An Implicit High-Order Preconditioned Flux Reconstruction Method for Low-Mach-Number Flow Simulation with Dynamic Meshes

Abstract

A fully implicit high-order preconditioned ux reconstruction/correction procedure via reconstruction (FR/CPR) method is developed to solve the compressible Navier{Stokes equations at low Mach numbers. A dual-time stepping approach with the second-order backward di erentiation formula (BDF2) is employed to ensure temporal accuracy for unsteady ow simulation. When dynamic meshes are used to handle moving/deforming domains, the geometric conservation law (GCL) is implicitly enforced to eliminate errors due to the resolution discrepancy between BDF2 and the spatial FR/CPR discretization. The large linear system resulting from the spatial and temporal discretizations is tackled with the restarted Generalized Minimal Residual (GMRES) solver in the PETSc (Portable, Extensible Toolkit for Scienti c Computation) library. Through several benchmark steady and unsteady numerical tests, the preconditioned FR/CPR methods have demonstrated good convergence and accuracy for simulating ows at low Mach numbers. The new ow solver is then used to study the e ects of Mach number on unsteady force generation over a plunging airfoil when operating in low-Mach-number ows. It is observed that weak compressibility has a signi cant impact on thrust generation but a negligible e ect on lift generation of an oscillating airfoil.