A collocated finite volume scheme to solve free convection for general non-conforming grids

We present a new collocated numerical scheme for the approximation of the Navier-Stokes and energy equations under the Boussinesq assumption for general grids, using the velocity-pressure unknowns. This scheme is based on a recent scheme for the diffusion terms. Stability properties are drawn from particular choices for the pressure gradient and the non-linear terms. Numerical results show the accuracy of the scheme on irregular grids

High order time integration and mesh adaptation with error control for incompressible Navier-Stokes and scalar transport resolution on dual grids

International audienceRelying on a building block developed by the authors in order to resolve the incompressible Navier-Stokes equation with high order implicit time stepping and dynamic mesh adaptation based on multiresolution analysis with collocated variables, the present contribution investigates the ability to extend such a strategy for scalar transport at relatively large Schmidt numbers using a finer level of refinement compared to the resolution of the hydrody-namic variables, while preserving space adaptation with error control. This building block is a key part of a strategy to construct a low-Mach number code based on a splitting strategy for combustion applications, where several spatial scales are into play. The computational efficiency and accuracy of the proposed strategy is assessed on a well-chosen three-vortex simulation

A formally second order cell centered scheme for convection-diffusion equations on unstructured non-conforming grids

International audienceWe propose, in this paper, a finite volume scheme to compute the solution of the convection-diffusion equation on unstructured and possibly non-conforming grids. The diffusive fluxes are approximated using the recently published SUSHI scheme in its cell centred version, that reaches a second-order spatial convergence rate for the Laplace equation on any unstructured two-dimensional/three-dimensional grids. As in the MUSCL method, the numerical convective fluxes are built with a prediction-limitation process, which ensures that the discrete maximum principle is satisfied for pure convection problems. The limitation does not involve any geometrical reconstruction, thus allowing the use of completely general grids, in any space dimension

A Novel Approach for Solving Navier-Stokes Equations on Complex Geometries

Wind turbines in a wind farm undergo significant interference through wake and terrain interaction. Numerical modeling of a complex terrain necessitates the use of curvilinear body fitted coordinates. This paper proposes a novel mixed basis formulation of the governing conservation equations for general curvilinear non-orthogonal grids with the physical covariant velocity as the primary solution variable. The result is an algorithm which has many advantages of orthogonal equations. The conservation equations written in this form retains the diagonal dominance of the pressure equation. The newly formed conservation equations are solved using the SIMPLER algorithm and are shown to converge well for non-orthogonal grids. Standard K - e model is used for turbulence closure