A Thorough Study on the Temporal Accuracy of ALE-URANS Solvers with and without Respecting Geometric Conservation Law

Abstract

The importance of satisfying the Geometric Conservation Law (GCL) to maintain second-order temporal accuracy for flow evaluations on dynamic grids are investigated for a Finite Volume Method (FVM)-based dual-time stepping Unsteady Reynolds-Averaged Navier-Stokes (URANS) solver. For a uniform flow and on prescribed grid motions, it is shown that standard first-and second-order Backwards Difference (BDF) approaches for grid velocity assessments do not preserve the uniform flow condition. In addition, except for rigid grid motions, analytic velocity assessment alters the flow uniform state as well. Only the scheme respecting GCL preserves the temporal accuracy of the solver and provides physically meaningful results. This is further confirmed through comprehensive temporal and frequency studies over two periodic flow problems; forced-and natural-laminar vortex shedding behind a 2D flapping plate and a 2D stationary cylinder, respectively. The obtained results emphasize the importance of GCL condition for unsteady flow solvers, which are developed based on Arbitrary-Lagrangian-Eulerian (ALE) formulation.