A residual-based artificial viscosity finite difference method for scalar conservation laws

In this paper, we present an accurate, stable and robust shock-capturing finite difference method for solving scalar non-linear conservation laws. The spatial discretization uses high-order accurate upwind summation-by-parts operators combined with weakly imposed boundary conditions via simultaneous-approximation-terms. is extension of the residual-based artificial viscosity methods developed in finite- spectral element communities to setting. three main ingredients proposed are: (i) shock detection provided by a error estimator; (ii) first-order applied regions strong discontinuities; (iii) additional dampening spurious oscillations dissipation from operators. shown be skew-symmetric discretizations advective flux. Accuracy robustness are several benchmark problems 2D convex non-convex fluxes.