Author(s): Xitong Sun; Georges Kesserwani
Linked Author(s): Georges Kesserwani
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 flow due to the interaction with emergent obstacles is often in a turbulent state, exhibiting a complex eddying motion. Vortical flow structures can effectively be captured by the two-dimensional (2D) Reynolds-Averaged Navier-Stokes (RANS) equations with the two-equation k-ε turbulence model (RANS-k-ε). Current RANS-k-ε simulators based on the finite difference/volume solvers rely on adding artificial treatments, such as unlocalised reconstruction for wet-dry front representations and extrinsic slope-limiter. Although these treatments can stabilize the approximation of vortical flow structures around emergent obstacles, they reduce the predictive accuracy. In contrast, the local second-order discontinuous Galerkin (DG2) solver inherently involves accurate wet-dry front presentations and locally (cellwise) applies slope-limiter, leading to accurate capturing of regular unmixed vortical flow structures, even when solving simpler shallow water equations (DG2-SWE). A new DG2 solver for RANS-k-ε (DG2- RANS-k-ε) is developed in this work, aiming to generally reproduce 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 solver is extended to the latter 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 reproduce irregular mixed vortical flow structures with turbulent eddies from the medium resolution.
Year: 2025