An implicit high‐order preconditioned flux reconstruction method for low‐Mach‐number flow simulation with dynamic meshes. (4th August 2019)

• Record Type: Journal Article
• Authors: Wang, Lai; Yu, Meilin
• Is Part Of: International journal for numerical methods in fluids. Volume 91:Number 7(2019)
• Page Start: 348
• Page End: 366
• Publication Date: 2019-08-04
• Subjects: dual‐time stepping -- dynamic meshes -- flux reconstruction/correction procedure via reconstruction -- high‐order methods -- low‐Mach‐number preconditioning -- unsteady flows -- weak compressibility; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4759
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: A fully implicit high‐order preconditioned flux 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 differentiation formula (BDF2) is employed to ensure temporal accuracy for unsteady flow simulation. When dynamic meshes are used to handle moving/deforming domains, the geometric conservation law is implicitly enforced to eliminate errors due to the resolution discrepancy between BDF2 and the spatial FR/CPR discretization. The large linear system resulted from the spatial and temporal discretizations is tackled with the restarted generalized minimal residual solver in the PETSc (portable, extensible toolkit for scientific computation) library. Through several benchmark steady and unsteady numerical tests, the preconditioned FR/CPR methods have demonstrated good convergence and accuracy for simulating flows at low Mach numbers. The new flow solver is then used to study the effects of Mach number on unsteady force generation over a plunging airfoil when operating in low‐Mach‐number flows. It is observed that weak compressibility has a significant impact on thrust generation but has a negligible effect on lift generation of an oscillating airfoil. Abstract : We have developed an implicit preconditioned flux reconstruction method for low‐Mach‐number flow simulation on moving grids for the first time. Geometric conservation law is implicitly enforced for moving grid simulation, and spatiotemporal convergence properties of the preconditioned solver on moving grids are thoroughly verified. Effects of weak compressibility on unsteady force generation over a plunging airfoil are studied.