Hybrid High-Order formulations with turbulence modelling capabilities for incompressible flow problems

TL;DR

This paper introduces a Hybrid High-Order (HHO) method for incompressible Navier-Stokes equations, enabling high-fidelity turbulent flow simulations with features like pressure-robustness, mass conservation, and high-order time integration.

Contribution

It develops a novel HHO formulation with turbulence modeling capabilities, combining high-order accuracy, robustness, and computational efficiency for complex flow simulations.

Findings

Successfully applied to 2D and 3D test cases.

Achieved high accuracy and stability in turbulent flow simulations.

Demonstrated effectiveness on Taylor-Green Vortex at Re=1600.

Abstract

We propose a Hybrid High-Order (HHO) formulation of the incompressible Navier--Stokes equations, that is well suited to be employed for the simulation of turbulent flows. The spatial discretization relies on hybrid velocity and pressure spaces and the temporal discretization is based on Explicit Singly Diagonal Implicit Runge-Kutta (ESDIRK) methods. The formulation possesses some attractive features that can be fruitfully exploited when high-fidelity computations are required, namely: pressure-robustness, conservation of mass enforced cell-by-cell up to machine precision, robustness in the inviscid limit, implicit high-order accurate time stepping with local time step adaptation, reduced memory footprint thanks to static condensation of both velocity and pressure, possibility to exploit inherited $p$-multilevel solution strategies to improve performance of iterative solvers. After demonstrating the relevant properties of the scheme in practice, performing challenging 2D and 3D test cases, we consider the simulation of the Taylor--Green Vortex flow problem at Reynolds 1600.