The present study develops implicit physical domain-based discontinuous Galerkin(DG)methods for efficient scale-resolving simulations on mixed-curved meshes.Implicit methods are essential to handle stiff systems in ma...The present study develops implicit physical domain-based discontinuous Galerkin(DG)methods for efficient scale-resolving simulations on mixed-curved meshes.Implicit methods are essential to handle stiff systems in many scale-resolving simulations of interests in computational science and engineering.The physical domain-based DGmethod can achieve high-order accuracy using the optimal bases set and preserve the required accuracy on non-affinemeshes.When using the quadraturebased DG method,these advantages are overshadowed by severe computational costs on mixed-curved meshes,making implicit scale-resolving simulations unaffordable.To address this issue,the quadrature-free direct reconstruction method(DRM)is extended to the implicit DG method.In this approach,the generalized reconstruction approximates non-linear flux functions directly in the physical domain,making the computing-intensive numerical integrations precomputable at a preprocessing step.The DRM operator is applied to the residual computation in the matrix-free method.The DRM operator can be further extended to the system matrix computation for the matrix-explicit Krylov subspace method and preconditioning.Finally,the A-stable Rosenbrock-type Runge–Kutta methods are adopted to achieve high-order accuracy in time.Extensive verification and validation from the manufactured solution to implicit large eddy simulations are conducted.The computed results confirm that the proposed method significantly improves computational efficiency compared to the quadrature-based method while accurately resolving detailed unsteady flow features that are hardly captured by scale-modeled simulations.展开更多
基金the financial support provided by the Defense Acquisition Program Administration(DAPA)under Grant UD200046CD(Data-driven Flow Modeling Research Laboratory)the Korea Research Institute for defense Technology planning and advancement(KRIT)under Grant KRIT-CT-22-030(Reusable Unmanned Space Vehicle Research Center,2023)supported by the program of the National Research Foundation of Korea(NRF-2021R1A2C2008348).
文摘The present study develops implicit physical domain-based discontinuous Galerkin(DG)methods for efficient scale-resolving simulations on mixed-curved meshes.Implicit methods are essential to handle stiff systems in many scale-resolving simulations of interests in computational science and engineering.The physical domain-based DGmethod can achieve high-order accuracy using the optimal bases set and preserve the required accuracy on non-affinemeshes.When using the quadraturebased DG method,these advantages are overshadowed by severe computational costs on mixed-curved meshes,making implicit scale-resolving simulations unaffordable.To address this issue,the quadrature-free direct reconstruction method(DRM)is extended to the implicit DG method.In this approach,the generalized reconstruction approximates non-linear flux functions directly in the physical domain,making the computing-intensive numerical integrations precomputable at a preprocessing step.The DRM operator is applied to the residual computation in the matrix-free method.The DRM operator can be further extended to the system matrix computation for the matrix-explicit Krylov subspace method and preconditioning.Finally,the A-stable Rosenbrock-type Runge–Kutta methods are adopted to achieve high-order accuracy in time.Extensive verification and validation from the manufactured solution to implicit large eddy simulations are conducted.The computed results confirm that the proposed method significantly improves computational efficiency compared to the quadrature-based method while accurately resolving detailed unsteady flow features that are hardly captured by scale-modeled simulations.
