CHECKERBOARD MODES AND WAVE EQUATION

Checkerboard modes are unphysical oscillations that sometime appear when the incompressible Navier-Stokes system is solved with a colocated scheme. In this paper, we study the rate of dissipation of these modes when the pressure and the velocity are solution of the linear wave equation solved with Godunov scheme on a cartesian mesh. More precisely, we show that the checkerboard modes are the fastest diffused modes when we use the Godunov scheme in monodimensional geometry and that they are constant modes when the Godunov scheme is modifies by centering the discretization of the pressure gradient. This study underlines, that on a cartesian mesh, the checkerboard modes do not exist at low Mach number when the compressible Navier-Stokes system is solved with Godunov type scheme and may appear at large Reynolds number when the Godunov type scheme is modified to obtain an accurate scheme at low Mach number.