithm for the unsteady potential equation in conservation form

An implicit finite difference scheme for an efficient computation of unsteady potential flow about airfoils is presented. The formulation uses density and velocity potential as dependent variables, and is cast in conservation form to assure the theoretically correct determination of shockwave location and speed. To enable boundary conditions to be imposed directly on the airfoil surface, a time varying sheared rectilinear coordinate transformation is employed. Calculated time history solutions on a pulsating airfoil are compared with the results of another unsteady transonic code. It is concluded that the method has excellent numerical stability and gives accurate solutions with sharply resolved shocks.

Chipman, R. R.↗

NASA NTRS1987

Uniformly high order accurate essentially non-oscillatory schemes. III

In the present continuation of development and analysis efforts towards essentially nonoscillatory shock-capturing approximations of hyperbolic conservation laws, the Godunov (1959) scheme and its MUSCL second-order-accurate extension are generalized to an arbitrary order of accuracy by means of a hierarchy of uniformly high-order-accurate schemes. The design method, which involves the solution's essentially nonoscillatory piecewise polynomial reconstruction on the basis of its cell averages, followed by time-evolution through an approximate solution of the resulting initial value problem and its averaging over each cell, employs an adaptive stencil of grid points to yield schemes that are highly nonlinear.

Harten, Ami↗

NASA NTRS2004

Balanced Central Schemes for the Shallow Water Equations on Unstructured Grids

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 terms. We first show that for general triangulations there is no discretization of the source terms that corresponds to a well-balanced form of the KP scheme. We then derive a new variant of a central scheme that can be balanced on triangular meshes. We note in passing that it is straightforward to extend the KP scheme to general unstructured conformal meshes. This extension allows us to recover our previous well-balanced scheme on Cartesian grids. We conclude with several simulations, verifying the second-order accuracy of our scheme as well as its well-balanced properties.

Bryson, Steve↗

NASA NTRS1983

Finite area method for nonlinear supersonic conical flows

A fully conservative numerical method for the computation of steady inviscid supersonic flow about general conical bodies at incidence is described. The procedure utilizes the potential approximation and implements a body conforming mesh generator. The conical potential is assumed to have its best linear variation inside each mesh cell; a secondary interlocking cell system is used to establish the flux balance required to conserve mass. In the supersonic regions the scheme is symmetrized by adding artificial viscosity in conservation form. The algorithm is nearly an order of a magnitude faster than present Euler methods and predicts known results accurately and qualitative features such as nodal point lift off correctly. Results are compared with those of other investigators.

Sritharan, S. S.↗

NASA NTRS1990

Computational analysis of rotor-stator interaction in turbomachinery using zonal techniques

The development of CFD zonal techniques which allow more intensive computational treatment in some regions than in others, in conjunction with robust, high-accuracy algorithms for the numerical solution of the Navier-Stokes equations, is presently shown to have facilitated the investigation of rotor-stator interactions in turbomachinery. Attention is given to integration schemes with two and three spatial dimensions, the conservative 'patched' and the nonconservative zonal boundary schemes, and such natural boundary conditions as those of the endwall, the stator inlet, the airfoil surface, and the rotor exit. Illustrative three-dimensional rotor-stator interaction calculations are presented.

Madavan, Nateri K.↗

NASA NTRS1990

Numerical methods for systems of conservation laws of mixed type using flux splitting

The essentially non-oscillatory (ENO) finite difference scheme is applied to systems of conservation laws of mixed hyperbolic-elliptic type. A flux splitting, with the corresponding Jacobi matrices having real and positive/negative eigenvalues, is used. The hyperbolic ENO operator is applied separately. The scheme is numerically tested on the van der Waals equation in fluid dynamics. Convergence was observed with good resolution to weak solutions for various Riemann problems, which are then numerically checked to be admissible as the viscosity-capillarity limits. The interesting phenomena of the shrinking of elliptic regions if they are present in the initial conditions were also observed.

Shu, Chi-Wang↗

NASA NTRS2001

Distributed Relaxation for Conservative Discretizations

A multigrid method is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work that is a small (less than 10) multiple of the operation count in one target-grid residual evaluation. The way to achieve this efficiency is the distributed relaxation approach. TME solvers employing distributed relaxation have already been demonstrated for nonconservative formulations of high-Reynolds-number viscous incompressible and subsonic compressible flow regimes. The purpose of this paper is to provide foundations for applications of distributed relaxation to conservative discretizations. A direct correspondence between the primitive variable interpolations for calculating fluxes in conservative finite-volume discretizations and stencils of the discretized derivatives in the nonconservative formulation has been established. Based on this correspondence, one can arrive at a conservative discretization which is very efficiently solved with a nonconservative relaxation scheme and this is demonstrated for conservative discretization of the quasi one-dimensional Euler equations. Formulations for both staggered and collocated grid arrangements are considered and extensions of the general procedure to multiple dimensions are discussed.

Diskin, Boris↗

NASA NTRS1977

Integration schemes for climate prediction

To assure the conservation of total mass, momentum, energy, vorticity, etc., a method of modifying any given algorithm is presented. The modified scheme has at least the same order of accuracy as the given scheme.

Isaacson, E.↗