A heterogeneous flow model based on DD method for free surface fluid-structure interaction problems

• Published in: International journal for numerical methods in fluids 2014-02, Vol.74 (4), p.292-312
• Main Authors: Zhang, Yi, Pin, Facundo Del, Yim, Solomon C.
• Format: Article
• Language: English
• Subjects: boundary element; Computational fluid dynamics; Computer simulation; domain decomposition; finite element; Finite element method; Fluid flow; Fluids; free surface; Mathematical analysis; Mathematical models; Navier-Stokes equations; potential flow; viscous flows
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.3852

SUMMARYAn efficient heterogeneous flow model that combines incompressible viscous flow and potential flow(PF)(both) with free‐surface boundaries for fluid–structure interaction(FSI) problems was developed and solved numerically. In the model, the near field(viscous) fluid subdomain of the FSI simulation is described by the Navier–Stokes equations(NSE), whereas the far field(inviscid) subdomain is described by PF. This method is particularly suitable for modeling a large fluid domain while avoid solving the NSE at the far field, where the inviscid flow assumption is appropriate and adopting a simplified(e.g., PF) flow description reduces computing cost. Numerically, the NSE are solved using a FEM, and the PF is solved using a BEM. Free surface tracking is achieved through a hybrid level set method for the NSE and the mixed Eulerian–Lagrangian method for the PF. The coupling is based on a non‐overlapping DD method similar to the Dirichlet–Neumann method. At the interface between the two flow model subdomains, velocity and pressure are matched to ensure continuity of the corresponding variables at the common boundary. In this framework of the heterogeneous DD method, an explicit scheme is developed and implemented. The relation between this scheme and the classical Dirichlet–Neumann method for a homogeneous problem is revealed. Numerical examples demonstrating the capability of the method to model nonlinear wave phenomena and FSI problems with flexible structures are presented. Copyright © 2013 John Wiley & Sons, Ltd. Potential flow (subdomain Ω2) and viscous flow (subdomain Ω1) models, both with free surface, are coupled to model the far field and near field, respectively, in fluid–structure interaction problems, based on a heterogeneous DD framework, following the philosophy of the Dirichlet–Neumann method. Matching condition of velocity and pressure are applied at the nonoverlapping interface G, for both explicit and implicit schemes are introduced. The explicit staggered scheme is implemented for numerical examples.