Code Verification of ReFRESCO with a Statistically Periodic Manufactured Solution

This paper presents a Code Verification study performed with the unsteady ensemble-averaged Navier-Stokes (URANS) solver ReFRESCO using the Method of Manufactured Solutions. The study uses a statistically periodic manufactured solution including the un-damped eddy-viscosity of the Spalart & Allmaras turbulence model. Three main aspects of the numerical calculations of unsteady flows are addressed in this study: iterative errors; discretization errors (space and time) and the determination of the observed order of (space and time) convergence.
The availability of an exact solution allows the determination of the numerical error and so the effects of iterative and discretization errors can be addressed. The paper presents grid and time refinement studies with different (iterative) convergence criteria and demonstrates that grid and time resolution are strongly connected when attempts are made to minimize the numerical uncertainty in the calculation of unsteady flows.
The paper also addresses error estimation based on power series expansions in the calculation of unsteady (space and time dependent) flows. Simultaneous grid and time refinement is compared to grid refinement with fixed time step and time refinement with fixed grid. The advantages and limitations of both options are discussed in the context of Code Verification (error evaluation) and Solution Verification (error estimation).