A mathematical interpolation bounce back wall modeled lattice Boltzmann method based on hierarchical Cartesian mesh applied to 30P30N airfoil aeroacoustics simulation

• Published in: Computers & mathematics with applications (1987) Vol. 158; pp. 21 - 35
• Main Authors: Liang, Wen-zhi, Liu, Pei-qing, Zhang, Jin, Yang, Shu-tong, Qu, Qiu-lin
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 15.03.2024
• Subjects: Aeroacoustics; Curved boundary treatment; Lattice Boltzmann method; Non-fitted Cartesian mesh; Wall model; Wall model; Curved boundary treatment; Lattice Boltzmann method; Aeroacoustics; Non-fitted Cartesian mesh
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/j.camwa.2024.01.008

Wall-modeled large eddy simulation (WMLES) is considered to be a powerful method in high Reynolds number wall-bounded fluid dynamics calculations. However, little research on aero-acoustic simulation by lattice Boltzmann method (LBM) combined with LES considering wall model has been found. Moreover, the discussion of the dominant geometric parameters of the wall model, which is dedicated to curved boundary modeling and based on a non-fitted Cartesian mesh, is rarely addressed. This paper proposes a WMLES algorithm based on a hierarchical Cartesian mesh and utilizing LBM, including the treatment of dominant geometric parameters. Firstly, based on the Green's formula, a strategy for obtaining detection point positions is developed using the mathematical formulas to solve the boundary free parameters, such as the normal direction of the curved surface and the distance from the lattice point to the solid-fluid boundary in the given direction. Secondly, a new wall model adapted to non-fitted Cartesian mesh is proposed to improve the precision of pressure fluctuation calculation. This model applies an interpolation bounce-back (IBB) scheme where slip velocity is estimated by an implicit wall function proposed by Spalart, and the eddy viscosity is reconstructed in the near-wall region. Finally, to enhance the accuracy of pressure fluctuation propagation, an appropriate transition zone treatment method of a multi-domain scheme with spatio-temporal second-order is applied and validated with a point source case. The aforementioned algorithms are implemented in a self-developed LBM code and validated through a three-element airfoil 30P30N benchmark, demonstrating their effectiveness and high accuracy in acoustic calculations.