An implementation of the Spalart–Allmaras turbulence model in a multi-domain lattice Boltzmann method for solving turbulent airfoil flows

Solving incompressible fluid flows on unstructured meshes with the lattice Boltzmann flux solver

“…In fact, commercial packages that can simulate unsteady 3D aerodynamics are available (Holman, Brionnaud, & Modena, 2014;König, Fares, & Nölting, 2014). Research has also been conducted in an effort to simulate turbulent airfoil flows with 2D lattices or meshes (Filippova et al, 2001;Imamura, Suzuki, Nakamura, & Yoshida, 2005;Li, Shock, Zhang, Chen, & Shih, 2005;Li, Zhong, Zhuo, & Cao, 2012;Pellerin, Leclaire, & Reggio, 2015).…”

“…Li et al (2012) also use coordinate transformation, however they retain a Cartesian mesh and stretch it to reduce grid spacing in the vicinity of the airfoil. In previous work (Pellerin et al, 2015), the current authors elected to use the multi-domain approach, and coupled it to a finite-difference implementation of the Spalart-Allmaras turbulence model. They identified mesh refinement near the airfoil's leading edge as a key element in obtaining accurate solutions.…”

“…While multi-domain lattices are easy to construct and can be adapted to arbitrary shapes, they do present certain drawbacks. First, their implementation in a solver, such as Pellerin et al's (2015) recursive solver, requires expending significant computational effort to transfer information between domains. Second, by definition, regular lattices cannot be refined along one specific direction, which would certainly be an advantage in terms of capturing high velocity gradients normal to walls, while limiting the number of chordwise lattice sites along an airfoil.…”

“…Its applicability will be tested on weakly compressible higher Reynolds flows around an airfoil, using high aspect ratio triangles near the wall to provide for differing mesh refinement in the normal and tangential directions. For the turbulence modeling, a finite-difference implementation of the Spalart-Allmaras model is applied, following the work of Pellerin et al (2015).…”

“…We first solve the laminar flows in a lid-driven cavity and over a circular cylinder to confirm that this LBFS implementation is accurate when no turbulence modeling is used. We then solve turbulent flows around the NACA0012 airfoil at moderate Reynolds numbers for the same test case as in Pellerin et al (2015). This provides a basis for comparing multi-domain and unstructured LBM solvers.…”