Finite Volume upwind schemes for the Euler equations in the low Mach number regime face a problem of lack of convergence toward the solutions of the incompressible system. However, if applied to cell centered triangular grid, this problem disappears and convergence toward the incompressible solution is recovered. Extending the work of [3] that prove this result for regular triangular grid, we g...

We consider a procedure for combining high order finite volumes and tree-based nonuniform grids. Especially, we focus on efficient algorithms third multidimensional volume interpolation communication between levels of refinement. In the end, numerical results are reviewed to validate our approach.

We present a high-order piecewise polynomial approximation for finite volume schemes. This method is designed for general unstructured polyhedral grids. A new algorithm for the calculation of the approximants is discussed. The main geometric property of the procedure is that the direct neighborhood only is needed. This allows for an efficient parallel implementation.

Interpolation of field data from unstructured meshes requires the potentially expensive identification of the finite element or volume within which the interpolating point lies. A number of geometric search algorithms have been proposed to reduce this expense at the cost of setting up and storing additional search tables. Using tetrahedral finite element models we show that a structured auxilia...

A new way of modelling and solving partial differential equations is derived. While the finite element (FE) methodology is based on the integration over finite elements, this novel approach utilizes edges (finite lines) instead, which results in a finite line integration (FLIM). We present how the FE-computations over elements (areas or volumes) can be rewritten for the stiffness matrix based o...