A consistent and versatile computational approach for general fluid‐structure‐contact interaction problems

In this paper, the in-house code based on the smoothed particle hydrodynamics is proposed to simulate a fluid-solid interaction (FSI) problem. This method is a Lagrangian, mesh-free method and it has a high ability to capture the free surface in two phase flows and also the interface in FSI problems. To compare ofweakly compressible SPH (WCSPH) and incompressible SPH (ISPH) schemes, fluid flow under a hypo-elastic gate is simulated in solid and fluid domains with both methods. At first fluid domain is simulated with ISPH method and solid domain is solved with WCSPH scheme. Another simulation is done with both fluid and solid parts solved with WCSPH method. The results of both methods are in a good agreement with each other and also with other researcher’s results. So it is concluded that it is easier to model the fluid flow with ISPH scheme and the solid part with WCSPH in coupling fluid-solid interaction problems with a good accuracy.

SummarySimulation approaches for fluid‐structure‐contact interaction, especially if requested to be consistent even down to the real contact scenarios, belong to the most challenging and still unsolved problems in computational mechanics. The main challenges are 2‐fold—one is to have a correct physical model for this scenario, and the other is to have a numerical method that is capable of working and being consistent down to a zero gap. Moreover, when analyzing such challenging setups of fluid‐structure interaction, which include contact of submersed solid components, it gets obvious that the influence of surface roughness effects is essential for a physical consistent modeling of such configurations. To capture this system behavior, we present a continuum mechanical model that is able to include the effects of the surface microstructure in a fluid‐structure‐contact interaction framework. An averaged representation for the mixture of fluid and solid on the rough surfaces, which is of major interest for the macroscopic response of such a system, is introduced therein. The inherent coupling of the macroscopic fluid flow and the flow inside the rough surfaces, the stress exchange of all contacting solid bodies involved, and the interaction between fluid and solid are included in the construction of the model. Although the physical model is not restricted to finite element–based methods, a numerical approach with its core based on the cut finite element method, enabling topological changes of the fluid domain to solve the presented model numerically, is introduced. Such a cut finite element method–based approach is able to deal with the numerical challenges mentioned above. Different test cases give a perspective toward the potential capabilities of the presented physical model and numerical approach.

We present a study of Richtmyer–Meshkov flow for elastic materials. This flow, in which a material interface is struck by a shock wave, was originally investigated for gases, where growth of perturbations of the interface is observed. Here we consider two elastic materials in frictionless contact. The governing system of equations comprises conservation laws supplemented by constitutive equations. To analyse it, we linearize the equations around a one-dimensional background solution under the assumption that the perturbation is small. The background problem defines a Riemann problem that is solved numerically; its solution contains transmitted and reflected shock waves in the longitudinal modes. The linearized Rankine–Hugoniot condition provides the interface conditions at the longitudinal and shear waves; the frictionless material interface conditions are also linearized. The resulting equations, a linear system of partial differential equations, is solved numerically using a finite-difference method supplemented by front tracking. In verifying the numerical code, we reproduce growth of the interface in the gas case. For the elastic case, in contrast, we find that the material interface remains bounded: the non-zero shear stiffness stabilizes the flow. In particular, the linear theory remains valid at late time. Moreover, we identify the principal mechanism for the stability of Richtmyer–Meshkov flow for elastic materials: the vorticity deposited on the material interface during shock passage is propagated away by the shear waves, whereas for gas dynamics it stays on the interface.

This article is concerned with a boundary-field equation approach to a class of boundary value problems exterior to a thin domain. A prototype of this kind of problems is the interaction problem with a thin elastic structure. We are interested in the asymptotic behavior of the solution when the thickness of the elastic structure approaches to zero. In particular, formal asymptotic expansions will be developed, and their rigorous justification will be considered. As will be seen, the construction of these formal expansions hinges on the solutions of a sequence of exterior Dirichlet problems, which can be treated by employing boundary element methods. On the other hand, the justification of the corresponding formal procedure requires an independence on the thickness of the thin domain for the constant in the Korn inequality. It is shown that in spite of the reduction of the dimensionality of the domain under consideration, this class of problems are, in general, not singular perturbation problems, because of appropriate interface conditions. ¶Dedicated to Wolfgang L. Wendland on the occasion of his 70th birthday.

In this paper a method was developed for solving the general mixed boundary‐value problem in static elasticity by numerically integrating a system of singular integral equations describing the boundary conditions of the problem, as well as the single‐valuedness of the displacements. The method was adapted to the solution of frictionless contact problems, in the case when one of the contacted bodies contains a crack. The solution of the problem yields not only the stress distribution along the contact zone but also the stress intensity factors at the tips of the crack, as well as the unknown contact length in cases of the praxis, where the contact zone is not assumed infinitesimal. The method was applied with success to the inclusion problem of an infinite cracked plate.

We present a 2D high‐order and easily accessible immersed‐boundary adaptive harmonic polynomial cell (IB‐AHPC) method to solve fully nonlinear wave‐structure interaction problems in marine hydrodynamics using potential‐flow theory. To reduce the total number of cells without losing accuracy, adaptive quad‐tree cell refinements are employed close to the free‐surface and structure boundaries. The present method is simpler to implement than the existing IB‐HPC alternatives, in that it uses standard square cells both in the fluid domain and at the boundaries, thus without having to use the more complex and expensive overlapping grids or irregular cells. The spurious force oscillations on moving structures, which is a known issue for immersed boundary methods (IBMs), are eliminated in this study by solving a separate boundary value problem (BVP) for a Lagrangian acceleration potential. We also demonstrate that solving a similar BVP for the corresponding Eulerian acceleration potential is far less satisfactory due to the involved second derivatives of the velocity potential in the body‐boundary condition, which are very difficult to calculate accurately in an IBM‐based approach. In addition, we present, perhaps for the first time since the HPC method was developed, a linear matrix‐based stability analysis for the time‐domain IB‐AHPC method. The stability analysis is also used in this study as a general guide to design robust and stable numerical algorithms, in particular related to the treatment of boundary conditions close to the intersection between a Dirichlet and a Neumann boundary, which is essential in time‐domain wave‐structure interaction analyses using IBMs. We confirm theoretically through the stability analysis that square cells have the best stability properties. The present method has been verified and validated satisfactorily by various cases in marine hydrodynamics, including a moving structure in an infinite fluid, fully nonlinear wave generation and propagation, and fully nonlinear diffraction and radiation of a ship cross section.

The fluid-structure interaction (FSI) problem plays significant roles in engineering simulations and design. This problem considers the interaction between the fluid domain and structural domain with one-way or two-way data transfer. There are several algorithms to solve the problem, mainly numerical duo to the complexity and nonlinearly. The numerical schemes focus on the modeling method of the coupling interface. However, there are several algorithms that merge the interface in the equations and deal with the domains as a unified set of equations. Future development could include artificial intelligence modeling and the inclusion of more physical domains into the systems.

In this note, we consider the nonzero surface tension Hele—Shaw problem in the presence of a sink when the initial fluid domain is bounded. We show that if the geometric center of the initial domain is not at the sink, either the solution will break down before all the fluid is sucked out or the fluid domain will eventually become unbounded with a zero area. We do not determine the mechanism of the breakdown. It could be caused by topological changes of the fluid domain, by the interface reaching the sink, or perhaps by some other means.

The response of a quartz crystal microbalance (QCM) is considered using a wave equation for the substrate and the Navier-Stokes equations for a finite liquid layer under a slip boundary condition. It is shown that when the slip length to shear wave penetration depth is small, the first-order effect of slip is only present in the frequency response. Importantly, in this approximation the frequency response satisfies an additivity relation with a net response equal to a Kanazawa liquid term plus an additional Sauerbrey “rigid” liquid mass. For the slip length to result in an enhanced frequency decrease compared to a no-slip boundary condition, it is shown that the slip length must be negative so that the slip plane is located on the liquid side of the interface. It is argued that the physical application of such a negative slip length could be to the liquid phase response of a QCM with a completely wetted rough surface. Effectively, the model recovers the starting assumption of additivity used in the trapped mass model for the liquid phase response of a QCM having a rough surface. When applying the slip boundary condition to the rough surface problem, slip is not at a molecular level, but is a formal hydrodynamic boundary condition which relates the response of the QCM to that expected from a QCM with a smooth surface. Finally, possible interpretations of the results in terms of acoustic reflectivity are developed and the potential limitations of the additivity result should vapor trapping occur are discussed.

Molecular dynamics simulations are employed to investigate the Poiseuille flow of NaCl aqueous solution through nanochannels with generic solid walls, with a specific focus on the coupled effects of wall-solution van der Waals interaction (WSI_VdW) energy and surface charge density (δ) on interfacial slip behavior. The results reveal that the contact density (ρc) exhibits a non-monotonic dependence on the δ, characterized by an initial decrease followed by an increase at sufficiently large δ. At low δ, both the fluid velocity and slip length (Ls) are significantly larger under low WSI_VdW energy than under high WSI_VdW energy. This disparity, however, diminishes rapidly with increasing δ. Beyond a critical δ value, the velocity and Ls exhibit minimal variation with further increases in δ and become insensitive to the WSI_VdW energy. The underlying mechanism is elucidated by analyzing the normalized in-plane structure factor S(G1)/S(0). Furthermore, the correlation between slip length and S(G1)/S(0), ρc, and δ is established. It is demonstrated that across a wide range of WSI_VdW energies and δ values, Ls can be accurately described by a single-variable function dependent on S(G1)/S(0), ρc, and δ. This study provides valuable theoretical insights for modeling interfacial slip boundary conditions in electrolyte flows through charged nanochannels.

Finite element master-slave a technique of contact interaction of elastic deformable bodies taking into account friction in a contact zone is realized. The proved from the of view of the solution of extreme tasks with restrictions like inequalities, projective which received the name algorithm of a projection of the next point was used. The model problem of contact interaction of two deformable subdesigns is solved, comparison of results with the data obtained by other authors is carried out.

A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part II: General formulation

It is known that an interface crack between dissimilar elastic solids exhibits oscillatory behavior if the crack tip is assumed to be open with a sharp transition between bonded interface and traction-free crack surfaces [10]. For interface cracks in isotropic solids, Comninou [ 1-4] showed that the peculiar oscillatory behavior, which predicts interpenetration of the crack faces, can be fully eliminated by introducing a zone of frictionless contact between the crack faces behind the crack tip. The effects of crack face contact can not be neglected under shear and/or compression dominated loading, for in that case the contact zone size could become of the same order as the total length of a crack [3,4]. Gautesen and Dundurs [6] solved exactly the integral equations involved in the Comninou formulation. Wang and Choi [8,9] applied the frictionless contact model to interface cracks between laminated composite materials. Wu [12] attempted to apply the frictionless contact model to general anisotropic interface cracks and found that the oscillatory behavior is still present. In this report, we propose a generalized contact model which completely eliminates the oscillatory behavior for interface cracks under arbitrary anisotropy.

Use of the method of manufactured solutions for the verification of conjugate heat transfer solvers

The problem of the hydrodynamic interaction with the arc-shaped bottom-mounted breakwaters is investigated theoretically. The breakwater is assumed to be rigid, thin, impermeable and vertically located in a finite water depth. The fluid domain is divided into two sub-regions of inner and outer by an auxiliary circular interface. Linear theory is assumed and the eigenfunction expansion approach is used to determine the wave field. In order to examine the validity of the theoretical model, the analytical solutions are compared to agree well with published results with the same parameters. Numerical results including wave amplitude, surge pressure, and wave force are presented with different model parameters. The major factors including wave parameters, structure configuration, and water depth that affect the surge pressure, wave forces, and wave amplitudes are discussed and illustrated by some graphs and cloud maps.