Code Verification Exercise of a Navier-Stokes Solver for Compressible Flows in the Laminar and Subsonic Regimes

Many of the flows of interest to the naval and offshore industries deal with fluids that are usually assumed to be incompressible, i.e. their equation of state is ρ = const. However, there are several phenomena, as for example slamming, sloshing or cavitation where the fluid compressibility must be taken into account. All these applications involve compressible two-phase flows, which are the ultimate goal of the present development of the flow solver ReFRESCO Vaz et al. (2009). As a first step of this development, this paper presents a Code Verification exercise performed with the Method of Manufactured Solutions, Roache and Steinberg (1984), Roache et al. (1990), for laminar compressible flows in the subsonic regime. The selected Manufactured Solution is based on the work presented in Roy et al. (2004) and Eça et al. (2012).

This first extension of ReFRESCO for a fluid that obeys the perfect gas equation of state requires two steps:
1. Adaptation of the SIMPLE algorithm used to determine the pressure field.
2. Solution of the energy equation to determine the temperature field.

This first step of the development is well documented in the open literature for both single phase Ferziger and Peric (2002) and multiphase Moukalled and Darwish (2006) and Miller et al. (2013) flows. On the other hand, the energy equation is already available in ReFRESCO but it is seldom solved in incompressible flow solutions. However, its formulation must be update due to the change of the equation of state. Nonetheless, the present paper presents one more manufactured solution for the Verification of compressible solvers and guarantees that we start this development with a good basis.