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This paper is about a new hybrid finite volume method/particle method for the numerical solution of systems of shallow water equations featuring transport of passive pollutants. The proposed numerical scheme discretizes the system of shallow water equations with pollutant transport (SWEPT) in a special way that maintains steady state solutions and ensures a reduced dissipation in the concentration of the pollutant. Selected test cases are considered and the generated numerical solution is reported. The observed numerical results endorse the potential of the proposed scheme to handle SWEPT problems accurately. [ABSTRACT FROM AUTHOR]

In this work we extend a previously developed unstaggered central finite volume method to the one-dimensional system of mixture two-phase flow problems. The numerical scheme is characterized by its simplicity and robustness as it evolves a piecewise linear numerical solution on a single grid and avoids the resolution of Riemann problems appearing at the faces of the control cells. The strategy consists of employing a second layer of staggered dual cells, on which the numerical solution is evolved at an intermediate time step before being projected back onto the cells of the original grid. The finite volume method is then implemented and used to solve classical mixture flow problems from the recent literature. The obtained numerical results are displayed; they confirm the potential of the unstaggered central scheme to properly and accurately solve mixture two-phase flow systems. [ABSTRACT FROM AUTHOR]

In this paper we present a new well-balanced, non-oscillatory, second-order accurate central scheme for the numerical solution of the two-dimensional system of the shallow water equations (SWE) on variable waterbeds, and with wet and dry states. The numerical scheme is a Riemann-free finite volume method and that evolves a piecewise linear numerical solution on a single Cartesian grid and preserves the positivity of the water height component, and maintains the equilibrium solution whenever applicable. [ABSTRACT FROM AUTHOR]

In this paper we extend a central finite volume method on nonuniform grids to the case of drift-flux two-phase flow problems. The numerical base scheme is an unstaggered, non oscillatory, second-order accurate finite volume scheme that evolves a piecewise linear numerical solution on a single grid and uses dual cells intermediately while updating the numerical solution to avoid the resolution of the Riemann problems arising at the cell interfaces. We then apply the numerical scheme and solve a classical drift-flux problem. The obtained results are in good agreement with corresponding ones appearing in the recent literature, thus confirming the potential of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper we develop a new central unstaggered finite volume method for solving systems of hyperbolic equations. Based on the Lax-Friedrichs central scheme and on the Nessyahu and Tadmor (NT) one-dimensional non-oscillatory central scheme, we construct a new class of unstaggered second-order non-oscillatory central finite volume schemes for approximating solutions of hyperbolic systems of conservation laws. In contrast with the original (NT) central scheme that evolves the numerical solution on an original grid (at even time steps) and on a staggered one (at odd time steps), the method we propose evolves the numerical solution on a single grid and uses a “ghost” staggered grid to avoid the time consuming resolution of the Riemann problems arising at the cell interfaces. The numerical solution is defined on the computational domain using piecewise linear interpolants. To avoid undesired oscillations a slope limiting process is applied; this results in a scheme that is second-order accurate in space. To guarantee second-order accuracy in time a second-order quadrature rule is applied. We apply our numerical scheme and solve some classical shallow water equation problems. The numerical results presented in this work show the efficiency and the potential of our unstaggered central scheme; they compare very well with those obtained using the original (NT) central scheme and are in a very good agreement with corresponding results appearing in the recent literature. [ABSTRACT FROM AUTHOR]