Coarse grid projection methodology: A partial mesh refinement tool for incompressible flow simulations

TL;DR

The paper introduces Coarse Grid Projection (CGP), a partial mesh refinement method for incompressible flow simulations that improves stability and accuracy by selectively refining the advection-diffusion grid while keeping the Poisson grid unchanged.

Contribution

It presents a novel partial mesh refinement approach for incompressible flows that enhances simulation stability and accuracy without full mesh refinement.

Findings

Partial mesh refinement stabilizes previously diverging flows.

Error in viscous lift force reduces significantly with CGP.

Selective refinement improves computational efficiency.

Abstract

We discuss Coarse Grid Projection (CGP) methodology as a guide for partial mesh refinement of incompressible flow computations for the first time. Based on it, if for a given spatial resolution the numerical simulation diverges or the velocity outputs are not accurate enough, instead of refining both the advection-diffusion and the Poisson grids, the CGP mesh refinement suggests to only refine the advection-diffusion grid and keep the Poisson grid resolution unchanged. The application of the novel mesh refinement tool is shown in the cases of flow over a backward-facing step and flow past a cylinder. For the backward facing step flow, a three-level partial mesh refinement makes a previously diverging computation numerically stable. For the flow past a cylinder, the error of the viscous lift force is reduced from 31.501% to 7.191% (with reference to the standard mesh refinement results) by the one-level partial mesh refinement technique.