A Nonlinear Variational Multiscale Stabilized Method for Compressible Navier-Stokes Equations

In this work, we solve the compressible Navier-Stokes equations using a nonlinear variational multiscale finite element methodology. The numerical scheme relies on decomposing the problem into macro and micro scales, wherein an artificial viscosity operator is incorporated into both scales of the discretization. The magnitude of artificial viscosity is adjusted based on the stabilization parameter of the Consistent Approximate Upwind (CAU) method. To assess the performance of the method, we solve some problems for compressible Navier-Stokes equations. The numerical results indicate that the new method yields solutions similar to those obtained with the CAU method, however, with a lower computational cost.