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

TL;DR

This paper introduces a high-accuracy numerical scheme combining WENO and dual meshing strategies to effectively simulate low-diffusivity scalar transport in unsteady flows, capturing steep gradients with minimal numerical diffusion.

Contribution

The paper presents a novel numerical approach that integrates a fourth-order WENO scheme with dual meshing for improved resolution of low-diffusive scalar transport.

Findings

Refined mesh improves scalar resolution with negligible numerical diffusion.

Coarse mesh suffices for fluid flow, refined mesh benefits scalar accuracy.

Method effectively captures steep concentration gradients in low-diffusivity scenarios.

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 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.