A curl preserving finite volume scheme by space velocity enrichment. Application to the low Mach number accuracy problem

In this article, we address the problem of accuracy of finite volume schemes in the low Mach number limit. It has been known for years that collocated finite volume schemes are naturally correctly behaving in this limit on triangular meshes [21,22,16], but fail in general on other types of mesh. We are first interested in the general problem of the conservation of vorticity for the wave system. By enriching the approximation space for vectors, we prove that the Hodge-Helmholtz context developed for triangular meshes in [16] can be recovered in the quadrangular mesh case. This leads to a numerical scheme for the wave system that naturally preserves the vorticity under mild assumption on the numerical flux. The new approximation space is then used with the barotropic Euler system. Numerical tests show that the new numerical scheme is accurate for both steady and acoustic problems at low Mach number. •New approximation space for vectors on quadrangular mesh.•Discrete preservation of the curl.•The curl preserved is defined in the adjoint sense.•A numerical scheme accurate for both steady and unsteady low Mach number flows without low Mach number fix.