TY - JOUR T1 - Implicit Quadrature-Free Direct Reconstruction Method for Efficient Scale-Resolving Simulations AU - You , Hojun AU - Kim , Juhyun AU - Kim , Chongam JO - Communications in Computational Physics VL - 4 SP - 992 EP - 1034 PY - 2023 DA - 2023/05 SN - 33 DO - http://doi.org/10.4208/cicp.OA-2022-0253 UR - https://global-sci.org/intro/article_detail/cicp/21667.html KW - Direct reconstruction method, implicit Runge–Kutta method, quadrature-free method, discontinuous Galerkin method, implicit large eddy simulation, high performance computing. AB -

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 DG method can achieve high-order accuracy using the optimal bases set and preserve the required accuracy on non-affine meshes. When using the quadrature-based 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.