Implementation of a Modified Lid Driven Cavity in OpenFOAM

The standard lid-driven cavity test case is one of the most used validation cases in CFD. Whilst comparisons with experimental and particularly DNS simulations are possible, there is no analytical solution, and the case is ill-posed when considering the boundary conditions. A modified lid driven cavity (MLDC) case exists in the literature in which the lid velocity is non-uniform and which introduces a spatially varying body force, and for which there is a closed-form analytical solution to the Navier-Stokes equations which is a function of the Reynolds number. In this paper I present an implementation of the MLDC as a modification of the standard OpenFOAM case, using run time coding for the boundary conditions and fvOptions, and show how convergence to the solution is affected by numerical parameters ofsimpleFoam such as choice of matrix inversion. The existance of an analytical solution also allows the investigation of the relation between the solver residual and the true solution error.