Fast sweeping methods for hyperbolic systems of conservation laws at steady state

Fast sweeping methods have become a useful tool for computing the solutions of static Hamilton–Jacobi equations. By adapting the main idea behind these methods, we describe a new approach for computing steady state solutions to systems of conservation laws. By exploiting the flow of information along characteristics, these fast sweeping methods can compute solutions very efficiently. Furthermore, the methods capture shocks sharply by directly imposing the Rankine–Hugoniot shock conditions. We present convergence analysis and numerics for several one- and two-dimensional examples to illustrate the use and advantages of this approach.