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

Abstract We explore the unsupervised clustering technique introduced in Otmani et al. (Phys Fluids 35:027112, 2023) 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 sets of equations) in neighboring 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 $$Re=10^3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>R</mml:mi> <mml:mi>e</mml:mi> <mml:mo>=</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>3</mml:mn> </mml:msup> </mml:mrow> </mml:math> and $$10^4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>4</mml:mn> </mml:msup> </mml:math> and large angles of attack, and the flow past a wind turbine, modelled using actuator lines. The computational cost is reduced by $$25\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>25</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> and $$29\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>29</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> 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 Tlales et al. (Eng Comput, 2024). When doing so, we reduce the computational cost by $$41\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>41</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> and $$45\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>45</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> for the flow around the airfoil section and the flow past the wind turbine, respectively.