A domain decomposition method for conservation laws with discontinuous flux function Original Research Article

A domain decomposition method for scalar conservation laws with discontinuous flux function is presented. The spatial domain is decomposed in subdomains at the location of the discontinuity of the flux function. The associated conservation law for each subdomain having then a continuous flux function is solved using a nonoscillatory relaxation scheme. Special coupling conditions at the subdomain interfaces are developed based on the direction of traveling waves. This method uses similar techniques recently used to treat junctions in network problems. The numerical performance of the method is illustrated on typical one-dimensional test examples like traffic models or two-phase flows.