A high-order finite volume method for hyperbolic systems: Multi-dimensional Optimal Order Detection (MOOD).

Stéphane Clain (1) , Steven Diot (1) , Raphaël Loubère (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

In this paper, we investigate an original way to deal with the problems generated by the limitation process of high-order finite volume methods based on polynomial reconstructions. Multi-dimensional Optimal Order Detection (MOOD) breaks away from classical limitations employed in high-order methods. The proposed method consists of detecting problematic situations after each time update of the solution and of reducing the local polynomial degree before recomputing the solution. As multi-dimensional MUSCL methods, the concept is simple and independent of mesh structure. Moreover MOOD is able to take physical constraints such as density and pressure positivity into account through an “a posteriori” detection. Numer- ical results on classical and demanding test cases for advection and Euler system are presented on quadrangular meshes to support the promising potential of this approach.

Keywords: polynomial reconstruction; limitation; MOOD.; MOOD; Finite Volume; high-order; conservation law; MUSCL

Domains: Modeling and Simulation; Numerical Analysis [math.NA]

Stéphane Clain, Steven Diot, Raphaël Loubère. A high-order finite volume method for hyperbolic systems: Multi-dimensional Optimal Order Detection (MOOD).. Journal of Computational Physics, 2011, pp.0-0. ⟨10.1016/j.jcp.2011.02.026⟩. ⟨hal-00518478v2⟩