TY - JOUR
T1 - Semi-monolithic formulation based on a projection method for simulating fluid–structure interaction problems
AU - Ha, Sang Truong
AU - Choi, Hyoung Gwon
N1 - Publisher Copyright:
© 2023 Elsevier Ltd
PY - 2023/3/15
Y1 - 2023/3/15
N2 - For the simulation of fluid–structure interaction (FSI) problems, the monolithic method provides more robust convergence than the partitioned method but requires solving a larger matrix for a saddle-point problem that is difficult to precondition. We extend the existing semi-implicit method to propose a new semi-monolithic method for FSI simulation that uses a velocity boundary equation of a pressure Poisson equation so that only the pressure variables of the fluid domain are coupled with the displacement variables of the solid domain in a monolithic manner. The fluid domain is solved by employing a fractional four-step method for the incompressible Navier–Stokes equations based on an arbitrary Lagrangian–Eulerian (ALE) formulation, and the solid domain is solved by an updated Lagrangian method for simulating large nonlinear deformations. We applied the proposed method to 2D/3D benchmark problems with various time steps and density ratios, and the results confirmed that FSI problems with not only a strong added-mass effect but also a large deformation are simulated well. The proposed method is faster than the existing monolithic method because it solves a smaller matrix whose diagonal blocks are diagonally dominant matrices, which are much easier to precondition.
AB - For the simulation of fluid–structure interaction (FSI) problems, the monolithic method provides more robust convergence than the partitioned method but requires solving a larger matrix for a saddle-point problem that is difficult to precondition. We extend the existing semi-implicit method to propose a new semi-monolithic method for FSI simulation that uses a velocity boundary equation of a pressure Poisson equation so that only the pressure variables of the fluid domain are coupled with the displacement variables of the solid domain in a monolithic manner. The fluid domain is solved by employing a fractional four-step method for the incompressible Navier–Stokes equations based on an arbitrary Lagrangian–Eulerian (ALE) formulation, and the solid domain is solved by an updated Lagrangian method for simulating large nonlinear deformations. We applied the proposed method to 2D/3D benchmark problems with various time steps and density ratios, and the results confirmed that FSI problems with not only a strong added-mass effect but also a large deformation are simulated well. The proposed method is faster than the existing monolithic method because it solves a smaller matrix whose diagonal blocks are diagonally dominant matrices, which are much easier to precondition.
KW - Fluid–structure interaction
KW - Large deformation
KW - Navier–Stokes equations
KW - Pressure Poisson equation
KW - Semi-monolithic method
UR - http://www.scopus.com/inward/record.url?scp=85147541611&partnerID=8YFLogxK
U2 - 10.1016/j.camwa.2023.01.029
DO - 10.1016/j.camwa.2023.01.029
M3 - Article
AN - SCOPUS:85147541611
SN - 0898-1221
VL - 134
SP - 207
EP - 224
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
ER -