Abstract

S. Truscott (s.truscott@fsc.qut.edu.au) and I.W. Turner (i.turner@fsc.qut.edu.au)
School of Mathematical Sciences
Queensland University of Technology, Brisbane
Australia

In this work the control volume finite element CVFE) method is used to discretise a two-dimensional advection diffusion transport equation. A travelling Gauss Pulse is chosen as the benchmark problem since an analytical solution can be exploited to assess the accuracy of the proposed computational scheme. Unstructured meshes consisting of triangular (linear) elements and quadrilateral (bilinear) elements are used for the background interpolation meshes. Control volumes are constructed around the nodes using the vertex centred approach. We analyse first order and second order temporal and spatial weighting schemes in order to identify the most accurate combination for use in the CVFE method. We also consider the impact that these weighting schemes can have on the performance of the linear iterative solvers GMRES and BiCGSTAB. The results highlight that the second order temporal scheme combined with flux limiting can substantially reduce numerical dispersion in comparison with upwinding schemes for relatively coarse meshes.

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