A new TVD flux-limiter method for solving nonlinear hyperbolic equations

We develop a new flux-limiter method based on the Richtmyer two-step Lax–Wendroff (R2LW) method coupled with a conservative upwind method and a nonconventional flux-limiter function. The proposed method is TVD stable and preserves the linear stability condition of the R2LW method. The numerical results show that this method improves on the approximations obtained by standard first-order and second-order TVD schemes. The new method provides accurate results for nonlinear hyperbolic equations with discontinuous solutions.