Speaker: Pascal Omnès (CEA Saclay, DM2S-STMF)
Title : Estimation of the diffusion rate of the Godunov scheme applied to the wave equation and analysis of the low Mach inaccuracy.
Godunov type schemes which are used for the numerical simulation of the Euler equations of gas dynamics are known to be inaccurate at low Mach number. This talk gives an explanation of this phenomena on a linearized system by relating the inaccuracy to two ingredients: – the structure of the kernel of the discrete wave operator, – and the rate at which the numerical diffusion of the scheme projects initial conditions onto this kernel. This analysis also shows how to modify the scheme in order to get rid of this inaccuracy and explains why triangular meshes perform much better than rectangular meshes.