Pressure-tight and non-stiff volume penalization for compressible flows

TL;DR

This paper introduces a pressure-tight, non-stiff volume penalization method for compressible flows that improves numerical stability and conservation properties while effectively modeling complex geometries in fluid simulations.

Contribution

A novel volume penalization approach that reduces numerical stiffness and maintains stability and conservation in compressible flow simulations with embedded geometries.

Findings

Effective reduction of flux through objects to near zero

Improved numerical stability and conservation of mass and energy

Successful testing in acoustic and compressible flow scenarios

Abstract

Embedding geometries in structured grids allows a simple treatment of complex objects in fluid simulations. Various methods for embedding geometries are available. The commonly used Brinkman-volume-penalization models geometries as porous media, and approximates a solid object in the limit of vanishing porosity. In its simplest form, the momentum equations are augmented by a term penalizing the fluid velocity, yielding good results in many applications. However, it induces numerical stiffness, especially if high-pressure gradients need to be balanced. Here, we focus on the effect of the reduced effective volume (commonly called porosity) of the porous medium. An approach is derived, which allows reducing the flux through objects to practically zero with little increase of numerical stiffness. Also, non-slip boundary conditions and adiabatic boundary conditions are easily constructed. The porosity terms allow keeping the skew symmetry of the underlying numerical scheme, by which the numerical stability is improved. Furthermore, very good conservation of mass and energy in the non-penalized domain can be achieved, for which the boundary smoothing introduces a small ambiguity in its definition. The scheme is tested for acoustic scenarios, for near incompressible and strongly compressible flows.