Comparative Studies to Solve Compressible Problems by Multiscale Finite Element Methods

In this work we evaluate two multiscale methodologies to solve compressible flow problems, named, Dynamic Diffusion (DD) and Nonlinear Multiscale Viscosity (NMV), using the well know predictor-multicorrector time integration scheme. The subgrid scale space is defined using bubble functions whose degrees of freedom are locally eliminated in favor of the degrees of freedom that live on the resolved scales. The time integration schemes assume that the resolved coarse scale advances in time by second order approximation and the unresolved scale can advance by first and second order approximations. Performance and accuracy comparisons are conducted based on benchmark 2D problems.