Fully-coupled pressure-based algorithm for compressible flows: linearisation and iterative solution strategies

TL;DR

This paper compares linearisation and iterative strategies for pressure-based algorithms in compressible flows, showing that a consistent Newton linearisation enhances convergence and stability across all Mach regimes.

Contribution

It demonstrates that fully-coupled Newton linearisation of all transient and advection terms improves performance and stability, eliminating the need for underrelaxation in compressible flow simulations.

Findings

Newton linearisation improves convergence significantly.

Consistent linearisation enhances stability at high Mach numbers.

Eliminates the need for underrelaxation in coupled algorithms.

Abstract

The impact of different linearisation and iterative solution strategies for fully-coupled pressure-based algorithms for compressible flows at all speeds is studied, with the aim of elucidating their impact on the performance of the numerical algorithm. A fixed-coefficient linearisation and a Newton linearisation of the transient and advection terms of the governing nonlinear equations are compared, focusing on test-cases that feature acoustic, shock and expansion waves. The linearisation and iterative solution strategy applied to discretise and solve the nonlinear governing equations is found to have a significant influence on the performance and stability of the numerical algorithm. The Newton linearisation of the transient terms of the momentum and energy equations is shown to yield a significantly improved convergence of the iterative solution algorithm compared to a fixed-coefficient linearisation, while the linearisation of the advection terms leads to substantial differences in performance and stability at large Mach numbers and large Courant numbers. It is further shown that the consistent Newton linearisation of all transient and advection terms of the governing equations allows, in the context of coupled pressure-based algorithms, to eliminate all forms of underrelaxation and provides a clear performance benefit for flows in all Mach number regimes.