Search

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]