A vertex centered high order MUSCL scheme applying to linearised Euler acoustics

Ilya Abalakin (1) , Alain Dervieux (2) , T.Atiana Kozubskaya (1)

1 IMM-RAS - Institute for Mathematical Modelling
2 SMASH - Simulation, modeling and analysis of heterogeneous systems

This report proposes a linearised Euler discretisation that will be compatibl- e with some existing state of art in numerical methods for compressible flows on unstructured triangulations. The important property is the use of a stabilisation terms involving sixth-order derivatives. The main idea is to realize this programme by developing a scheme that enjoys superconvergence, i.e. a high convergence order when it is applied to a cartesian triangulation. We present a test case validating the theoretical order of accuracy and the so-called Tam test case, allowing some comparisons with two other typical numerical schemes for acoustics.

Mots clés: ACOUSTICS; NUMERICAL SCHEMES; HYPERBOLIC MODELS; LINEARISED EULER EQUATIONS; UNSTRUCTURED MESHES

Domaines: Autre [cs.OH]

Ilya Abalakin, Alain Dervieux, T.Atiana Kozubskaya. A vertex centered high order MUSCL scheme applying to linearised Euler acoustics. [Research Report] RR-4459, INRIA. 2002. ⟨inria-00072129⟩