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

•A robust shock-capturing finite difference method, capable of accurately solving non-linear scalar conservation laws.•Shock-capturing is based on non-linear viscous regularization, applying first-order viscosity to the shock region.•Shock detection is provided by a high-order accurate residual-based error estimator.•Upwind SBP finite differences provide additional high-order accurate artificial dissipation.•Computations in 1D and 2D demonstrate robustness, accuracy and stability of the method.