Application of the SIMPLE Algorithm to a Manufactured Subsonic Flow

In general, numerical flow simulations in naval and offshore industries consider the fluids to be incompressible, i.e., with constant density. Although this approximation is valid for most flow cases, there are several phenomena, e.g., slamming, sloshing and cavitation, that involve compressible fluids. The goal of the present development of ReFRESCO is to modify the current flow solver to accurately solve compressible two-phase flows.
The first step of this development is to extend the current ReFRESCO pressure-based SIMPLE solver to laminar subsonic flows of perfect gases. The new solver will be based on the pressure-velocity-density coupling described in Ferziger and Peri´c, 2001. Besides the introduction of a new pressure correction equation the momentum and energy equations must be updated. It is also necessary to introduce an equation of state that relates pressure, density and temperature.
In the present work a code verification exercise for the modifications done in the momentum and pressure correction equations is presented. In this exercise the Method of Manufactured Solution is used to obtain an analytical solution for the compressible Navier-Stokes equations.