Browsing by Subject "unsteady flow simulations"
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ItemA High-Order Dual-Time Stepping FR/CPR Method for Unsteady Incompressible Navier-Stokes Equations on Unstructured Moving Grids(AIAA SciTech Forum, 2016) Wang, Lai; Yu, MeilinA high-order accurate flux reconstruction/correction procedure via reconstruction (FR/CPR) method is developed to solve incompressible Navier-Stokes equations on unstructured moving grids. An artificial compressibility method is adopted to facilitate the common flux reconstruction on element interfaces. For unsteady flow simulations, a dual-time stepping method is used for temporal discretization. For simulations on deformable/moving grids, the Geometric Conservation Law (GCL) introduced in dynamic spatial coordinate transformation has been enforced. The newly developed method is verified with several steady and unsteady benchmark incompressible flow problems. ItemA Preconditioned Flux Reconstruction/Correction Procedure via Reconstruction Formulation for Unsteady Low Mach Number Flows on Dynamic Unstructured Meshes(AIAA SciTech Forum, 2017) Wang, Lai; Yu, MeilinPreconditioning 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.