Residual based artificial viscosity for compressible flows

Murtazo Nazarov
Numerical Analysis
School of Computer Science and Communication


We present a residual based artificial viscosity finite element method to solve conservation laws. The novelty of the method is that the Galerkin approximation is stabilized by only residual based artificial viscosity, without any least-squares, SUPG, or streamline diffusion terms. We discuss the convergence of the method applied to a scalar conservation law in two space dimensions for implicit and explicit time stepping. We then continue with the implementation of the method for the compressible Euler equations. Various benchmark problems in 1D and 2D are solved computationally to validate the method.