Numerical Analysis and Scientific Computing Seminar | Ayaboe Edoh, Split Forms for Discrete Secondary Preservations of the Navier-Stokes Equations

For Zoom Link please contact ddelreyfernandez@uwaterloo.ca  

Speaker

Dr. Ayaboe Edoh, Research engineer with Jacobs Engineering Group, Inc. (AFRL Contractor)

Title

Split Forms for Discrete Secondary Preservations of the Navier-Stokes Equations

Abstract

Enforcing discrete secondary properties has been leveraged as a means of improving solution accuracy and robustness for Navier-Stokes calculations. An approach for satisfying these secondary quantities (e.g., kinetic energy preservation -- KEP) is to employ split forms, which discretize alternate representations of divergence terms. By re-grouping such non-linear terms as quadratic products, the resulting splitting schemes can furthermore maintain primary conservation via a discrete product rule. The choice in quadratic groupings, however, can impact aliasing properties and furthermore determines the admissible secondary properties. 

This talk considers split forms for the Navier-Stokes convective terms within the context of finite differencing. Starting at the incompressible limit, we identify a one-parameter family of KEP methods that are characterized by small-scale corrections to the momentum pressure gradient. Specific parameter values are shown to recover the additional properties of angular momentum conservation, helicity conservation, or minimized aliasing. The new class of schemes is then extended to the compressible setting via a square-root density weighting. Commentary on the importance of splitting choice for the mass, momentum, and energy equations is then provided with respect to non-linear stability. And the potential impact of solution filtering techniques (e.g., for removing noise) on the entropy dynamics is highlighted. 

Finally, time permitting, a new quadratic splitting method for entropy stable viscous terms that is based on primitive variable gradients is introduced for the first time. This new formulation is then compared to traditional treatments as well as the current state-of-the-art approach based on entropy variable gradients.