A post-processing technique for stabilizing the discontinuous pressure projection operator in marginally-resolved incompressible inviscid flow

TL;DR

This paper introduces a post-processing method to stabilize the pressure projection in under-resolved, discontinuous, inviscid flow simulations, enhancing stability and smoothness in environmental fluid mechanics models.

Contribution

A novel post-processing technique that enforces inter-element discontinuity and divergence-free conditions, improving stability and smoothness in discontinuous element-based flow simulations.

Findings

Post-processed velocity remains stable longer than non-processed.

The method reduces divergence and improves smoothness.

Enhanced conservation properties in the velocity field.

Abstract

A method for post-processing the velocity after a pressure projection is developed that helps to maintain stability in an under-resolved, inviscid, discontinuous element-based simulation for use in environmental fluid mechanics process studies. The post-processing method is needed because of spurious divergence growth at element interfaces due to the discontinuous nature of the discretization used. This spurious divergence eventually leads to a numerical instability. Previous work has shown that a discontinuous element-local projection onto the space of divergence-free basis functions is capable of stabilizing the projection method, but the discontinuity inherent in this technique may lead to instability in under-resolved simulations. By enforcing inter-element discontinuity and requiring a divergence-free result in the weak sense only, a new post-processing technique is developed that simultaneously improves smoothness and reduces divergence in the pressure-projected velocity field at the same time. When compared against a non-post-processed velocity field, the post-processed velocity field remains stable far longer and exhibits better smoothness and conservation properties.