Hyperviscosity stabilisation of the RBF-FD solution to natural convection

TL;DR

This paper investigates how hyperviscosity stabilizes meshless RBF-FD methods for simulating natural convection flows near turbulence, addressing a gap in understanding its effects in flow problems.

Contribution

It provides an in-depth analysis of hyperviscosity's impact on natural convection flow simulations, a topic not extensively explored before.

Findings

Hyperviscosity enhances numerical stability in natural convection simulations.

Optimal hyperviscosity parameters depend on flow regime.

Hyperviscosity effectively dampens instabilities near turbulence.

Abstract

The numerical stability of fluid flow is an important topic in computational fluid dynamics as fluid flow simulations usually become numerically unstable in the turbulent regime. Many mesh-based methods have already established numerical dissipation procedures that dampen the effects of the unstable advection term. When it comes to meshless methods, the prominent stabilisation scheme is hyperviscosity. It introduces numerical dissipation in the form of a higher-order Laplacian operator. Many papers have already discussed the general effects of hyperviscosity and its parameters. However, hyperviscosity in flow problems has not yet been analyzed in depth. In this paper, we discuss the effects of hyperviscosity on natural convection flow problems as we approach the turbulent regime.