  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.
