Multigrid and Runge-Kutta time-stepping applied to the uniform non-oscillatory scheme

It is known that Harten's uniformly non-oscillatory scheme is a second-order accurate scheme for discretizing conservation laws. In this paper a multigrid technique and Runge-Kutta time stepping with frozen dissipation is applied to Harten's scheme in order to obtain the steady-state solution. It is shown that these techniques applied to Harten's scheme lead to a better convergence to the steady-state solution of a first-order conservation law than applied to Jameson's scheme.