A Preconditioned Flux Reconstruction/Correction Procedure via Reconstruction Formulation for Unsteady Low Mach Number Flows on Dynamic Unstructured Meshes

Author/Creator ORCID

Date

2017

Department

Program

Citation of Original Publication

Lai Wang and Meilin Yu. "A Preconditioned Flux Reconstruction/Correction Procedure via Reconstruction Formulation for Unsteady Low Mach Number Flows on Dynamic Unstructured Meshes", 55th AIAA Aerospace Sciences Meeting, AIAA SciTech Forum, (AIAA 2017-0737) https://doi.org/10.2514/6.2017-0737

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This item may be protected under Title 17 of the U.S. Copyright Law. It is made available by UMBC for non-commercial research and education. For permission to publish or reproduce, please contact the author.

Abstract

Preconditioning methods can signicantly decrease the condition number of the linear system resulted from the discretization of compressible Navier-Stokes equations at low Mach numbers by replacing the physical acoustic wave speeds with numerical ones. In the present study, the high-order accurate flux reconstruction/correction procedure via reconstruction (FR/CPR) method with low Mach number preconditioning is used to solve Navier-Stokes equations at low Mach numbers (Ma ~ O (10⁻³)). The dual time stepping method is used to handle un-steady flow simulations, wherein the second-order backward differentiation formula (BDF2) is adopted to discretize the temporal derivative with respect to the physical time. A simple modi cation of the preconditioning formulation is proposed to deal with dynamic meshes. Numerical results of several benchmark tests have demonstrated that the preconditioned FR/CPR method works well for low Mach number flows.