A pressure-based Mach-uniform method for viscous fluid flows

A combined momentum-interpolation and advection upstream splitting pressure-correction algorithm for simulation of convective and acoustic transport at all levels of Mach number

“…As a recent example, we discuss the method of Ong and Chan [14]. The upwinding of the advection part is done with a Rusanov flux: the flux of a transported quantity is the face volume flux multiplied with the average of the values on both face sides of the transported quantity per unit of volume minus the absolute value of the face mass flux multiplied with half of the difference on both face sides of the transported quantity per unit of mass.…”

“…Regarding the latter, the capability of solving the full set of compressible Euler or Navier-Stokes equations over an as wide as possible range of Mach number, possibly involving a complex equation of state, while preserving the correctness of the asymptotic behavior when the Mach number tends to zero, has been the subject of a significant number of recent studies (see e.g. [14,15]). In that framework, contributing to the improvement of a pressure-based approach for solving the full compressible flow equations within a finite volume co-located framework has been an objective we pursued during the last ten years.…”

Diffusion and dissipation in acoustic propagation simulation by convection-pressure split algorithms in all Mach number form

“…There are some methods of this type, including our own method [10,11]. Other examples are by Ong and Chan [23], and by Xiao et al, Denner et al and Bartholomew et al [24][25][26]. A method by Li and Gu [27] is similar, but the face velocity at the old time level is interpolated with as consequence that the face velocity is not completely time accurate.…”