Benchmark numerical solutions for two-dimensional fluid–structure interaction involving large displacements with the deforming-spatial-domain/stabilized space–time and immersed boundary–lattice Boltzmann methods

Abstract

Body-fitted and Cartesian grid methods are two typical types of numerical approaches used for modelling fluid–structure interaction problems. Despite their extensive applications, there is a lack of comparing the performance of these two types of approaches. In order to do this, the present paper presents benchmark numerical solutions for two two-dimensional fluid–structure interaction problems: flow-induced vibration of a highly flexible plate in an axial flow and a pitching flexible plate. The solutions are obtained by using two partitioned fluid–structure interaction methods including the deforming-spatial-domain/stabilized space–time fluid–structure interaction solver and the immersed boundary–lattice Boltzmann method. The deforming-spatial-domain/stabilized space–time fluid–structure interaction solver employs the body-fitted-grid deforming-spatial-domain/stabilized space–time method for the fluid motions and the finite-difference method for the structure vibrations. A new mesh update strategy is developed to prevent severe mesh distortion in cases where the boundary does not oscillate periodically or needs a long time to establish a periodic motion. The immersed boundary–lattice Boltzmann method uses lattice Boltzmann method as fluid solver and the same finite-difference method as structure solver. In addition, immersed boundary method is used in the immersed boundary–lattice Boltzmann solver to handle the fluid–structure interaction coupling. Results for the characteristic force coefficients, tail position, plate deformation pattern and the vorticity fields are presented and discussed. The present results will be useful for evaluating the performance and accuracy of existing and new numerical methodologies for fluid–structure interaction.

Recent trends and progress in the immersed boundary method

“…The drag coefficient of a flag flapping in uniform flow: (a) 2D flag with data from the study by Xu et al. 125 and (b) 3D flag with data from the earlier studies. 15,227–229 IBM: immersed boundary method; DSD/SST: deforming-spatial-domain/stabilized space-time method; 2,3,5,6,219–226 IB-LBM: immersed boundary-lattice Boltzmann method.…”

Recent progress of immersed boundary method and its applications in compressible fluid flow

“…此 外, 对于运动边界, 还需要在固体边界发生运动后, 专门处理网格运动甚至重新生成新的贴体网格. 这 样将不可避免地带来巨大的时间开销, 从而大大降 低计算的效率, 而且计算精度也难以保证 [5][6][7][8][9] . 为了使得网格生成过程简化, 有效的解决生 成贴体网格, 网格移动和网格重生等造成的计算 效率降低的问题, Peskin [10] 首先提出了浸入边界 法(Immersed Boundary Method).…”

Effects of Inclined Interface Angle on Compressible Rayleigh–Taylor Instability: A Numerical Study Based on the Discrete Boltzmann Method

“…In order to reveal the complex TNE effects in the process of compressible fluid flow, the discrete Boltzmann method (DBM) came into being [20][21][22][23][24]. The DBM is a coarse-grained physical model based on the non-equilibrium statistical physics, which is developed from the lattice Boltzmann method [25][26][27][28][29][30]. From the perspective of physical modeling, the DBM is approximately equivalent to a continuous fluid model plus a coarse-grained model describing TNE effects.…”