Low-diffusivity scalar transport using a WENO scheme and dual meshing
  Interfacial mass transfer of low-diffusive substances in an unsteady flow environment is marked by a very thin boundary layer at the interface and other regions with steep concentration gradients. A numerical scheme capable of resolving accurately most details of this process is presented. In this scheme, the fourth-order accurate WENO method developed by Liu et al. (1994) was implemented on a non-uniform staggered mesh to discretize the scalar convection while for the scalar diffusion a fourth-order accurate central discretization was employed. The discretization of the scalar convection-diffusion equation was combined with a fourth-order Navier-Stokes solver which solves the incompressible flow. A dual meshing strategy was employed, in which the scalar was solved on a finer mesh than the incompressible flow. The solver was tested by performing a number of two-dimensional simulations of an unstably stratified flow with low diffusivity scalar transport. The unstable stratification led to buoyant convection which was modelled using a Boussinesq approximation with a linear relationship between flow temperature and density. The order of accuracy for one-dimensional scalar transport on a stretched and uniform grid was also tested. The results show that for the method presented above a relatively coarse mesh is sufficient to accurately describe the fluid flow, while the use of a refined mesh for the low-diffusive scalars is found to be beneficial in order to obtain a highly accurate resolution with negligible numerical diffusion. 
Boris Kubrak and Jan Wissink and Herlina Herlina and Friedrich Greve
math-ph math.MP