Omid Seyedashraf

A new numerical scheme based on the fniteelement method with a total-variation-diminishing property is developed with the aim of studying the shock-capturing capability of the combination. The proposed model is formulated within the framework of the one-step Taylor– Galerkin scheme in conjunction with the Van Leer’s limiter function. The approach is applied to the two-dimensional shallow water equations by different test cases, i.e., the partial, circular, and one-dimensional dam-break fow problems. For the one-dimensional case, the sub- and supercritical fow regimes are considered. The results are compared with the analytical, fnite-difference, and smoothed particle hydrodynamics solutions in the literature. The fndings show that the proposed model can effectively mask the sources of errors in the abrupt changes of the fow conditions and is able to resolve the shock and rarefaction waves where other numerical models produce spurious oscillations.