Communications in Mathematical Sciences

Volume 1 (2003)

Number 3

An IMEX finite volume scheme for reactive Euler equations arising from kinetic theory

Pages: 449 – 470

DOI: http://dx.doi.org/10.4310/CMS.2003.v1.n3.a5

Authors

Maria Groppi

Micol Pennacchio

Abstract

A class of reactive Euler-type equations derived from the kinetic theory of chemical reactions is presented and a finite-volume scheme for such problem is developed. The proposed method is based on a flux-vector splitting approach and it is second-order in space and time. The final non-linear problem coming from the discretization has a characteristic block diagonal structure that allows a decoupling in smaller subproblems. Finally, a set of numerical tests shows interesting behaviors in the evolution of the space-dependent fluid-dynamic fields driven by chemical reactions, not present in previous space homogeneous simulations.

Keywords

Boltzmann equation; chemical reactions; finite volumes; semi-implicit schemes

2010 Mathematics Subject Classification

76M12, 82C40

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