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