Very Thin Layer Method for Solving High Schmidt Number Flow on Unstructured Hybrid Mesh

A CFD code based on unstructured mesh consisting of tetrahedrons and triangular prisms has been developed. The prisms are generated along body boundaries to resolute momentum boundary layers. A cell-centered finite volume discretization, the fractional step algorithm, third order compact scheme for convection term, a central difference for the diffusion term are adopted. In high Schmidt number problems, mass boundary layer is much thinner than that of momentum so that very thin layers (VTL) are generated in one layer of prisms attached to the interface only for solving mass transfer. It is noted that the explicit time integration is used for momentum, while mass is solved implicitly in time for reducing computational time. The Sherwood numbers of a solid sphere are obtained in our numerical experiments and are in good agreement with some typical empirical equations.