Dilatation-driven spurious dissipation in weakly compressible methods

TL;DR

This paper investigates the causes of non-physical dissipation in weakly compressible flow simulations, revealing that dilatation effects, rather than mass conservation errors alone, significantly influence accuracy and offering insights for improved methods.

Contribution

It provides a detailed analysis of dilatation-driven dissipation mechanisms, advancing understanding of accuracy limitations in weakly compressible methods and guiding future development.

Findings

Dilatation terms significantly influence dissipation in weakly compressible methods.

Mass conservation errors are not the sole factor affecting accuracy.

Insights enable development of methods with higher artificial Mach numbers.

Abstract

The weakly compressible methods to simulate incompressible flows are in a state of rapid development, owing to the envisaged efficiency they offer for parallel computing. The pressure waves in such methods travel at finite speeds, and hence they yield non-solenoidal velocity fields. This inherent inability to satisfy mass conservation corresponding to incompressible flows is a crucial concern for weakly compressible methods. Another widely reported observation is the progressive enhancement of non-physical dissipation with the increase in the artificial compressibility parameter. By scrutinizing the dilatation terms appearing in the kinetic energy equation, we provide vital insights into the influence of mass conservation error on the accuracy of these methods, and explain the mechanism behind the dissipative nature of the compressibility. Analysing transient laminar and turbulent flows, we show that the dilatation-driven dissipation terms, not the mass conservation error alone, govern the accuracy of weakly compressible methods. The insights provided in this work are not only of fundamental importance but will be of considerable value in aiding the development of weakly compressible methods that can allow a larger artificial Mach number, thus alleviating the stringent time step restriction in such methods.