Accelerating high order discontinuous Galerkin solvers through a clustering-based viscous/turbulent-inviscid domain decomposition

TL;DR

This paper introduces a clustering-based domain decomposition method within a discontinuous Galerkin framework to efficiently distinguish viscous/turbulent regions from inviscid ones, reducing computational costs in flow simulations.

Contribution

It presents a novel unsupervised clustering approach for domain decomposition that selectively solves Navier-Stokes or Euler equations, significantly lowering computational expenses while maintaining accuracy.

Findings

Cost reduction of 25-29% in flow simulations.

Further acceleration with P-adaptation reduces costs by 41-45%.

Validated across diverse flow regimes, including airfoils and wind turbines.

Abstract

We explore the unsupervised clustering technique introduced in [25] to identify viscous/turbulent from inviscid regions in incompressible flows. The separation of regions allows solving the Navier-Stokes equations including Large Eddy Simulation closure models only in the viscous/turbulent ones, while solving the Euler equations in the remaining of the computational domain. By solving different sets of equations, the computational cost is significantly reduced. This coupling strategy is implemented within a discontinuous Galerkin numerical framework, which allows discontinuous solutions (i.e., different set of equations) in neighbouring elements that interact through numerical fluxes. The proposed strategy maintains the same accuracy at lower cost, when compared to solving the full Navier-Stokes equations throughout the entire domain. Validation of this approach is conducted across diverse flow regimes, spanning from unsteady laminar flows to unsteady turbulent flows, including an airfoil section at Reynolds numbers Re = 103 and 104 and large angles of attack, and the flow past a wind turbine, modelled using actuator lines. The computational cost is reduced by 25% and 29% for the unsteady turbulent flow around an airfoil section and the flow past the wind turbine, respectively. In addition, to further accelerate the simulations, we combine the proposed decoupling with local P -adaptation, as proposed in [ 30]. When doing so, we reduce the computational cost by 41% and 45% for the flow around the airfoil section and the flow past the wind turbine, respectively