Proceedings Article10.2514/6.1987-1163
Convection algorithms based on a diagonalization procedure for the multidimensional Euler equations
Ch. Hirsch,C. Lacor,Herman Deconinck +2 more
- 09 Jun 1987
51
TL;DR: In this paper, the authors proposed a wave front propagation model for the multidimensional Euler equations, which is based on characteristic propagation properties, with the aim of following closely the physical transfer of information.
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Abstract: Convection algorithms for the multidimensional Euler equations are presented based on characteristic propagation properties, with the aim of following closely the physical transfer of information. As opposed to the one dimensional case, information in two or three dimensional Euler flows is propagated in infinitely many directions, each one corresponding to an arbitrary wave front normal. It is shown that a complete decoupling (diagonalization) of the Euler equations can be obtained by an appropriate choice of wave front propagation directions. Actually,two directions are sufficient, one related to the pressure gradient and another related to the local strain tensor. This new formulation allows the definition of numerical schemes with upwind properties depending only on the local flow properties and not on the mesh geometry.
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Characteristic decomposition methods for the multidimensional euler equations
H. Deconinek,Ch. Hirsch,J. Peuteman +2 more
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TL;DR: In this article, an algebraically simple decomposition of the Euler equations for two-dimensional flows has been presented, which makes ise of two acoustic waves with orientation depending on the local strain rate tensor, and one entropy and shear wave with orientation parallel to the local pressure gradient.
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TL;DR: In this paper, a new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains.
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An Implicit Factored Scheme for the Compressible Navier-Stokes Equations
TL;DR: An implicit finite-difference scheme is developed for the numerical solution of the compressible Navier-Stokes equations in conservation- law form and, although a three-time-lev el scheme, requires only two time levels of data storage.
2.1K
Upwind difference schemes for hyperbolic systems of conservation laws
Stanley Osher,Fred Solomon +1 more
TL;DR: In this article, a new upwind finite difference approximation to systems of nonlinear hyperbolic conservation laws has been derived. But the scheme has desirable properties for shock calculations, such as unique and sharp shocks.
875
The λ-scheme
TL;DR: A scheme for integrating the Euler equations of compressible flow in any hyperbolic case is presented in this paper, which relies on the concept of characteristics but is strictly a finite difference scheme.
235