Subgrid Resolution of Fluid Discontinuities, II

In computation of discontinuities in solutions of hyperbolic equations, the random choice method gives a zero viscosity numerical solution with perfect resolution but first-order position errors ∼±2.5Δ x. The Lax-Wendroff scheme gives very small first-order position errors, but resolution errors ∼±2.5Δ x. We propose two very simple tracking methods in the context of the random choice method, which combine the best features of both methods: perfect resolution and good accuracy. We compare the above with tracking in the context of the Lax-Wendroff scheme. The latter method is morre complicated, but much more accurate than any of the other methods considered here.