An analysis of three formulations of the tensor artificial viscosity in two-dimensional Cartesian geometry

Abstract This paper analyzes three formulations of the tensor artificial viscosity in two-dimensional Cartesian geometry, namely, Campbell-Shashkov viscosity, Lipnikov-Shashkov viscosity and Wendroff viscosity. We first present a general derivation of these three ones. The discrepancy between Campbell-Shashkov viscosity and Lipnikov-Shashkov viscosity is then provided, followed by the non-triviality proof of both viscosities. Some numerical results are provided to verify the analysis at the end.