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Implicit Kinetic Schemes for Scalar Conservation Laws

Abstract : Based on kinetic formulation for scalar conservation laws we present implicit kinetic schemes. For timestepping the schemes require resolution of linear systems of algebraic quations. We justify that the developed implicit framework is very suitable for steady state calculations. Namely, we prove the convergence towards steady state when $ t \rightarrow \infty$. To our knowledge this is the first theoretical result of this type for nonlinear scalar conservation laws. Then for the equation with stiff source term we construct a stiff numerical scheme with discontinuous coefficients that ensure the scheme to be equilibrium conserving. We couple the developed implicit approach with the stiff space discretization thus providing improved stability and equilibrium conservation property in the resulting scheme. Numerical results demonstrate high computational capabilities (stability for large CFL numbers, fast convergence, accuracy) of the developed implicit approach.
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https://hal.inria.fr/inria-00072676
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Submitted on : Wednesday, May 24, 2006 - 10:33:41 AM
Last modification on : Thursday, February 3, 2022 - 11:18:57 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:17:59 PM

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  • HAL Id : inria-00072676, version 1

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Ramaz Botchorishvili. Implicit Kinetic Schemes for Scalar Conservation Laws. [Research Report] RR-3972, INRIA. 2000. ⟨inria-00072676⟩

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