PhD defense - V. Auffray

Comparison of numerical schemes for the modelling
of diffusive phenomena on hybrid grids

Delivered by INP Toulouse
Speciality: Fluid dynamics

March 23, 2007 - CERFACS

Initially, the CFD code N3S-Natur used a Finite Volume/Finite Element approach that is only defined on triangular and tetrahedral cells. The objective of this work is to define a new numerical method that can handle hybrid meshes. First, we extend the metric to all kinds of elements. Then, six different modellings for the diffusive operator, that constitute the main issue, are proposed and tested. These methods are studied in terms of consistency, accuracy and stability. The comparison is carried out both theoretically and numerically using grid convergence and Fourier analysis. Only one method satisfies all the industrial criteria and is therefore implemented in the code. The higher order schemes for the convective operator are modified consequently and the linearisation of the new diffusive flux, that is required for the implicitation, is treated. The code is successfully validated on a flat plate test case.