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



Maria Groppi

Micol Pennacchio


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.


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

2010 Mathematics Subject Classification

76M12, 82C40

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