Adaptive Mesh Coarsening using Interpolation Technique in CFD

Description

When computing complex flow fields modelled by hyperbolic equations one is interested in the reduction of computational costs by using adaptive methods. Based on a finite volume discretization on structured meshes Harten suggested multiresolution algorithms depending on the local smoothness of the solution. He distinguishes fluxes near discontinuities which have to be evaluated with a given complex upwinding scheme from those in smooth regions which can be interpolated.

Instead of interpolating fluxes a similar indicator can be used to decide which fraction of the computational domain can be reconstructed accurately from coarse grids. This yields a conservative multilevel grid coarsening approach. Using multivariate interpolation techniques, e.g. radial basis functions, these ideas generalize naturally to several space dimensions.

Following the above ideas we develop an adaptive method for solving the system of Euler equations in two space dimensions. The calculation of the fluxes is performed by the genuine multidimensional Method of Transport.

A second objective is the efficient use of massively parallel computers in CFD calculations. To get the full power of these machines adaptive codes require special efforts in the development of a dynamic load balancing. For our adaptation we developed a suitable strategy to get convincing improvements for the parallel code compared with the sequential code.

Contacts

Prof. Rolf Jeltsch and Tim Gutzmer (gutzmer@sam.math.ethz.ch).