Switch flux limiter method for viscous and nonviscous conservation laws

In this work we develop an efficient shock capturing scheme of the TVD flux limiter family for viscous and nonviscous conservation laws. The new flux limiter method is based on the monotone FORWE scheme which is optimized by the inclusion of an appropriate switch function. For the viscous case, a conservative formulation of the type viscous flux limiter defined by Toro is used. Theoretical properties such as nonlinear stability and weak convergence are proven using TVD-stability. An efficiency analysis of the method is achieved by validating the numerical results with the analytical solutions of benchmark nonviscous and viscous problems. We compare the switch flux limiter results with those obtained by some of the well known flux limiter methods.