Strong formulations of the generalised Navier-Stokes momentum equation

TL;DR

This paper explores alternative strong formulations of the generalized Navier-Stokes momentum equation, focusing on shear-stress divergence, to improve computational efficiency and accuracy in numerical simulations.

Contribution

It introduces a novel alternative formulation of shear-stress divergence that simplifies numerical schemes and potentially allows for larger time steps.

Findings

Alternative formulation relocates strain information under Laplacian

Potential for larger time-step sizes in numerical schemes

Improved computational convenience for Navier-Stokes simulations

Abstract

In this paper, the strong formulation of the generalised Navier-Stokes momentum equation is investigated. Specifically, the formulation of shear-stress divergence is investigated, due to its effect on the performance and accuracy of computational methods. It is found that the term may be expressed in two different ways. While the first formulation is commonly used, the alternative derivation is found to be potentially more convenient for direct numerical manipulation. The alternative formulation relocates a part of strain information under the variable-coefficient Laplacian operator, thus making future computational schemes potentially simpler with larger time-step sizes.