Author(s): Xitong Sun; Georges Kesserwani

Linked Author(s): Xitong Sun

Keywords: Depth-averaged Reynolds-Averaged Navier-Stokes; K-ε turbulence closure model; Second-order discontinuous Galerkin; Turbulent flow simulation; Vortical flow structure around obstacle

Abstract: Shallow vortical flows interacting with emergent obstacles often exhibit turbulent behaviour, characterized by complex eddying motions. Traditional numerical solvers for the 2D Reynolds-Averaged Navier-Stokes (RANS) equations with the two-equation k-ε turbulence model (RANS-k-ε) rely on artificial treatments, such as non-local slope limiters and wet-dry front reconstructions, which compromise predictive accuracy. In contrast, the second-order discontinuous Galerkin (DG2) method inherently employs local, cellwise approximations, offering more accurate representations of topography and flow variables. This work develops a novel DG2 solver for RANS-k-ε (DG2-RANS-k-ε), designed to capture irregular mixed vortical flow structures with turbulence. To develop such a solver, a 5×5 RANS-k-ε system is first transformed into a 13×13 advection-dominated system. Next, the local DG2 formulation is extended to solve this system with robustness treatments for the mean-flow variables. Finally, novel treatments are introduced to further ensure stability and preserve positivity for turbulent-flow variables. The capability of the DG2-RANS-k-ε solver is evaluated by simulating turbulent flow past a square obstacle in a diverting T-junction at coarse, medium and fine resolutions. Results show that DG2-RANS-k-ε can reliably reproduces irregular mixed vortical flow structures with turbulent eddies, outperforming the simpler DG2-SWE solver, especially from the medium resolution. The DG2-RANS-k-ε solver 's computational efficiency is further enhanced by GPU parallelization, making it a promising tool for practical turbulent flow simulations.

DOI: https://doi.org/10.64697/978-90-835589-7-4_41WC-P1973-cd

Year: 2025