An Overset Generalized Minimal Residual Method for the Multi-Solver Paradigm in Helios

摘要

An extension of the Generalized Minimal Residual Method is proposed to improve convergence in overset grid based computational fluid dynamics frameworks. The presented Overset-GMRES algorithm operates using the global residual of all meshes and demonstrates improved convergence over traditional approaches. Initial validation is conducted for the Poisson equation on Cartesian grids, demonstrating convergence in few iterations. Two cases are analyzed for the Navier-Stokes equations on Cartesian grids. The first is time-accurate vortex convection between nested meshes. The second is wake-capture analysis for an actuator-line model of the NREL Phase VI turbine using both time-accurate and steady, rotating-frame approaches. Finally, multi-solver analysis is conducted for a sphere in cross-flow simulated using a near-body sphere mesh overset within multiple nested Cartesian grids. For all cases the Overset-GMRES algorithm shows improved convergence over traditional techniques.