Panuelos, Jonathan – Central Schemes and Shearing Diffusion in Particle Methods (Dr. James Wadsley, Dr. Nicholas Kevlahan)

Computational hydrodynamics is significant in the study of physical phenomena in astronomy, with the bulk of the universe’s matter being low-density gas.The Kurganov-Tadmor (KT) central scheme is a robust numerical flux scheme that performs well in simulating compressible fluids. It performs admirably at the supersonic regime, but is found to cause excessive diffusion, especially in the case of shearing problems. Diffusion is required to maintain stability and prevent formation of spurious structures, but too much suppresses even physically relevant structures.

A new method of controlling the diffusion in the KT scheme is proposed, based on determining whether the local flow is shearing or not. This is shown to be effective at reducing diffusion while retaining stability through an implementation in the GIZMO hydrodynamics code, which uses an unstructured geometry where fluid is simulated by representing it as a collection of particles whose movement represents the flow.

The method was tested using a range of problems, focusing on its behaviour in both shearing flows as well as in the supersonic regime. Results show that diffusion is noticeably reduced in shearing cases, while stability is not impacted in the supersonic regime. Additionally, it was shown to perform on-par with, or better than, other methods in a difficult test containing both shearing and supersonic components. Thus, the new method achieves the desired reduction of diffusion while maintaining the robustness of the KT scheme.