High-order projection-based upwind method for simulation of transitional turbulent flows

TL;DR

The paper develops a scalable, high-order implicit large-eddy simulation (ILES) framework for incompressible transitional flows using a mass-conserving mixed stress (MCS) discretization and a projection-based operator-splitting strategy. It introduces high-order projection-based upwind (HOPU) stabilization to selectively dissipate only the high-frequency, small-scale content, preserving large-scale transition dynamics. Through Eppler 387 wing benchmarks at Reynolds numbers up to $3 \cdot 10^5$, the authors demonstrate accurate prediction of transition and boundary-layer characteristics, with HOPU providing improved near-wall profiles while maintaining good agreement in pressure, lift, and drag compared to experimental data. The work delivers a parallel, DG-based solver with a robust preconditioned CG strategy and adaptive dissipation control that is suitable for under-resolved turbulence and transitional aerodynamic studies, with future work targeting adaptive schemes and fully turbulent, high-Re flows.

Abstract

We present a scalable, high-order implicit large-eddy simulation (ILES) approach for incompressible transitional flows. This method employs the mass-conserving mixed stress (MCS) method for discretizing the Navier-Stokes equations. The MCS method's low dissipation characteristics, combined with the introduced operator-splitting solution technique, result in a high-order solver optimized for efficient and parallel computation of under-resolved turbulent flows. We further enhance the inherent capabilities of the ILES model by incorporating high-order upwind fluxes and are examining its approximation behaviour in transitional aerodynamic flow problems. In this study, we use flows over the Eppler 387 airfoil at Reynolds numbers up to $3 \cdot 10^5$ as benchmarks for our simulations.

Figures (10)

• Figure 1: Illustration for $\mathcal{X}_h$ (left): Local basis functions (green circles) on two elements and the normal continuous (blue arrows) and tangential continuous (orange arrows) edge basis functions on the common edge. Illustration for $\mathcal{X}^{BDDC}_h$ (right): The normal/tangential continuous basis functions where "broken" in two parts. The solid arrows are associated to the left element, and the dashed ones to the right element. The operator $R$ averages the coefficients of corresponding solid and dashed basis functions.
• Figure 2: (a) computational mesh, (b) curved boundary elements.
• Figure 3: Mode of local polynomial order $l_{loc}$ located in the middle point of its respective facet for (a) $R1/\alpha 10$ and (b) $R3/\alpha 4$.
• Figure 4: Distribution of the pressure coefficient $\overline{c_p}$ over the Eppler 387 airfoil for (a) $R1/\alpha 10$ and (b) $R3/\alpha 4$ case.
• Figure 5: Instantaneous velocity magnitude $|\underline{u}|/U_{\infty}$ field at given point in time for (a) $R1/\alpha 10$ and (b) $R3/\alpha 4$.

Theorems & Definitions (2)

• remark 1
• remark 2