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On second-order antidiffusive Lagrangian-remap schemes for multispecies kinematic flow models

Abstract : This paper focuses on the numerical approximation of the solutions of multi-species kinematic flow models. These models are strongly coupled nonlinear first-order conservation laws with various applications like sedimentation of a polydisperse suspension in a viscous fluid, or traffic flow modeling. Since the eigenvalues and eigenvectors of the corresponding flux Jacobian matrix have no closed algebraic form, this is a challenging issue. A new class of simple schemes based on a Lagrangian- Eulerian decomposition (the so-called Lagrangian-remap (LR) schemes) was recently advanced in [4] for traffic flow models with nonnegative velocities, and extended to models of polydisperse sedimentation in [5]. These schemes are supported by a partial numerical analysis when one species is considered only, and turned out to be competitive in both accuracy and efficiency with several existing schemes. Since they are only first-order accurate, it is the purpose of this contribution to propose an extension to second-order accuracy using quite standard MUSCL and Runge-Kutta techniques. Numerical illustrations are proposed for both applications and involving eleven species (sedimentation) and nine species (traffic) respectively.
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Raimund Buerger, Christophe Chalons, Luis Miguel Villada. On second-order antidiffusive Lagrangian-remap schemes for multispecies kinematic flow models. Boletim da Sociedade Brasileira de Matemática / Bulletin of the Brazilian Mathematical Society, Springer Verlag, 2016, 47 (1), pp.187-200. ⟨10.1007/s00574-016-0131-4⟩. ⟨hal-02166368⟩



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