Unified one‐fluid formulation for incompressible flexible solids and multiphase flows: Application to hydrodynamics using the immersed structural potential method (ISPM)

Abstract

SummaryIn this paper, we present a two-dimensional computational framework for the simulation of fluid-structure interaction problems involving incompressible flexible solids and multiphase flows, further extending the application range of classical immersed computational approaches to the context of hydrodynamics. The proposed method aims to overcome shortcomings such as the restriction of having to deal with similar density ratios among different phases or the restriction to solve single-phase flows.First, a variation of classical immersed techniques, pioneered with the immersed boundary method (IBM), is presented by rearranging the governing equations, which define the behaviour of the multiple physics involved. The formulation is compatible with the "one-fluid" formulation for two-phase flows and can deal with large density ratios with the help of an anisotropic Poisson solver. Second, immersed deformable structures and fluid phases are modelled in an identical manner except for the computation of the deviatoric stresses. The numerical technique followed in this paper builds upon the immersed structural potential method developed by the authors, by adding a level set-based method for the capturing of the fluid-fluid interfaces and an interface Lagrangian-based meshless technique for the tracking of the fluid-structure interface. The spatial discretisation is based on the standard marker-and-cell method used in conjunction with a fractional step approach for the pressure/velocity decoupling, a second-order time integrator, and a fixed-point iterative scheme. The paper presents a wide d range of two-dimensional applications involving multiphase flows interacting with immersed deformable solids, including benchmarking against both experimental and alternative numerical schemes.

Full Eulerian deformable solid‐fluid interaction scheme based on building‐cube method for large‐scale parallel computing

“…36 The second-order Adams-Bashforth method is utilized for the temporal discretization of the incompressible mixture equations, and the advection equations of the VOF function and the left Cauchy-Green deformation tensor, respectively. The incompressible mixture Equations (7) and (8) are solved using the fractional step method 37 in which the velocity and the pressure fields are separated. The mixture equation of motion (8) is rewritten as…”

“…In these formulations, an immersed boundary method is used for the communication of quantities between the Eulerian and Lagrangian meshes. Another Lagrangian‐Eulerian approach is the immersed structural potential method (ISPM) . In this method, the solid domain is modeled as a set of Lagrangian particles (integration points), which deform according to the kinematics defined by the background fluid.…”

“…Another Lagrangian-Eulerian approach is the immersed structural potential method (ISPM). [6][7][8] In this method, the solid domain is modeled as a set of Lagrangian particles (integration points), which deform according to the kinematics defined by the background fluid. Other methods such as spatial-domain/space-time (DSD/ST) [9][10][11] or arbitrary Lagrangian-Eulerian methods 12 are able to satisfy the fluid-solid interface conditions more accurately due to the use of body fitted meshes.…”

A three-phase interpenetrating continua approach for wave and porous structure interaction

“…The interface is fully resolved by interface tracking or capturing methods. The most popular approaches of capturing interface are established by Volume of Fluid [15,16,17] and the Level Set method [3,6] Another approach worth mentioning is the particle-based methods, Smoothed…”

A staggered procedure for fluid–object interaction with free surfaces, large rotations and driven by adaptive time stepping

“…The works of [27,46,66] and [22,26] illustrate these methods for unstructured grid formulations based on the finite element method to solve free-surface flows. In [78,80], the level set method is considered using an alternative approach: a fully Eulerian one-fluid formulation. An overview of the different FSI methods with moving boundaries and interfaces is given in [71].…”