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Interfacial mass transfer of low-diffusive substances in an unsteady flowenvironment is marked by a very thin boundary layer at the interface and otherregions with steep concentration gradients. A numerical scheme capable ofresolving accurately most details of this process is presented. In this scheme,the fourth-order accurate WENO method developed by Liu et al. (1994) wasimplemented on a non-uniform staggered mesh to discretize the scalar convectionwhile for the scalar diffusion a fourth-order accurate central discretizationwas employed. The discretization of the scalar convection-diffusion equationwas combined with a fourth-order Navier-Stokes solver which solves theincompressible flow. A dual meshing strategy was employed, in which the scalarwas solved on a finer mesh than the incompressible flow. The solver was testedby performing a number of two-dimensional simulations of an unstably stratifiedflow with low diffusivity scalar transport. The unstable stratification led tobuoyant convection which was modelled using a Boussinesq approximation with alinear relationship between flow temperature and density. The order of accuracyfor one-dimensional scalar transport on a stretched and uniform grid was alsotested. The results show that for the method presented above a relativelycoarse mesh is sufficient to accurately describe the fluid flow, while the useof a refined mesh for the low-diffusive scalars is found to be beneficial inorder to obtain a highly accurate resolution with negligible numericaldiffusion.

Low-diffusivity scalar transport using a WENO scheme and dual meshing