Abstract

For the one-dimensional Saint-Venant system of shallow water euqations, we develop a fully well-balanced PAMPA method by using the conservative-primitive formulations and local equilibrium variables decompsition. The proposed scheme is able to preserve both the lake-at-rest and moving-water equilibria. For the two-dimensional shallow water equations with horizontal temperature gradients, we develop a well-balanced PAMPA method capable of preserving both lake-at-rest and isobaric steady states. This is acieved by using suitable Gaussian quadrature rules in the souce terms' approximation in conservative formulation and by rewritting the non-conservative formulation in terms of pressure-momentum-temperature variables. The nonlinear stabilization needed for positivity preserving of water depth (and potential temperature) and reduce spurious oscillations is carried out by implementing a-posteriori MOOD paradigm equipped with first-order schemes.