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In this paper, the linear model of Moore–Gibson–Thompson thermoporoelasticity is considered and the governing equations of motion and steady vibrations are given. The basic system of equations of steady vibrations with respect to the displacement vector, the changes of temperature and fluid pressure are proposed. Then the radiation conditions are established and Green’s first identity is obtained. Finally, on the basis of this identity, the uniqueness theorems for classical solutions of the boundary value problems of steady vibrations in the theory of MGT thermoporoelaticity are proved. [ABSTRACT FROM AUTHOR]

The effects of a harmonically exciting monopole source on an infinitely long cylindrical cavity embedded entirely within a fluid-saturated poroelastic formation of infinite extent are examined theoretically. It is assumed that the source is located outside the cavity at a specified distance from the borehole axis. The magnitudes of the hoop and radial stresses beside the pore pressures exerted on the interface and inside the porous medium surrounding the borehole are calculated and discussed. Biot's poroelastic modeling along with three types of boundary conditions for the cylindrical interface including the ideal fluid, empty borehole, and rigid inclusion with a hard boundary is employed for the analysis. Utilizing a proper translational addition theorem for expressing the incident spherical wave in terms of cylindrical wave expansions, the proposed boundary conditions at the interface are satisfied. Stresses are formulated by means of wave potential functions in a three-dimensional (3D) manner. The effects of the frequency and the radial distance between the source and borehole on the induced stresses are examined for the first cylindrical modes over frequency spectra. Two permeability conditions for the interface and three types of soils for the porous formation are considered throughout the analysis. To give an overall outline of the study, a numerical example is presented. The results clearly indicate that the distance is a key parameter and has considerable effects on the induced stress values. In addition, the interface permeability condition and soil characteristics play an important role in determining the dynamic response of the borehole. Finally, the obtained results are compared with the relevant analyses existing in the literature for some limit cases, and good agreement is achieved. [ABSTRACT FROM AUTHOR]

We investigate problems of convection with double diffusion in a saturated porous medium, where the saturating fluid is one of viscoelastic type, being specifically a Navier–Stokes–Voigt fluid, or a Kelvin–Voigt fluid. The double diffusion problem is analysed for a porous medium with Darcy and Brinkman terms, for a Navier–Stokes–Voigt fluid, and then for a general Kelvin–Voigt fluid of order N. The case where N has the value one is analysed in detail. We also propose a theory where the fluid and solid temperatures may be different, i.e. a local thermal non-equilibrium (LTNE) theory for a porous medium saturated by a Kelvin–Voigt fluid. A further generalization to include heat transfer by a model due to C. I. Christov is analysed in the context of Kelvin–Voigt fluids in porous media. Finally, we examine the question of whether a Navier–Stokes–Voigt theory should be used for nonlinear flows, or whether a suitable objective derivative is required. [ABSTRACT FROM AUTHOR]

We consider the aeroelastic simulation of flexible mechanical structures submerged in subsonic fluid flows at low Mach numbers. The nonlinear kinematics of flexible bodies are described in the total Lagrangian formulation and discretized by finite elements. The aerodynamic loads are computed using the unsteady vortex-lattice method wherein a free wake is tracked over time. Each implicit time step in the dynamic simulation then requires solving a nonlinear equation system in the structural variables with additional aerodynamic load terms. Our focus here is on the efficient numerical solution of this system by accelerating the Newton algorithm. The particular structure of the aeroelastic nonlinear system suggests the structural derivative as an approximation to the full derivative in the linear Newton system. We investigate and compare two promising algorithms based on this approximation, a quasi-Newton type algorithm and a novel inexact Newton algorithm. Numerical experiments are performed on a flexible plate and on a wind turbine. Our computational results show that the approximation can indeed accelerate the Newton algorithm substantially. Surprisingly, the theoretically preferable inexact Newton algorithm is much slower than the quasi-Newton algorithm, which motivates further research to speed up derivative evaluations. [ABSTRACT FROM AUTHOR]

Liquid Crystal Elastomers (LCEs) are responsive materials that undergo significant, reversible deformations when exposed to external stimuli such as light, heat, and humidity. Light actuation, in particular, offers versatile control over LCE properties, enabling complex deformations. A notable phenomenon in LCEs is self-oscillation under constant illumination. Understanding the physics underlying this dynamic response, and especially the role of interactions with a surrounding fluid medium, is still crucial for optimizing the performance of LCEs. In this study, we have developed a multi-physics fluid-structure interaction model to explore the self-oscillation phenomenon of immersed LCE beams exposed to light. We consider a beam clamped at one end, originally vertical, and exposed to horizontal light rays of constant intensity focused near the fixed edge. Illumination causes the beam to bend towards the light due to a temperature gradient. As the free end of the beam surpasses the horizontal line through the clamp, self-shadowing induces cooling, initiating the self-oscillation phenomenon. The negative feedback resulting from self-shadowing injects energy into the system, with sustained self-oscillations in spite of the energy dissipation in the surrounding fluid. Our investigation involves parametric studies exploring the impact of beam length and light intensity on the amplitude, frequency, and mode of oscillation. Our findings indicate that the self-oscillation initiates above a certain critical light intensity, which is length-dependent. Also, shorter lengths induce oscillations in the beam with the first mode of vibration, while increasing the length changes the elasticity property of the beam and triggers the second mode. Additionally, applying higher light intensity may trigger composite complex modes, while the frequency of oscillation increases with the intensity of the light if the mode of oscillation remains constant. [ABSTRACT FROM AUTHOR]

The narrow attenuation bands of traditional marine structures have long been a challenge in mitigating water waves. In this paper, a metastructure (MS) composed of floating periodic pontoons is proposed for broadband water wave attenuation. The interaction of surface gravity waves with the MS is investigated using linear wave theory. The potential solutions of water waves by the MS with a finite array are developed by using the eigenfunction expansion matching method (EEMM), and the band structure of the MS is calculated by the transfer matrix method (TMM), in which the evanescent modes of waves are considered. The solution is verified against the existing numerical result for a special case. Based on the present solution, the association between Bragg resonance reflection and Bloch bandgaps is examined, the effects of pontoon geometry are analyzed, and the comparison between floating MS and bottom-mounted periodic structures is conducted. A computational fluid dynamics (CFD) model is further developed to assess the structures in practical fluid environments, and the floating MS presents excellent wave attenuation performance. The study presented here may provide a promising solution for protecting the coast and offshore structures. [ABSTRACT FROM AUTHOR]

A prototype model for a Fluid–Structure interaction is considered. We aim to stabilize [enhance stability of] the model by having access only to a portion of the state. Toward this goal we shall construct a compensator-based Luenberger design, with the following two goals: (1) reconstruct the original system asymptotically by tracking partial information about the full state, (2) stabilize the original unstable system by feeding an admissible control based on a system which is obtained from the compensator. The ultimate result is boundary control/stabilization of partially observed and originally unstable fluid–structure interaction with restricted information on the current state and without any knowledge of the initial condition. This prevents applicability of known methods in either open-loop or closed loop stabilization/control. [ABSTRACT FROM AUTHOR]

The identification of optimally sparse Taylor partial derivatives presents a new opportunity in efficient nonlinear model reduction for complex aeroelastic systems. Unfortunately, for this class of reduced order model (ROM), the robustness that is observed in the linear regime to parameters including; dynamic pressure, control hinge linear stiffness, or even freeplay, can be quickly compromised in the nonlinear regime. In this paper, the nonlinear sensitivity of selected critical parameters is addressed by interpolating a library of nonlinear unsteady aerodynamic ROMs across a compact subspace in dynamic pressure and freeplay magnitude. The ROM, based on Lagrange interpolation of sparse higher-order Taylor partial derivatives, demonstrates excellent precision in modelling high amplitude transonic limit cycle oscillations for an all-movable wing with freeplay, capturing the LCO region (up to 96% of the linear flutter boundary), and for a range of freeplay values. [ABSTRACT FROM AUTHOR]

We propose and analyze a simple model for the evolution of an immersed, inextensible filament which incorporates linear viscoelastic effects of the surrounding fluid. The model is a closed-form system of equations along the curve only which includes a 'memory' term due to viscoelasticity. For a planar filament, given a forcing in the form of a preferred curvature, we prove well-posedness of the fiber evolution as well as the existence of a unique time-periodic solution in the case of time-periodic forcing. Moreover, we obtain an expression for the swimming speed of the filament in terms of the preferred curvature. The swimming speed depends in a complicated way on the viscoelastic parameters corresponding to the fluid relaxation time and additional polymeric viscosity. We study this expression in detail, accompanied by numerical simulations, and show that this simple model can capture complex effects of viscoelasticity on swimming. In particular, the viscoelastic swimmer is shown to be faster than its Newtonian counterpart in some situations and slower in others. Strikingly, we even find an example where viscoelastic effects may lead to a reversal in swimming direction from the Newtonian setting, although this occurs when the displacement for both the Newtonian and viscoelastic swimmers is practically negligible. [ABSTRACT FROM AUTHOR]

In this paper, the coupled linear theory of thermoelasticity for nanomaterials with triple porosity is considered in which the combination of Darcy's law and the volume fraction concept for three levels of pores (macro-, meso- and micropores) is provided. The 3D basic boundary value problems (BVPs) of steady vibrations of this theory are formulated and these BVPs are investigated using the potential method (boundary integral equation method) and the theory of singular integral equations. Namely, the formula of integral representation of regular vectors is obtained. The surface (single-layer and double-layer) and volume potentials are introduced and their basic properties are given. Some useful singular integral operators are defined for which Noether's theorems are valid. The symbolic determinants and indexes of these operators are calculated. The BVPs of steady vibrations are reduced to the equivalent singular integral equations. Finally, with the help of the potential method, we prove the existence theorems for classical solutions of the aforementioned BVPs. [ABSTRACT FROM AUTHOR]

A second-order multiscale theory based on the concept of a Representative Volume Element (RVE) is proposed to link a classical poromechanical model at the RVE scale to a high-order poromechanical model at the macro-scale in the context of finite-strain kinematics. The proposed theory is carefully derived from the Principle of Multiscale Virtual Power, which is a generalization of the Hill-Mandel Principle of Macrohomogeneity. The coupled governing equations of the low-scale and the homogenization rules for the flux and stress-like quantities are obtained by means of standard variational arguments. The main theoretical result is that the minimally constrained space for the pore pressure field allows for non-zero net fluid flow across the RVE boundaries, unlike first-order theories. The direct consequence of this finding is that the present theory can be consistently applied in cases where the low-scale (RVE level) exhibits substantial volume changes (swelling or shrinking) as a consequence of the evolution of the macro-scale kinematics. Details of formulation development and expression for the homogenized tangent operators are presented for those interested in the computational implementation of the model. [ABSTRACT FROM AUTHOR]

In this paper, we focused on a one-dimensional elastic system with a double porosity structure and frictional damping acting on both porous equations. We introduce two stability numbers χ 0 {\chi_{0}} and χ 1 {\chi_{1}} and prove that the solution of the system decays exponentially provided that χ 0 = 0 {\chi_{0}=0} and χ 1 ≠ 0 {\chi_{1}\neq 0} . Otherwise, we prove the absence of exponential decay. Our results improve the results of [N. Bazarra, J. R. Fernández, M. C. Leseduarte, A. Magaña and R. Quintanilla, On the thermoelasticity with two porosities: Asymptotic behaviour, Math. Mech. Solids 24 2019, 9, 2713–2725] and [A. Nemsi and A. Fareh, Exponential decay of the solution of a double porous elastic system, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 83 2021, 1, 41–50]. [ABSTRACT FROM AUTHOR]

We consider numerical shape optimization of a fluid–structure interaction model. The constrained system involves multiscale coupling of a two-dimensional unsteady Navier–Stokes equation and a one-dimensional ordinary differential equation for fluid flows and structure, respectively. We derive shape gradients for both objective functionals of least-squares type and energy dissipation. The state and adjoint state equations are numerically solved on the time-dependent domains using the Arbitrary-Lagrangian–Eulerian method. Numerical results are presented to illustrate effectiveness of algorithms. [ABSTRACT FROM AUTHOR]

Motivated by a design of a vertical axis wind turbine, we present a theory of dynamical similarity for mechanical systems consisting of interacting elastic solids, rigid bodies and incompressible fluids. Throughout, we focus on the geometrically nonlinear case. We approach the analysis by analyzing the equations of motion: we ask that a change of variables take these equations and mutual boundary conditions to themselves, while allowing a rescaling of space and time. While the disparity between the Eulerian and Lagrangian descriptions might seem to limit the possibilities, we find numerous cases that apparently have not been identified, especially for stiff nonlinear elastic materials (defined below). The results appear to be particularly adapted to structures made with origami design methods, where the tiles are allowed to deform isometrically. We collect the results in tables and discuss some particular numerical examples. [ABSTRACT FROM AUTHOR]

Mathematical models of vibration devices intended for intensifying technological processes are considered. Mathematical models are initial-boundary-value problems for coupled systems of partial differential equations for hydrodynamic functions and deformation functions of elastic elements. We examine the dynamics and dynamic stability of elastic elements. The study of dynamics is based of the Bubnov–Galerkin method. The study of dynamic stability is based on the construction of positive definite Lyapunov-type functionals. [ABSTRACT FROM AUTHOR]

The dynamic model of a bistable laminated composite shell simply supported by four corners is further developed to investigate the resonance responses and chaotic behaviors. The existence of the 1:1 resonance relationship between two order vibration modes of the system is verified. The resonance response of this class of bistable structures in the dynamic snap-through mode is investigated, and the four-dimensional (4D) nonlinear modulation equations are derived based on the 1:1 internal resonance relationship by means of the multiple scales method. The Hopf bifurcation and instability interval of the amplitude frequency and force amplitude curves are analyzed. The discussion focuses on investigating the effects of key parameters, e.g., excitation amplitude, damping coefficient, and detuning parameters, on the resonance responses. The numerical simulations show that the foundation excitation and the degree of coupling between the vibration modes exert a substantial effect on the chaotic dynamics of the system. Furthermore, the significant motions under particular excitation conditions are visualized by bifurcation diagrams, time histories, phase portraits, three-dimensional (3D) phase portraits, and Poincare maps. Finally, the vibration experiment is carried out to study the amplitude frequency responses and bifurcation characteristics for the bistable laminated composite shell, yielding results that are qualitatively consistent with the theoretical results. [ABSTRACT FROM AUTHOR]

A novel method is presented for explicitly solving inhomogeneous initial-boundary-value problems (IBVPs) on the half-line for a well-known coupled system of evolution partial differential equations. The so-called double-diffusion model, which is based on a simple, yet general, inhomogeneous diffusion configuration, describes accurately several important physical and mechanical processes and thus emerges in miscellaneous applications, ranging from materials science, heat-mass transport and solid–fluid dynamics, to petroleum and chemical engineering. For instance, it appears in nanotechnology and its inhomogeneous version has recently appeared in the area of lithium-ion rechargeable batteries. Our approach is based on the extension of the unified transform (also called the Fokas method), so that it can be applied to systems of coupled equations. First, we derive formally effective solution representations and then justify a posteriori their validity rigorously. This includes the reconstruction of the prescribed initial and boundary conditions, which requires careful analysis of the various integral terms appearing in the formulae, proving that they converge in a strictly defined sense. The novel solution formulae are also utilized to rigorously deduce the solution's regularity properties near the boundaries of the spatiotemporal domain. In particular, we prove uniform convergence of the solution to the data, its rapid decay at infinity as well as its smoothness up to (and beyond) the boundary axes, provided certain data compatibility conditions at the quarter-plane corner are satisfied. As a sample of important applications of our analysis and investigation of the boundary behavior of the solution and its derivatives, we both prove a novel uniqueness theorem and construct a 'non-uniqueness counterexample'. These supplement the preceding 'constructive existence' result, within the framework of well-posedness. Moreover, one of the advantages of the unified transform is that it yields representations which are defined on contours in the complex Fourier λ -plane, which exhibit exponential decay for large values of λ . This important characteristic of the solutions is expected to allow for an efficient numerical evaluation; this is envisaged in future numerical-analytic investigations. The new formulae and the findings reported herein are also expected to find utility in the study of questions pertaining to well-posedness for nonlinear counterparts too. In addition, our rigorous approach can be extended to IBVPs for other significant models of mathematical physics and potentially also to higher-dimensional and variable-coefficient cases. [ABSTRACT FROM AUTHOR]

We consider a viscous incompressible fluid interacting with a linearly elastic shell of Koiter type which is located at some part of the boundary. Recently models with stochastic perturbation in the shell equation have been proposed in the literature but only analysed in simplified cases. We investigate the full model with transport noise, where (a part of) the boundary of the fluid domain is randomly moving in time. We prove the existence of a weak martingale solution to the underlying system. [ABSTRACT FROM AUTHOR]

We propose, analyse and implement a virtual element discretisation for an interfacial poroelasticity/elasticity consolidation problem. The formulation of the time–dependent poroelasticity equations uses displacement, fluid pressure and total pressure, and the elasticity equations are written in displacement-pressure formulation. The construction of the virtual element scheme does not require Lagrange multipliers to impose the transmission conditions (continuity of displacement and total traction, and no-flux for the fluid) on the interface. We show the stability and convergence of the virtual element method for different polynomial degrees, and the error bounds are robust with respect to delicate model parameters (such as Lamé constants, permeability, and storativity coefficient). Finally we provide some simple numerical examples that illustrate the properties of the scheme. [ABSTRACT FROM AUTHOR]

We address a quasi-stationary fluid–structure interaction problem coupled with cell reactions and growth, which comes from the plaque formation during the stage of the atherosclerotic lesion in human arteries. The blood is modeled by the incompressible Navier-Stokes equation, while the motion of vessels is captured by a quasi-stationary equation of nonlinear elasticity. The growth happens when both cells in fluid and solid react, diffuse and transport across the interface, resulting in the accumulation of foam cells, which are exactly seen as the plaques. Via a fixed-point argument, we derive the local well-posedness of the nonlinear system, which is sustained by the analysis of decoupled linear systems.

The divergence free velocity field for a flow in the annulus between concentric circular pipes with a moving lateral boundary is studied. A dependence of velocity components on the domain deformation is determined. [ABSTRACT FROM AUTHOR]

We use the Stroh sextic formalism for anisotropic elasticity and Muskhelishvili’s complex variable formulation for isotropic elasticity to derive a full-field closed-form solution to the generalized plane strain problem of an elliptical incompressible liquid inclusion embedded in an infinite anisotropic elastic matrix subjected to a line force and a line dislocation. An explicit expression for the internal uniform hydrostatic tension within the liquid inclusion is obtained. Furthermore, in the case when the line force and line dislocation approach the elliptical liquid–solid interface, we develop a real-form solution for the internal uniform hydrostatic tension in terms of the Barnett–Lothe tensors for the matrix. [ABSTRACT FROM AUTHOR]

We consider a suspension of spherical inertialess particles in a Stokes flow on the torus T 3 . The particles perturb a linear extensional flow due to their rigidity constraint. Due to the singular nature of this perturbation, no mean-field limit for the behavior of the particle orientation can be valid. This contrasts with widely used models in the literature such as the FENE and Doi models and similar models for active suspensions. The proof of this result is based on the study of the mobility problem of a single particle in a non-cubic torus, which we prove to exhibit a nontrivial coupling between the angular velocity and a prescribed strain. [ABSTRACT FROM AUTHOR]

We study the interaction of an incompressible fluid in two dimensions with an elastic structure yielding the moving boundary of the physical domain. The displacement of the structure is described by a linear viscoelastic beam equation. Our main result is the existence of a unique global strong solution. Previously, only the ideal case of a flat reference geometry was considered such that the structure can only move in vertical direction. We allow for a general geometric set-up, where the structure can even occupy the complete boundary. Our main tool—being of independent interest—is a maximal regularity estimate for the steady Stokes system in domains with minimal boundary regularity. In particular, we can control the velocity field in W 2 , 2 in terms of a forcing in L 2 provided the boundary belongs roughly to W 3 / 2 , 2. This is applied to the momentum equation in the moving domain (for a fixed time) with the material derivative as right-hand side. Since the moving boundary belongs a priori only to the class W 2 , 2 , known results do not apply here as they require a C 2 -boundary. [ABSTRACT FROM AUTHOR]

We propose a new Cahn–Hilliard phase field model coupled to incompressible viscoelasticity at large strains, obtained from a diffuse interface mixture model and formulated in the Eulerian configuration. A new kind of diffusive regularization, of Allen–Cahn type, is introduced in the transport equation for the deformation gradient, together with a regularizing interface term depending on the gradient of the deformation gradient in the free energy density of the system. The designed regularization preserves the dissipative structure of the equations. We obtain the global existence of a weak solution in three space dimensions and for generic nonlinear elastic energy densities with polynomial growth, comprising the relevant cases of polyconvex Mooney–Rivlin and Ogden elastic energies. Also, our analysis considers elastic free energy densities which depend on the phase field variable and which can possibly degenerate for some values of the phase field variable. We also propose two kinds of unconditionally energy stable finite element approximations of the model, based on convex splitting ideas and on the use of a scalar auxiliary variable respectively, proving the existence and stability of discrete solutions. We finally report numerical results for different test cases with shape memory alloy type free energy, showing the interplay between phase separation and finite elasticity in determining the topology of stationary states with pure phases characterized by different elastic properties. [ABSTRACT FROM AUTHOR]

We propose in this paper a new nonlinear mathematical model of an oscillating water column (OWC). The one-dimensional shallow water equations in the presence of this device are reformulated as a transmission problem related to the interaction between waves and a fixed partially immersed structure. By imposing the conservation of the total fluid-OWC energy in the non-damped scenario, we are able to derive a transmission condition that involves a time-dependent air pressure inside the chamber of the device, instead of a constant atmospheric pressure as in Bocchi et al. (ESAIM Proc Surv 70:68–83, 2021). We then show that the transmission problem can be reduced to a quasilinear hyperbolic initial boundary value problem with a semi-linear boundary condition determined by an ODE depending on the trace of the solution to the PDE at the boundary. Local well-posedness for general problems of this type is established via an iterative scheme by using linear estimates for the PDE and nonlinear estimates for the ODE. [ABSTRACT FROM AUTHOR]

A mechanical interaction of compressible viscoelastic fluids with viscoelastic solids in Kelvin–Voigt rheology using the concept of higher-order (so-called 2nd-grade multipolar) viscosity is investigated in a quasistatic variant. The no-slip contact between fluid and solid is considered and the Eulerian-frame return-mapping technique is used for both the fluid and the solid models, which allows for a "monolithic" formulation of this fluid–structure interaction problem. Existence and a certain regularity of weak solutions is proved by a Schauder fixed-point argument combined with a suitable regularization. [ABSTRACT FROM AUTHOR]

We study numerical algorithms for solving Biot’s model. Based on a three-field reformulation, we present some algorithms that are inspired by the work of Chaabane et al. (Comput Math Appl 75(7):2328–2337) and Lee (Unconditionally stable second order convergent partitioned methods for multiple-network poroelasticity , 2019) for decoupling the computation of Biot’s model. A new theoretical framework is developed to analyze the algorithms. Considering a uniform temporal discretization, these algorithms solve the coupled model on the first time level. On the remaining time levels, one algorithm solves a reaction-diffusion subproblem first and then solves a generalized Stokes subproblem. Another algorithm reverses the order of solving the two subproblems. Our algorithms manage to decouple the numerical computation of the coupled system while retaining the convergence properties of the original coupled algorithm. Theoretical analysis is conducted to show that these algorithms are unconditionally stable and optimally convergent. Numerical experiments are also carried out to validate the theoretical analysis and demonstrate the advantages of the proposed algorithms. [ABSTRACT FROM AUTHOR]

We study the equilibrium configurations of a possibly asymmetric fluid–structure interaction problem. The fluid is confined in a bounded planar channel and is governed by the stationary Navier–Stokes equations with laminar inflow and outflow. A body is immersed in the channel and is subject to both the lift force from the fluid and to some external elastic force. Asymmetry, which is motivated by natural models, and the possibly non-vanishing velocity of the fluid on the boundary of the channel require the introduction of suitable assumptions to prevent collisions of the body with the boundary. With these assumptions at hand, we prove that for sufficiently small inflow/outflow there exists a unique equilibrium configuration. Only if the inflow, the outflow and the body are all symmetric, the configuration is also symmetric. A model application is also discussed. [ABSTRACT FROM AUTHOR]

We consider the motion of a compressible viscous fluid containing a moving rigid body confined to a planar domain Ω ⊂ R 2 . The main result states that the influence of the body on the fluid is negligible if (i) the diameter of the body is small and (ii) the fluid is nearly incompressible (the low Mach number regime). The specific shape of the body as well as the boundary conditions on the fluid–body interface are irrelevant and collisions with the boundary ∂ Ω are allowed. The rigid body motion may be enforced externally or governed solely by its interaction with the fluid. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a coupled system modeled by fluid and thermoelastic plate, while the heat effects are modeled by the Cattaneo's law giving rise to a "second sound" effect. We proved that the coupled system admits a unique global mild solution. Furthermore, we construct the second-order energy to control the term ‖ ∇ θ ‖ L 2 (Γ 0) so as to establish the exponential decay of the solutions. [ABSTRACT FROM AUTHOR]

The flow field induced by internal solitary waves (ISWs) is peculiar wherein water motion occurs in the whole water depth, and the strong shear near the pycnocline can be generated due to the opposite flow direction between the upper and lower layers, which is a potential threat to marine risers. In this paper, the flow field of ISWs is obtained with the Korteweg-de Vries (KdV) equation for a two-layer fluid system. Then, a linear analysis is performed for the dynamic response of a riser with its two ends simply supported under the action of ISWs. The explicit expressions of the deflection and the moment of the riser are deduced based on the modal superposition method. The applicable conditions of the theoretical expressions are discussed. Through comparisons with the finite element simulations for nonlinear dynamic responses, it is proved that the theoretical expressions can roughly reveal the nonlinear dynamic response of risers under ISWs when the approximation for the linear analysis is relaxed to some extent. [ABSTRACT FROM AUTHOR]

Wetting of a liquid droplet on another liquid substrate is governed by the well-known Neumann equations. The present work aims to develop an explicit modified version of the Neumann equations for axisymmetric wetting of a liquid droplet on a highly stretched elastic membrane of non-zero bending rigidity. An explicit modified form of the Neumann equations is derived to determine the two contact angles, which is reduced to Young's equation for a liquid droplet on a rigid membrane or to the Neumann equations for a liquid droplet on another liquid substrate. Further implications of the modified Neumann equations are examined by comparison with some previous results reported in the recent literature, particularly considering the ranges of material and geometrical parameters of the liquid droplet-membrane system which have not been recently addressed in the literature. [ABSTRACT FROM AUTHOR]

This paper is concerned with the inverse scattering of acoustic waves by an unbounded periodic elastic medium in the three-dimensional case. A novel uniqueness theorem is proved for the inverse problem of recovering a bi-periodic interface between acoustic and elastic waves using the near-field data measured only from the acoustic side of the interface, corresponding to a countably infinite number of quasi-periodic incident acoustic waves. The proposed method depends only on a fundamental a priori estimate established for the acoustic and elastic wave fields and a new mixed-reciprocity relation established in this paper for the solutions of the fluid-solid interaction scattering problem. [ABSTRACT FROM AUTHOR]

This article presents a variational and numerical analysis for a thermal fluid–elastic structure interaction problem related to the blood flow through a vessel. We prove the existence and the uniqueness of the weak solution to the mathematical model associated with this physical problem and we establish some estimates that give the regularity for the unknown functions. Since the variational problem introduced in order to obtain these results does not provide enough regularity in the elastic domain, we approximate it with a family of viscoelastic problems, depending on a small parameter ε . The viscoelastic problems contain an additional term that corresponds to the regularity “uncovered” by the initial variational problem. This approximation is justified by an error estimate theorem, followed by a convergence result. We associate to any viscoelastic problem a numerical scheme. The additional viscoelastic term allows us to establish suitable estimates for the solution to the numerical scheme, used for obtaining stability properties. Relying on these properties, we prove the convergence of the numerical scheme to the viscoelastic problem. [ABSTRACT FROM AUTHOR]

Due to the influence of deep-sea environment, deep-sea sediments are usually heterogeneous, and their moduli of elasticity and density change as depth changes. Combined with the characteristics of deep-sea sediments, the thermo-hydro-mechanical coupling dynamic response model of heterogeneous saturated porous sediments can be established to study the influence of elastic modulus, density, frequency, and load amplitude changes on the model. Based on the Green-Lindsay generalized thermoelasticity theory and Darcy's law, the thermo-hydro-mechanical coupled dynamic response model and governing equations of heterogeneous deep-sea sediments with nonlinear elastic modulus and density are established. The analytical solutions of dimensionless vertical displacement, vertical stress, excess pore water pressure, and temperature are obtained by means of normal modal analysis, which are depicted graphically. The results show that the changes of elastic modulus and density have few effects on vertical displacement, vertical stress, and temperature, but have great effects on excess pore water pressure. When the mining machine vibrates, the heterogeneity of deep-sea sediments has great influence on vertical displacement, vertical stress, and excess pore water pressure, but has few effects on temperature. In addition, the vertical displacement, vertical stress, and excess pore water pressure of heterogeneous deep-sea sediments change more gently. The variation trends of physical quantities for heterogeneous and homogeneous deep-sea sediments with frequency and load amplitude are basically the same. The results can provide theoretical guidance for deep-sea mining engineering construction. [ABSTRACT FROM AUTHOR]

In this paper we consider a fluid-structure interaction problem given by the steady Navier Stokes equations coupled with linear elasticity taken from (Lasiecka et al. in Nonlinear Anal 44:54–85, 2018). An elastic body surrounded by a liquid in a rectangular domain is deformed by the flow which can be controlled by the Dirichlet boundary condition at the inlet. On the walls along the channel homogeneous Dirichlet boundary conditions and on the outflow boundary do-nothing conditions are prescribed. We recall existence results for the nonlinear system from that reference and analyze the control to state mapping generalizing the results of (Wollner and Wick in J Math Fluid Mech 21:34, 2019) to the setting of the nonlinear Navier-Stokes equation for the fluid and the situation of mixed boundary conditions in a domain with corners. [ABSTRACT FROM AUTHOR]

The main purpose of this work presents some explicit solutions of boundary value problems in the theory of thermoelasticity for solids with double porosity. Special representations are constructed for the general solution of basic equations. They are expressed through of elementary functions, whose properties are well known. Applying these concepts, in the proposed work, the boundary value problems of statics of the theory of thermoelasticity for an elastic circle with double porosity are solved explicitly, in the form of absolutely and uniformly converging series. [ABSTRACT FROM AUTHOR]

In this paper, we study a nonlinear interaction problem between compressible viscous fluids and plates. For this problem, we introduce relative entropy and relative energy inequality for the finite energy weak solutions (FEWS). First, we prove that for all FEWS, the structure displacement enjoys improved regularity by utilizing the dissipation effects of the fluid onto the structure and that all FEWS satisfy the relative energy inequality. Then, we show that all FEWS enjoy the weak-strong uniqueness property, thus extending the classical result for compressible Navier–Stokes system to this fluid-structure interaction problem. [ABSTRACT FROM AUTHOR]

In this work, we numerically study a problem including several dissipative mechanisms. A particular case involving the symmetry of the coupling matrix and three mechanisms is considered, leading to the exponential decay of the corresponding solutions. Then, a fully discrete approximation of the general case in two dimensions is introduced by using the finite element method and the implicit Euler scheme. A priori error estimates are obtained and the linear convergence is derived under some appropriate regularity conditions on the continuous solution. Finally, some numerical simulations are performed to illustrate the numerical convergence and the behavior of the discrete energy depending on the number of dissipative mechanisms. [ABSTRACT FROM AUTHOR]

This paper develops a new coupled enriched Galerkin (EG) scheme for Biot’s poroelasticity model based on the displacement-pressure formulation. The aim of this work is to provide a stable and robust numerical method for a wide range of physical and numerical parameters. The finite-dimensional solution spaces are enriched linear Lagrange spaces, and the inf-sup condition between the two spaces is achieved by adding a stabilization term. The resulting coupled EG method is locally conservative and provides stable solutions without spurious oscillations or overshoots/undershoots. The well-posedness and optimal a priori error estimates are established. Numerical results in various scenarios are provided. [ABSTRACT FROM AUTHOR]

We present a geometric variational discretization of nonlinear elasticity in 2D and 3D in the Lagrangian description. A main step in our construction is the definition of discrete deformation gradients and discrete Cauchy–Green deformation tensors, which allows for the development of a general discrete geometric setting for frame indifferent isotropic hyperelastic models. The resulting discrete framework is in perfect adequacy with the multisymplectic discretization of fluids proposed earlier by the authors. Thanks to the unified discrete setting, a geometric variational discretization can be developed for the coupled dynamics of a fluid impacting and flowing on the surface of an hyperelastic body. The variational treatment allows for a natural inclusion of incompressibility and impenetrability constraints via appropriate penalty terms. We test the resulting integrators in 2D and 3D with the case of a barotropic fluid flowing on incompressible rubber-like nonlinear models. [ABSTRACT FROM AUTHOR]

The goal of this study is to show how velocity, temperature, solutal and microorganism slip effects coupled with suction/injection affect mixed convective fluid flow through a vertical cone containing gyrotactic microorganism. To execute numerical computations, the controlling partial differential equations which comprise steady momentum, energy, conservation of mass and motile microorganism balances are initially reduced to a collection of linked non linear ordinary differential equations by similarity transformations, utilizing the MATLAB bvp4c scheme to solve numerically. The current study's findings have been graphically compared to those of earlier research, revealing a high level of compatibility. The flow fields are numerically exhibited for diversified parameters. For some precise parameter values, dual solutions can be discovered throughout the domain of free, mixed and forced convection and only in the free convection zone do dual solutions exist beyond a critical point. This research has applications for microbial fuel cells, a green sustainable technology for the production of bioelectricity and the treatment of wastewater. [ABSTRACT FROM AUTHOR]

The full quasistatic thermomechanical system of PDEs, describing water diffusion with the possibility of freezing and melting in a visco-elasto-plastic porous solid, is studied in detail under the hypothesis that the pressure-saturation hysteresis relation is given in terms of the Preisach hysteresis operator. The resulting system of balance equations for mass, momentum, and energy coupled with the phase dynamics equation is shown to admit a global solution under general assumptions on the data. [ABSTRACT FROM AUTHOR]