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.
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Abstract: The Split Coefficient Matrix (SCM) finite difference method for solving hyperbolic systems of equations is presented. This new method is based on the mathematical theory of characteristics. The development of the method from characteristic theory is presented. Boundary point calculation procedures consistent with the SCM method used at interior points are explained. The split coefficient matrices that define the method for steady supersonic and unsteady inviscid flows are given for several examples. The SCM method is used to compute several flow fields to demonstrate its accuracy and versatility. The similarities and differences between the SCM method and the lambda-scheme are discussed.
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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 characteristic-type formulation of the Navier–Stokes equations for high order upwind schemes
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A time-domain differential solver for electromagnetic scattering problems
V. Shankar,W.F. Hall,A.H. Mohammadian +2 more
- 01 May 1989
TL;DR: In this paper, a finite-volume scheme is developed with appropriate representations for the electric and magnetic fluxes at a cell interface, accounting for variations in material properties in both space and time.
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Numerical experiments with the Osher upwind scheme for the Euler equations
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References
Diagonalization and simultaneous symmetrization of the gas-dynamic matrices
TL;DR: In this paper, it is shown that the individual matrices are simultaneously symmetrized by the similarity transformation and their norms can be applied to the well-posedness of the Cauchy problem, linear stability theory for finite-difference approximations, and simplification of block-tridiagonal systems that arise in implicit time-split algorithms.
152
Coefficient matrices for implicit finite difference solution of the inviscid fluid conservation law equations
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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