The use of implicit flux limiting schemes in the simulation of the drying process: A new maximum flow sensor applied to phase mobilities

Abstract

In this work, a previously proposed two-dimensional wood drying computational model is modified so that an analysis of the use of flux limiters for reducing numerical dispersion in the drying kinetics can be undertaken. In particular, a new sensor based on the ratio of phase fluxes is used to flux limit the liquid and gas phase mobility tensors. An extremely important physical phenomenon that arises during high temperature drying, and one that is exacerbated by the use of the flux limiter, relates to the medium becoming fully saturated. To overcome the numerical convergence problems associated with this phenomenon, the concept of a fixed compressible phase is introduced within the model and the averaged air density is used as one of the primary solution variables. A comparison of the simulation results for high temperature drying will be presented for three different case studies. In case one, a completely isotropic sample is considered while in case two, a slight anisotropy (1:2) is introduced for the modelling of a radial–transverse wood cross-section. In case three, for a wood sample modelled in the radial–longitudinal cross-section, a strongly anisotropic medium (1:1000) is analysed. It is found in all cases that when the new sensor is used during flux limiting, superior results to upstream weighting are obtained. In fact, it is possible with this method to attain the accuracy offered by upstream weighting on a much finer mesh at a considerable reduction of at least a factor of 5 in the overall computation time.