A new upwind scheme on triangular meshes using the finite volume method Original Research Article

In this paper, a new upwind scheme (MUST) for the solution of advection problems on triangular meshes is presented. The discretization of the convective terms is performed using the finite volume method on cell-centered triangular elements. The solution procedure uses an explicit Runge-Kutta time marching scheme. The MUST scheme is compared with three existing schemes from the literature on five illustrative cases: (i) rotation of a scalar ‘cone’ field, (ii) transport of a scalar ‘square’ field, (iii) mixing of a cold with a hot front, (iv) deformation of a scalar ‘cone’ field, and (v) non-linear shock interaction. These problems test the ability of the MUST scheme to produce oscillation-free and accurate results in critical convective situations. Results on accuracy, economy and monotonicity are presented and discussed. It is found that the MUST scheme gives impressive results, especially in the linear problems.