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In this work the control volume finite element (CVFE) method is used to discretise a two-dimensional non-linear transport model on an unstructured mesh. First and second order temporal weighting, combined with various flux limiting techniques (spatial weighting) are analysed in order to identify the most accurate and efficient numerical scheme. An inexact Newton method is used to resolve the underlying discrete non-linear system. In computing the Newton step the performance of the preconditioned iterative solvers BiCGSTAB and GMRES, in conjunction with a two-node Jacobian approximation is also examined. A linear benchmark problem that admits an analytical solution is used to assess the accuracy and computational efficiency of the numerical model. The results show that the flux limited second order temporal scheme substantially reduce numerical diffusion on relatively coarse meshes. The low temperature wood drying non-linear case study highlights that the first order temporal scheme combined with flux limiting achieves good accuracy on a relatively coarse mesh and improves the overall computational efficiency.

An investigation of spatial and temporal weighting schemes for use in unstructured mesh control volume finite element methods