Accelerating high order discontinuous Galerkin solvers through a clustering-based viscous/turbulent-inviscid domain decomposition
arxiv(2024)
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
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
the flow past the wind turbine, respectively
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