A second-order accurate non-intrusive staggered scheme for the interaction of ultra-lightweight rigid bodies with fluid flow

Abstract

This paper presents a staggered scheme with second-order temporal accuracy for fluid-structure interaction problems involving ultra-lightweight rigid bodies. The staggered scheme is based on the Dirichlet-Neumann coupling and is non-intrusive. First, the spectral properties of the staggered scheme are studied and also compared against the monolithic scheme using a linear model problem. Later, the suitability and effectiveness of the staggered scheme for problems involving incompressible flows and lightweight rigid solids are illustrated by using the examples of galloping of a square cylinder and lock-in of a circular cylinder for mass-ratio values as low as 0.01. This is the first time in the literature flow-induced vibrations of rigid bodies with such low mass ratio values are successfully simulated using a staggered scheme. Two different fluid solvers are considered to illustrate the non-intrusive nature of the proposed scheme. Guidelines for choosing the relaxation parameter are also provided. With its iteration-free nature and with a single (relaxation) parameter, the proposed staggered scheme renders itself as an accurate and computationally efficient scheme for fluid-rigid body interaction problems, including those involving lightweight structures.

A comprehensive assessment of accuracy of adaptive integration of cut cells for laminar fluid-structure interaction problems

“…In this work, the coupled FSI problem is solved using a staggered scheme proposed in Dettmer and Perić [7] and Kadapa [16] in which the fluid and solid problems are solved separately, once per time step, using their respective solvers after obtaining the appropriate data from solid and fluid problems, respectively. The CutFEM framework based on hierarchical b-spline grids used in the present work is already published in Dettmer et al [5] and Kadapa et al [17,19,21,22].…”

Insights into the performance of loosely-coupled FSI schemes based on Robin boundary conditions

“…The iterative version of the partitioned FSI scheme based on the force predictor [4,12] that has been recently presented in Dettmer et al [26] is employed for resolving the coupling between fluid and solid sub-problems. The pseudocode for iterative partitioned schemes is presented in Algorithm 1 and Algorithm 2, respectively, for the explicit and implicit treatment of solid velocity.…”

“…Since the ratio of densities of solid and fluid domains is one in both the examples, they pose significant added-mass instabilities for partitioned FSI approaches, and therefore, ideally suitable for demonstration in this work. The numerical framework adopted in this work is the cut-cell based finite element method that has been studied extensively in [12,21,22,27]. The reader is referred mainly to Kadapa et al [22,27] for the application of the framework to FSI problem with flexible structures.…”

“…As per this instability, partitioned approaches in which the fluid-solid coupling is resolved by iterating over individual solvers for fluid and solid sub-problems have a stability limit with respect to the ratio of densities of solid and fluid domains, the thickness of the structure and flexibility of the structure. During the past two decades, significant efforts have been made into understanding these instabilities [1][2][3][4] as well as towards improving the stability limits [4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”

“…For the demonstration, two numerical examples consisting of thick and thin beams in cross-flow in two dimensions are used. The numerical simulation framework used for this study is the cutcell based methodology studied extensively in [12,[20][21][22]. The governing equations and the formulation are presented in Section 2.…”