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Title: Low-diffusivity scalar transport using a WENO scheme and dual meshing
Authors: Kubrak, B
Herlina, H
Greve, F
Wissink, JG
Keywords: Air-water interface;DNS;Gas transfer;WENO scheme;Scalar transport;High Schmidt number
Issue Date: 2013
Publisher: Elsevier
Citation: Journal of Computational Physics, 240, 158 - 173, 2013
Abstract: 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 fifth-order accurate WENO method developed by [13] 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 order of accuracy of the solver for one-dimensional scalar transport was tested on both stretched and uniform grids. Compared to the fifth-order WENO implementation of [10], the [13] method was found to be superior on very coarse meshes. The solver was further tested by performing a number of two-dimensional simulations. At first a grid refinement test was performed at zero viscosity with shear acting on an initially axisymmetric scalar distribution. A second refinement test was conducted for 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 results show that for the method presented a relatively coarse mesh is sufficient to accurately describe the fluid flow, while the use of a refined dual mesh for the low-diffusive scalars is found to be beneficial in order to obtain a highly accurate resolution with negligible numerical diffusion.
Description: This is the post-print version of the final paper published in Journal of Computational Physics. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2013 Elsevier B.V.
ISSN: 0021-9991
Appears in Collections:Mechanical and Aerospace Engineering
Dept of Mechanical Aerospace and Civil Engineering Research Papers

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