Un esquema de volúmenes finitos de alto orden para las ecuaciones de aguas someras con topografía y áreas secas

Presentamos un esquema de volúmenes finitos para la resolución de las ecuaciones de aguas someras con término fuente debido a la topografía del fondo. Se trata de un esquema de alto orden, bien equilibrado y capaz de afrontar situaciones en las que aparecen zonas secas. El esquema se ha desarrollado en un marco no conservativo general, y se basa en reconstrucciones hiperbólicas de estados. El tratamiento de situaciones seco/mojado se lleva a cabo mediante la resolución de problemas de Riemann no lineales en las interceldas donde se detecta una transición

Five-equation model for compressible two-fluid flow

An interface-capturing, five-equation model for compressible two-fluid flow is presented, that is based on a consistent, physical model for the flow in the numerical transition layer. The flow model is conservative and pressure-oscillation free. Due to the absence of an interface model in the capturing technique, the implementation of the model in existing flow solvers is very simple. The flow equations are the bulk-fluid equations, combined with mass and energy equations for one of the two fluids. The latter equation contains a source term, to account for the energy exchange between the fluids. The physical flow model enables the derivation of an exact expression for this source term, both in continuous and in discontinuous flow. The system is solved numerically with a limited second-order accurate finite-volume technique. Linde's HLL Riemann solver is used. This solver is simplified here and its combination with the second-order scheme is studied. When the solver is adapted to two-fluid flow, the source term in the flow equations is incorporated in the Riemann solver. Further, the total source term in the cells is integrated over each cell. Numerical tests are performed on 1D shock-tube problems and on 2D shock-bubble interactions. The results confirm that the method is pressure-oscillation free and show that shocks are captured sharply. Good agreement with known solutions is obtained. Two appendices show an approximate model for shocks in physical two-phase media and a theoretical study of the interaction of shocks with plane interfaces, which is used to analyse the shock-bubble interaction

A bi-hyperbolic finite volume method on quadrilateral meshes

A non-oscillatory, high resolution reconstruction method on quadrilateral meshes in 2D is presented. It is a two-dimensional extension of Marquina's hyperbolic method. The generalization to quadrilateral meshes allows the method to simulate realistic flow problems in complex domains. An essential point in the construction of the method is a second order accurate approximation of gradients on an irregular, quadrilateral mesh. The resulting scheme is optimal in the sense that it is third order accurate and the reconstruction requires only nearest neighbour information. Numerical experiments are presented and the computational results are compared to experimental data