Minimal intervention to simulations of shallow-water equations

A minimal intervention (MI) strategy is employed to manage the unphysical oscillations in the classical finite volume (CFV) numerical solution of the shallow-water equations. Only the missing variables on the face of the finite volume are modified for Total Variation Diminishing (TVD). The MI strategy maintains long-term computational stability without compromising the accuracy of the numerical solution. Flux limiters are implemented by imposing downwind weighting factor constraints on the missing variables on a staggered grid as the shallow-water equations are updated by a fourth-order Runge-Kutta scheme. The shock capturing capability of this MI-CFV method is verified by comparing the simulations with the exact solutions. A series of turbulence simulations for sub-critical and super-critical flows demonstrates the long-term numerical stability of the computation scheme developed using the MI strategy.