Date of this Version
Shock Waves (2007) 17:185–193, DOI 10.1007/s00193-007-0104-z.
Simulation of a 2-D Richtmyer–Meshkov instability (RMI), including inviscid, viscous and magnetic field effects was conducted comparing recently developed sixthorder filter schemes with various standard shock-capturing methods. The suppression of the inviscid gas dynamics RMI in the presence of a magnetic field was investigated by Samtaney and Wheatley et al. Numerical results illustrated here exhibit behavior similar to the work of Samtaney. Due to the different amounts and different types of numerical dissipation contained in each scheme, the structures and the growth of eddies for the chaotic-like inviscid gas dynamics RMI case are highly grid size and scheme dependent, even with many levels of refinement. The failure of grid refinement for all studied numerical methods extends to the viscous gas dynamics case for high Reynolds number. For lower Reynolds number, grid convergence has been achieved by all studied methods. To achieve similar resolution, standard shock-capturing methods require more grid points than filter schemes and yet the CPU times using the same grid for all studied methods are comparable.