A Preconditioned Flux Reconstruction/Correction Procedure via Reconstruction Formulation for Unsteady Low Mach Number Flows on Dynamic Unstructured Meshes
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Type of Work17 pages
conference papers and proceedings
Citation of Original PublicationLai 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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Subjectsdynamic unstructured meshes
discretization of compressible Navier-Stokes equations
flux reconstruction/correction procedure via reconstruction
time stepping method
dual time stepping
unsteady flow simulations
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.