Convective mixing in porous media is triggered by a Rayleigh-Bénard-type hydrodynamic instability as a result of an unstable density stratification of fluids. While convective mixing has been studied extensively, the fundamental behavior of the dissolution flux and its dependence on the system parameters are not yet well understood. Here, we show that the dissolution flux and the rate of fluid mixing are determined by the mean scalar dissipation rate. We use this theoretical result to provide computational evidence that the classical model of convective mixing in porous media exhibits, in the regime of high Rayleigh number, a dissolution flux that is constant and independent of the Rayleigh number. Our findings support the universal character of convective mixing and point to the need for alternative explanations for nonlinear scalings of the dissolution flux with the Rayleigh number, recently observed experimentally.

SUMMARYThis paper introduces the use of Moving Least Squares (MLS) approximations for the development of high-order finite volume discretizations on unstructured grids. The field variables and their succesive derivatives can be accurately reconstructed using this meshfree technique in a general nodal arrangement. The methodology proposed is used in the construction of low-dissipative highorder high-resolution schemes for the shallow water equations. In particular, second and third-orderreconstruction upwind schemes for unstructured grids based on Roe's flux difference splitting are developed and applied to inviscid and viscous flows. This class of meshfree reconstruction techniques provide a robust and general approximation framework which represents an interesting alternative to the existing procedures, allowing, in addition, an accurate computation of the viscous fluxes. Copyright

SUMMARYA finite volume turbulence model for the resolution of the two-dimensional shallow water equations with turbulent term is presented. After making a finite volume discretization of the depth-averaged kequations in conservative form, the q-r equations, that give stability to the process, are obtained. Wall and inlet boundary conditions for the turbulent equations and wall conditions for the hydrodynamic equations are discussed. A comparison between the k-and q-r models and some experimental results is made.

SUMMARYA first-order finite volume model for the resolution of the 2D shallow water equations with turbulent term is presented. An upwind discretization of the equations that include the turbulent term is carried out. A method to reduce the excess of numerical viscosity (or diffusion) produced by the upwinding of the flux term is proposed. Two different discretizations of the turbulent term are compared, and results for uniform distributions of the viscosity are presented. Finally, two discretizations of the time derivative which are more efficient than Euler's are proposed and compared.