MAST solution of irrotational flow problems in 2D domains with strongly unstructured triangular meshes

A new methodology for the solution of irrotational 2D flow problems in domains with strongly unstructured meshes is presented. A fractional time step procedure is applied to the original governing equations, solving consecutively a convective prediction system and a diffusive corrective system. The non linear components of the problem are concentrated in the prediction step, while the correction step leads to the solution of a linear system, of the order of the number of computational cells. A MArching in Space and Time (MAST) approach is applied for the solution of the convective prediction step. The major advantages of the model, as well as its ability to maintain the solution monotonicity even in strongly irregular meshes, are briefly described. The algorithm is applied to the solution of diffusive shallow water equations in a simple domain.