A multiple--resolution strategy for Direct Numerical Simulation of scalar turbulence

TL;DR

This paper introduces a multiple-resolution numerical method for simulating low diffusivity scalar turbulence, optimizing computational efficiency by using different grids for scalar and momentum fields, especially effective for high Prandtl or Schmidt number flows.

Contribution

The paper presents a novel multiple-resolution approach that reduces computational costs in scalar turbulence simulations by employing separate grids for scalar and momentum fields.

Findings

Significant CPU time savings in simulations.

Memory usage is reduced compared to traditional methods.

Method is particularly effective for high Prandtl or Schmidt number flows.

Abstract

In this paper a numerical procedure to simulate low diffusivity scalar turbulence is presented. The method consists of using a grid for the advected scalar with a higher spatial resolutions than that of the momentum. The latter usually requires a less refined mesh and integrating both fields on a single grid tailored to the most demanding variable, produces an unnecessary computational overhead. A multiple resolution approach is used also in the time integration in order to maintain the stability of the scalars on the finer grid. The method is the more advantageous the less diffusive the scalar is with respect to momentum, therefore it is particularly well suited for large Prandtl or Schmidt number flows. However, even in the case of equal diffusivities the present procedure gives CPU time and memory occupation savings. The reason is that the absence of the pressure term in the scalar equation leads to much steeper gradients in the scalar field as compared to the velocity field.