Stable numerical methods for conservation laws with discontinuous flux function

摘要

We develop numerical methods for solving nonlinear equations of conservation laws with flux function that depends on discontinuous coefficients. Using a relaxation approximation, the nonlinear equation is transformed to a semilinear diagonalizable problem with linear characteristic variables. Eulerian and Lagrangian methods are used for the advection stage while an implicit–explicit scheme solves the relaxation stage. The main advantages of this approach are neither Riemann problem solvers nor linear iterations are required during the solution process. Moreover, the characteristic-based relaxation method is unconditionally stable such that no CFL conditions are imposed on the selection of time steps. Numerical results are shown for models on traffic flows and two-phase flows.