An FSI solution technique based on the DSD/SST method and its applications

Abstract

Communicated by T. E. TezduyarThis paper presents a fluid-structure interaction (FSI) solution technique in which the incompressible fluid dynamics involving moving boundaries is solved with the deformingspatial-domain/stabilized space-time (DSD/SST) method and the structural dynamics is solved with the finite difference (FD) method. The DSD/SST and FD solvers are coupled by an implicit partitioned coupling strategy based on staggered subiterations. Three types of relaxation are applied on the FSI surface velocity and hydrodynamic force. The first one is applied to delay the coupling conditions at the beginning of each simulation; the second one is applied to relax the increment during each subiteration; and the third one is applied to filter high frequency oscillations between each time step. A pitching plate in a uniform flow is calculated to validate the FSI technique. The present results are in good agreement with data predicted by other methods. In addition, two problems are calculated to demonstrate the capability of this solver: an orbital flow over flapping foil propulsion and energy harvesting and a flexible plate in a cavity excited by an external force. An FSI solution technique 3expense. The mesh moves following the immersed boundary motion every time step if moving boundaries are involved, and may be regenerated if the distortion of elements is severe. The advantage of these methods is that the boundary conditions can be directly imposed and thus it has high-order accuracy near the boundary. This treatment could be computationally expensive and complicated, especially for the cases involving complex geometries and large displacements/deformations. The DSD/SST method is one of the earliest space-time formulations for fluid dynamics simulations involving moving boundaries and interfaces. This method is based on stabilized finite element formulations written over the space-time domain of the fluid. In this method, the streamline-upwind/Petrov-Galerkin 42,43 and pressurestabilizing/Petrov-Galerkin 25,44 formulations are the stabilization strategies used to prevent numerical instabilities encountered in solving flow problems with high Reynolds number, high Mach number, shocks or strong boundary layers, and when using equal-order interpolation functions for both velocity and pressure. In addition, the DSD/SST method allows the spatial domain at various time levels to vary without introducing additional interpolation routines if the grid topology is preserved, and thus can be effectively applied to fluid dynamics computations involving moving boundaries and interfaces. 25-27 Since the work by Tezduyar et al. [25][26][27] the DSD/SST formulation has been extensively used to simulate problems involving moving boundaries and FSI. Some examples of these applications are animal swimming and flight, 39,45-55 flag flapping, 29,34 spacecraft parachutes, 56-68 cardiovascular fluid mechanics, 69-75 wind-turbine aerodynamics, 76-80 and non-Newtonian flow. 38,81 Some of these applications have been reported in two rece...

Heat Transfer in Non-Newtonian Flows by a Hybrid Immersed Boundary–Lattice Boltzmann and Finite Difference Method

“…The geometrically nonlinear motion for the filament considered here is governed by [38][39][40][41][42][43] …”

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).…”

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

“…Therefore, it can be effectively applied to simulate complex flows and FSI problems where moving boundaries and interfaces are involved. [17][18][19] Since its birth, the DSD/SST method has been extensively used to model complex flows and FSI, such as animal swimming and flight, 29,30,[34][35][36][37][38][39][40][41][42][43][44][45] flag flapping, 2,3 and non-Newtonian flow. 28,46 Body-fitted grid methods could be time consuming and complicated due to the difficulties associated with grid generation in complex geometries and mesh movement/re-generation in large displacement/deformation problems.…”

“…Later, this FSI coupling strategy has been further improved and applied to a variety of biological problems. 8,[11][12][13]29,30,60,61 Though IB method has many advantages in handling computational mesh, it is hard to control the mesh size within the boundary layer. 49 Although both body-fitted and Cartesian grid methods have been extensively applied to FSI problems, seldom effort has been made to compare their performance.…”

“…Here we consider two typical FSI problems: flow-induced vibration of a highly flexible plate in an axial flow and a pitching flexible plate. [1][2][3][4][5][6][7]13,29,30 Previous effort has been made to study the vibration patterns of a highly flexible plate in an axial flow, and both deformation and total force of a pitching flexible plate. For future validation purpose, more data are required, including deformation, vibration patterns, pressure drag, viscous drag and local force distribution.…”