An efficient vortex-resolved direct discontinuous Galerkin method with adaptive mesh refinement

Vortex-resolved simulations often require fine grids to capture multi-scale vortices, which leads to extremely high computational costs. This work proposes a direct discontinuous Galerkin method (DDGM) integrated with adaptive mesh refinement (AMR) for effectively reducing the expensive computational overhead of vortex-resolved simulations. First, a symbolic regression inspired vortex indicator is developed and generalized to arbitrary incompatible grids, enabling the concentration of computational grid resources on vortex regions. The most attractive advantage of this vortex indicator lies in its theoretically analyzed capability to capture dissipative small-scale vortices even on coarse grids, which is naturally compatible with AMR. Second, by integrating the AMR strategy guided by the present vortex indicator, an efficient and vortex-resolved DDGM is established. Numerical results validate that the vortex-resolved DDGM with AMR is able to resolve vortices of different scales in complex flows with a slight increase in computational overhead, providing a promising numerical method for exploring vortex-induced lift mechanisms and underlying flow physics in aerospace applications.