ECCOMAS 2024

Implicit Near-wall Domain Decomposition Method for Wall-bounded Turbulent Flows

  • Lyu, Shiyu (Technical University of Munich)
  • Adams, Nikolaus (Technical University of Munich)

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Near-wall turbulence modeling leads to a challenging problem, which is, in large part, due to the excessively high computational effort of handling the thin sublayer in the vicinity of the wall. The near-wall non-overlapping domain decomposition (NDD) method [1] has been proposed to significantly reduce the wall-resolved computational cost while maintaining reasonable accuracy. Typically, with the NDD approach, the computational domain is split into two subdomains: the inner domain for near-wall region and the outer domain for remaining region. Both domains are related by a common boundary patch termed interface. The interface boundary conditions for velocity and other variables (such as the turbulent kinetic energy k and its dissipation rate ε in the k − ε model) in the approximate NDD algorithm are formulated in a Robin-type based on the thin-boundary layer model and prescribed turbulent viscosity profile in the inner region. To avoid the complexity of splitting the entire domain explicitly, using recently developed implicit NDD [2], the interface boundary condition for velocity can be transferred back to the wall following a novel scheme, leading to a Robin-type slip wall boundary condition. It is worth noting that the slip wall boundary condition guarantees the composite solution is smooth across the interface. In this way, the solution can be calculated with a dynamic slip wall boundary condition on a relatively coarse mesh and then be corrected in the near-wall region at every iteration through a turbulent viscosity profile computed from the corresponding turbulence model or estimated from a trained neural network model [3]. The overall good accuracy and efficiency of the implicit method are demonstrated in modeling turbulent flows in a channel and asymmetric diffuser. REFERENCES [1] S. Utyuzhnikov, Domain decomposition for near-wall turbulent flows, Computers &Fluids 38 (9) (2009) 1710–1717. [2] S. Lyu, S. Utyuzhnikov, A computational slip boundary condition for near-wall turbulence modeling, Computers & Fluids 246 (2022) 105628. [3] S. Lyu, J. Kou, N. A. Adams, Machine-learning-augmented domain decomposition method for near-wall turbulence modeling, Physical Review Fluids 9 (4) (2024) 044603.