Well-Balanced schemes for conservation laws with source terms based on a local discontinuous flux formulation
Kenneth H. Karlsen, Siddhartha Mishra and Nils Henrik Risebro
Abstract: We propose and analyse a finite volume scheme of the Godunov type that preserves discrete steady states. The scheme works in resonance regime as well as for problems with discontinuous flux. Moreover, no additional modifications of the scheme are required to resolve transience and solutions of non-linear algebraic equations are not involved. Our well balanced scheme is based on modifying the flux locally due to source term and to use a numerical scheme especially designed for conservation laws with discontinuous flux. Due to the difficulty involved in obtaining BV estimates, we use the compensated compactness method to obtain convergence to entropy solution. We include numerical experiments in order to show the features of the scheme and to compare it with other existing well balanced schemes in literature.