W24-06 Research on Convergence and Optimal Parameters of Inertial Relaxed LBM for Fluid and Solid Simulations

Instructor(s):  Guangcai Gong, College of Civil Engineering, Hunan University; Ziche Gong, School of Mathematics, Hunan University; Yuan Lei, School of Mathematics, Hunan University.


The handling of boundary conditions in fluid-structure interaction (FSI) is a difficult task. The lattice Boltzmann method (LBM) has been proven to be efficient in processing boundary conditions in fluid simulations, its application is generalized for solid simulations in recent years. However, LBM usually suffers from slow convergence, which limits its applicable scenarios. To adress this issue, an accelerated LBM suitable for both fluid and solid simulations based on the inertia relaxed Bhatnagar-Gross-Krook operator (BGK-IR) is proposed. Combining the Chapman-Enskog theory and our previous work, the Navier-Stokes equations and the equation of elastic lamina deformation are restored from the BGK-IR, and the Boltzmann equation based on the BGK-IR has a second-order error with respect to the time step and the inertia term.

During numerical tests, the D2Q9 and the D3Q15 lattice velocity models are selected. The elastic lamina, the 2-D square cavity flow and the 3-D cubic cavity flow are selected as simulation objects. Series of numerical are conducted, and the results are compared with the benchmark solution in detail. The results proves that comparing with the original BGK-LBM, BGK-IR-LBM possessed acceptable accuracy and superior convergence rate. Based on optimal parameters, the time consumption in fluid simulation and solid simulation has been reduced by 60.72% and 35.25% respectively.

Our work discusses the application of the BGK-IR operator in fluid and solid simulations for the first time. The superior convergence of BGK-IR-LBM, as well as its applicability for both fluid and solid simulations, are demonstrated. Despite that BGK-IR-LBM incurs ill accuracy as the value of the inertial term becomes large, given its rapid convergence rate, a hybrid algorithm could be developed to restart the calculation process from the relaxed solution and compensate for the lack of calculation accuracy. This is our future work.