Shock capturing and related numerical methods in computational fluid dynamics.
Chen, G.-Q. (2001)
Acta Mathematica Universitatis Comenianae. New Series
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Chen, G.-Q. (2001)
Acta Mathematica Universitatis Comenianae. New Series
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Edwige Godlewski, Kim-Claire Le Thanh, Pierre-Arnaud Raviart (2005)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We study the theoretical and numerical coupling of two hyperbolic systems of conservation laws at a fixed interface. As already proven in the scalar case, the coupling preserves in a weak sense the continuity of the solution at the interface without imposing the overall conservativity of the coupled model. We develop a detailed analysis of the coupling in the linear case. In the nonlinear case, we either use a linearized approach or a coupling method based on the solution of a Riemann...
Christophe Berthon, Didier Reignier (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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The paper deals with the numerical resolution of the convection-diffusion system which arises when modeling combustion for turbulent flow. The considered model is of compressible turbulent reacting type where the turbulence-chemistry interactions are governed by additional balance equations. The system of PDE's, that governs such a model, turns out to be in non-conservation form and usual numerical approaches grossly fail in the capture of viscous shock layers. Put in other words, classical...
Sébastien Martin, Julien Vovelle (2008)
ESAIM: Mathematical Modelling and Numerical Analysis
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This paper deals with the problem of numerical approximation in the Cauchy-Dirichlet problem for a scalar conservation law with a flux function having finitely many discontinuities. The well-posedness of this problem was proved by Carrillo [ (2003) 687–705]. Classical numerical methods do not allow us to compute a numerical solution (due to the lack of regularity of the flux). Therefore, we propose an implicit Finite Volume method based on an equivalent formulation of the initial problem....
Nicola Botta, Rolf Jeltsch (1995)
Applications of Mathematics
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A high resolution finite volume method for the computation of unsteady solutions of the Euler equations in two space dimensions is presented and validated. The scheme is of Godunov-type. The first order part of the flux function uses the approximate Riemann problem solver of Pandolfi and here a new derivation of this solver is presented. This construction paves the way to understand the conditions under which the scheme satisfies an entropy condition. The extension to higher order is...