A Very High-Order Accurate Staggered Finite Volume Scheme for the Stationary Incompressible Navier–Stokes and Euler Equations on Unstructured Meshes

Ricardo Costa (1, 2) , Stéphane Clain (1) , Gaspar Machado (1) , Raphaël Loubère (2)

1 CMAT - Centro de Matemática [Minho]
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We propose a sixth-order staggered finite volume scheme based on polynomial reconstructions to achieve high accurate numerical solutions for the incompressible Navier-Stokes and Euler equations. The scheme is equipped with a fixed-point algorithm with solution relaxation to speed-up the convergence and reduce the computation time. Numerical tests are provided to assess the effectiveness of the method to achieve up to sixth-order con-2 Ricardo Costa et al. vergence rates. Simulations for the benchmark lid-driven cavity problem are also provided to highlight the benefit of the proposed high-order scheme.

Mots clés: Finite volume method; High-order scheme; Polynomial reconstruction · Navier-Stokes equations · Euler equations · Fixed-point algorithm

Domaines: Analyse numérique [math.NA]

Ricardo Costa, Stéphane Clain, Gaspar Machado, Raphaël Loubère. A Very High-Order Accurate Staggered Finite Volume Scheme for the Stationary Incompressible Navier–Stokes and Euler Equations on Unstructured Meshes. Journal of Scientific Computing, 2017, pp.1-34. ⟨10.1007/s10915-016-0348-9⟩. ⟨hal-01294244⟩