@Article{CiCP-33-4,
author = {You, Hojun and Kim, Juhyun and Kim, Chongam},
title = {Implicit Quadrature-Free Direct Reconstruction Method for Efficient Scale-Resolving Simulations},
journal = {Communications in Computational Physics},
year = {2023},
volume = {33},
number = {4},
pages = {992--1034},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2022-0253},
url = {https://global-sci.com/article/79440/implicit-quadrature-free-direct-reconstruction-method-for-efficient-scale-resolving-simulations}
}