A More Rigorous Test Problem For Viscous Hydrodynamics Codes

TL;DR

This paper proposes a more rigorous test for viscous hydrodynamics codes using a nonuniform-density shear problem to better verify the accuracy of flux and stress calculations in simulations.

Contribution

It introduces a new, more stringent test problem for viscous hydrodynamics codes involving density gradients to evaluate their correctness.

Findings

The test reveals inaccuracies in flux and stress tensor calculations.

It provides a detailed exposition of Navier-Stokes equations in various coordinate systems.

Abstract

We advocate for a more stringent test problem for codes that aim to solve the equations of viscous hydrodynamics. Specifically, we discuss a nonuniform-density version of the common (uniform-density) Gaussian velocity shear test, where density gradients transverse to the direction of velocity shear cause the velocity profile to drift over time. By employing a nonunifom density, this test provides a test that the full viscous stress (and velocity shear) tensors are calculated correctly from the conserved variables, and checks the correctness of the fluxes and source terms calculated therefrom. In Appendix A, we present a detailed exposition of the Navier Stokes equations, particularly their fluxes and source terms in a variety of common coordinate systems.