A nonlinear finite element formulation based on multiscale approach to solve compressible euler equations

Abstract

This work presents a nonlinear finite element method for solving compressible Euler equations. The formulation is based on the strategy of separating scales – the core of the variational multiscale (finite element) methodology. The proposed method adds a nonlinear artificial viscosity operator that acts only on the unresolved mesh scales. The numerical model is completed by adding the YZβ shock-capturing operator to the resolved scale, taking into account the Mach number. We evaluate the efficiency of the new formulation through numerical studies, comparing it with other methodologies such as the SUPG combined with a shock-capturing operator.