Vidar Stiernström
Department of Information Technology, Uppsala University
We present a residual-based artificial viscosity finite difference method for solving scalar hyperbolic conservation laws. The artificial viscosity act as a non-linear stabilization and is constructed such that (at most) first order viscosity is applied in regions close to the shock, without destroying the accuracy in smooth regions. The method is benchmarked against a set of test cases, covering problems both with convex as well as non-convex fluxes. Expected convergence is obtained for the linear advection equation, for smooth and non-smooth initial data. Although more work is yet to be done, the initial results are promising.