Journal Article10.1016/0045-7825(78)90056-7
Coefficient matrices for implicit finite difference solution of the inviscid fluid conservation law equations
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TL;DR: Conservative for coefficient matrices are found which are similar to Jacobian linearization and which reduce the computational work of various implicit schemes for the Euler equations of inviscid fluid flow.
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About: This article is published in Computer Methods in Applied Mechanics and Engineering. The article was published on 01 Feb 1978. The article focuses on the topics: Euler equations & Inviscid flow.
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Citations
Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods
TL;DR: The conservation-law form of the inviscid gasdynamic equations has the remarkable property that the nonlinear flux vectors are homogeneous functions of degree one as mentioned in this paper, which readily permits the splitting of flux vectors into subvectors by similarity transformations so that each subvector has associated with it a specified eigenvalue spectrum.
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A diagonal form of an implicit approximate-factorization algorithm
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TL;DR: The modification transforms the coupled system of equations into an uncoupled diagonal form that requires less computational work and has an important effect on the application of implicit finite-difference schemes to vector processors.
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One-sided difference approximations for nonlinear conservation laws
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TL;DR: In this article, one-sided or up-wind finite difference approximations to hyperbolic partial differential equations and, in particular, nonlinear conservation laws are analyzed and a second order scheme is designed for which they prove both nonlinear stability and that the entropy condition is satisfied for limit solutions.
383
On the structure and use of linearized block implicit schemes
W. R. Briley,Henry McDonald +1 more
TL;DR: It is demonstrated that the two-level version of the second and more recent “delta” form approximate factorization scheme of Warming and Beam and the earlier method of Briley and McDonald have identical linearized block implicit structures.
213
The Split Coefficient Matrix method for hyperbolic systems of gasdynamic equations
S. R. Chakravarthy,D. A. Anderson,M. D. Salas +2 more
- 01 Jan 1980
TL;DR: The Split Coefficient Matrix (SCM) finite difference method for solving hyperbolic systems of equations is presented in this paper, which is a new method based on the mathematical theory of characteristics.
102
References
Systems of conservation laws
Peter D. Lax,Burton Wendroff +1 more
TL;DR: In this article, a wide class of difference equations is described for approximating discontinuous time dependent solutions, with prescribed initial data, of hyperbolic systems of nonlinear conservation laws, and the best ones are determined, i.e., those which have the smallest truncation error and in which the discontinuities are confined to a narrow band of 2-3 meshpoints.
Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics
S. K. Godunov,I. Bohachevsky +1 more
- 01 Jan 1959
TL;DR: In this paper, the authors proposed a method of characteristics used for numerical computation of solutions of fluid dynamical equations is characterized by a large degree of non standardness and therefore is not suitable for automatic computation on electronic computing machines, especially for problems with a large number of shock waves and contact discontinuities.
2.6K
The Effect of Viscosity in Hypervelocity Impact Cratering
TL;DR: In this paper, a numerical method for time dependent compressible Navier-Stokes equations applied to axisymmetric flow field produced by hypervelocity impact, examining viscous effects is presented.
1.3K