Accuracy of high-order density-based compressible methods in low Mach vortical flows

At low Mach numbers, Godunov-type approaches, based on the method of lines, suffer from an accuracy problem. This paper shows the importance of using the low Mach number correction in Godunov-type methods for simulations involving low Mach numbers by utilising a new, well-posed, two-dimensional, two-mode Kelvin–Helmholtz test case. Four independent codes have been used, enabling the examination of several numerical schemes. The second-order and fifth-order accurate Godunov-type methods show that the vortex-pairing process can be captured on a low resolution with the low Mach number correction applied down to 0.002. The results are compared without the low Mach number correction and also three other methods, a Lagrange-remap method, a fifth-order accurate in space and time finite difference type method based on the wave propagation algorithm, and fifth-order spatial and third-order temporal accurate finite volume Monotone Upwind Scheme for Conservation Laws (MUSCL) approach based on the Godunov method and Simple Low Dissipation Advection Upstream Splitting Method (SLAU) numerical flux with low Mach capture property. The ability of the compressible flow solver of the commercial software, ANSYS FLUENT, in solving low Mach flows is also demonstrated for the two time-stepping methods provided in the compressible flow solver, implicit and explicit. Results demonstrate clearly that a low Mach correction is required for all algorithms except the Lagrange-remap approach, where dissipation is independent of Mach number.