An implicit immersed boundary method for three-dimensional fluid–membrane interactions

We present an implicit immersed boundary method for the incompressible Navier–Stokes equations capable of handling three-dimensional membrane–fluid flow interactions. The goal of our approach is to greatly improve the time step by using the Jacobian-free Newton–Krylov method (JFNK) to advance the location of the elastic membrane implicitly. The most attractive feature of this Jacobian-free approach is Newton-like nonlinear convergence without the cost of forming and storing the true Jacobian. The Generalized Minimal Residual method (GMRES), which is a widely used Krylov-subspace iterative method, is used to update the search direction required for each Newton iteration. Each GMRES iteration only requires the action of the Jacobian in the form of matrix–vector products and therefore avoids the need of forming and storing the Jacobian matrix explicitly. Once the location of the boundary is obtained, the elastic forces acting at the discrete nodes of the membrane are computed using a finite element model. We then use the immersed boundary method to calculate the hydrodynamic effects and fluid–structure interaction effects such as membrane deformation. The present scheme has been validated by several examples including an oscillatory membrane initially placed in a still fluid, capsule membranes in shear flows and large deformation of red blood cells subjected to stretching force.     

An efficient fluid–solid coupling algorithm for single-phase flows

We present a simple and efficient fluid–solid coupling method in two and three spatial dimensions. In particular, we consider the numerical approximation of the Navier–Stokes equations on irregular domains and propose a novel approach for solving the Hodge projection step on arbitrary shaped domains. This method is straightforward to implement and leads to a symmetric positive definite linear system for both the projection step and for the implicit treatment of the viscosity. We demonstrate the accuracy of our method in the L¹$L^1$ and L^∞$L^{\infty }$ norms and present its removing the errors associated with the conventional rasterization-type discretizations. We apply this method to the simulation of a flow past a cylinder in two spatial dimensions and show that our method can reproduce the known stable and unstable regimes as well as correct lift and drag forces. We also apply this method to the simulation of a flow past a sphere in three spatial dimensions at low and moderate Reynolds number to reproduce the known steady axisymmetric and non-axisymmetric flow regimes. We further apply this algorithm to the coupling of flows with moving rigid bodies.     

Stable Robin solid wall boundary conditions for the Navier–Stokes equations

In this paper we prove stability of Robin solid wall boundary conditions for the compressible Navier–Stokes equations. Applications include the no-slip boundary conditions with prescribed temperature or temperature gradient and the first order slip-flow boundary conditions. The formulation is uniform and the transitions between different boundary conditions are done by a change of parameters. We give different sharp energy estimates depending on the choice of parameters.     

Numerical investigation of shock-induced bubble collapse dynamics and fluid–solid interactions during shock-wave lithotripsy

In this paper we investigate the bubble collapse dynamics under shock-induced loading near soft and rigid bio-materials, during shock wave lithotripsy. A novel numerical framework was developed, that employs a Diffuse Interface Method (DIM) accounting for the interaction across fluid–solid-gas interfaces. For the resolution of the extended variety of length scales, due to the dynamic and fine interfacial structures, an Adaptive Mesh Refinement (AMR) framework for unstructured grids was incorporated. This multi-material multi-scale approach aims to reduce the numerical diffusion and preserve sharp interfaces. The presented numerical framework is validated for cases of bubble dynamics, under high and low ambient pressure ratios, shock-induced collapses, and wave transmission problems across a fluid–solid interface, against theoretical and numerical results. Three different configurations of shock-induced collapse applications near a kidney stone and soft tissue have been simulated for different stand-off distances and bubble attachment configurations. The obtained results reveal the detailed collapse dynamics, jet formation, solid deformation, rebound, primary and secondary shock wave emissions, and secondary collapse that govern the near-solid collapse and penetration mechanisms. Significant correlations of the problem configuration to the overall collapse mechanisms were found, stemming from the contact angle/attachment of the bubble and from the properties of solid material. In general, bubbles with their center closer to the kidney stone surface produce more violent collapses. For the soft tissue, the bubble movement prior to the collapse is of great importance as new structures can emerge which can trap the liquid jet into induced crevices. Finally, the tissue penetration is examined for these cases and a novel tension-driven tissue injury mechanism is elucidated, emanating from the complex interaction of the bubble/tissue interaction during the secondary collapse phase of an entrapped bubble in an induced crevice with the liquid jet.     

Numerically stable fluid–structure interactions between compressible flow and solid structures

We propose a novel method to implicitly two-way couple Eulerian compressible flow to volumetric Lagrangian solids. The method works for both deformable and rigid solids and for arbitrary equations of state. The method exploits the formulation of [11] which solves compressible fluid in a semi-implicit manner, solving for the advection part explicitly and then correcting the intermediate state to time tⁿ⁺¹ using an implicit pressure, obtained by solving a modified Poisson system. Similar to previous fluid–structure interaction methods, we apply pressure forces to the solid and enforce a velocity boundary condition on the fluid in order to satisfy a no-slip constraint. Unlike previous methods, however, we apply these coupled interactions implicitly by adding the constraint to the pressure system and combining it with any implicit solid forces in order to obtain a strongly coupled, symmetric indefinite system (similar to [17], which only handles incompressible flow). We also show that, under a few reasonable assumptions, this system can be made symmetric positive-definite by following the methodology of [16]. Because our method handles the fluid–structure interactions implicitly, we avoid introducing any new time step restrictions and obtain stable results even for high density-to-mass ratios, where explicit methods struggle or fail. We exactly conserve momentum and kinetic energy (thermal fluid–structure interactions are not considered) at the fluid–structure interface, and hence naturally handle highly non-linear phenomenon such as shocks, contacts and rarefactions.     

An improved penalty immersed boundary method for fluid–flexible body interaction

An improved penalty immersed boundary (pIB) method has been proposed for simulation of fluid–flexible body interaction problems. In the proposed method, the fluid motion is defined on the Eulerian domain, while the solid motion is described by the Lagrangian variables. To account for the interaction, the flexible body is assumed to be composed of two parts: massive material points and massless material points, which are assumed to be linked closely by a stiff spring with damping. The massive material points are subjected to the elastic force of solid deformation but do not interact with the fluid directly, while the massless material points interact with the fluid by moving with the local fluid velocity. The flow solver and the solid solver are coupled in this framework and are developed separately by different methods. The fractional step method is adopted to solve the incompressible fluid motion on a staggered Cartesian grid, while the finite element method is developed to simulate the solid motion using an unstructured triangular mesh. The interaction force is just the restoring force of the stiff spring with damping, and is spread from the Lagrangian coordinates to the Eulerian grids by a smoothed approximation of the Dirac delta function. In the numerical simulations, we first validate the solid solver by using a vibrating circular ring in vacuum, and a second-order spatial accuracy is observed. Then both two- and three-dimensional simulations of fluid–flexible body interaction are carried out, including a circular disk in a linear shear flow, an elastic circular disk moving through a constricted channel, a spherical capsule in a linear shear flow, and a windsock in a uniform flow. The spatial accuracy is shown to be between first-order and second-order for both the fluid velocities and the solid positions. Comparisons between the numerical results and the theoretical solutions are also presented.     

A simple and efficient direct forcing immersed boundary framework for fluid–structure interactions

A direct forcing immersed boundary framework is presented for the simple and efficient simulation of strongly coupled fluid–structure interactions. The immersed boundary method developed by Yang and Balaras [J. Yang, E. Balaras, An embedded-boundary formulation for large-eddy simulation of turbulent flows interacting with moving boundaries, J. Comput. Phys. 215 (1) (2006) 12–40] is greatly simplified by eliminating several complicated geometric procedures without sacrificing the overall accuracy. The fluid–structure coupling scheme of Yang et al. [J. Yang, S. Preidikman, E. Balaras, A strongly-coupled, embedded-boundary method for fluid–structure interactions of elastically mounted rigid bodies, J. Fluids Struct. 24 (2008) 167–182] is also significantly expedited by moving the fluid solver out of the predictor–corrector iterative loop without altering the strong coupling property. Central to these improvements are the reformulation of the field extension strategy and the evaluation of fluid force and moment exerted on the immersed bodies, by taking advantage of the direct forcing idea in a fractional-step method. Several cases with prescribed motions are examined first to validate the simplified field extension approach. Then, a variety of strongly coupled fluid–structure interaction problems, including vortex-induced vibrations of a circular cylinder, transverse and rotational galloping of rectangular bodies, and fluttering and tumbling of rectangular plates, are computed. The excellent agreement between the present results and the reference data from experiments and other simulations demonstrates the accuracy, simplicity, and efficiency of the new method and its applicability in a wide range of complicated fluid–structure interaction problems.     

Absorption of ultrashort intense lasers in laser–solid interactions

With the advent of ultrashort high intensity laser pulses,laser absorption during the laser–solid interactions has received significant attention over the last two decades since it is related to a variety of applications of high intensity lasers,including the hot electron production for fast ignition of fusion targets,table-top bright X-ray and gamma-ray sources,ion acceleration,compact neutron sources,and generally the creation of high energy density matters.Normally,some absorption mechanisms found for nanosecond long laser pulses also appear for ultrashort laser pulses.The peculiar aspects with ultrashort laser pulses are that their absorption depends significantly on the preplasma condition and the initial target structures.Meanwhile,relativistic nonlinearity and ponderomotive force associated with the laser pulses lead to new mechanisms or phenomena,which are usually not found with nanosecond long pulses.In this paper,we present an overview of the recent progress on the major absorption mechanisms in intense laser–solid interactions,where emphasis is paid to our related theory and simulation studies.     

Ion–solid interactions: current status,new perspectives

In the past half century, we have witnessed an explosive growth of effort in that cross-discipline which is characterized by the deposition of localized high–energy densities in condensed matter by means of energetic ions—the field of ion–solid interactions. In this overview, the fundamental physical processes of ion–solid interaction are outlined. A brief discussion is given of the basic energy transfer mechanisms and the consequences of ion impact into solids such as scattering, sputtering and radiation damage. It is now understood that radiation damage is itself far from being restricted to deleterious and detrimental consequences. Our knowledge of the growing variety of changes in the physical, chemical and biological properties of target materials are growing exponentially. Many valuable beneficial technological applications, some of which we discuss, have their origin in physical processes taking place at the nanometric level.     

On the boundary slip of fluid flow

For hundreds of years, in all the textbooks of classical fluid mechanics and lubrica- tion mechanics it is assumed that there was no wall slip (boundary slip) at a liquid-solid interface, i.e. no relative motion between liquid and solid at the interface. This is the no-slip boundary condition. It has been widely applied to engineering and experiments and to almost all the rheology or viscosity measurements of fluids. Rheology is one of the most important bases for fluid mechanics and lubricati…     

An efficient high-order boundary element method for nonlinear wave–wave and wave-body interactions

A highly efficient high-order boundary element method is developed for the numerical simulation of nonlinear wave–wave and wave-body interactions in the context of potential flow. The method is based on the framework of the quadratic boundary element method (QBEM) for the boundary integral equation and uses the pre-corrected fast Fourier transform (PFFT) algorithm to accelerate the evaluation of far-field influences of source and/or normal dipole distributions on boundary elements. The resulting PFFT–QBEM reduces the computational effort of solving the associated boundary-value problem from O(N^2～3) (with the traditional QBEM) to O(N ln N) where N represents the total number of boundary unknowns. Significantly, it allows for reliable computations of nonlinear hydrodynamics useful in ship design and marine applications, which are forbidden with the traditional methods on the presently available computing platforms. The formulation and numerical issues in the development and implementation of the PFFT–QBEM are described in detail. The characteristics of accuracy and efficiency of the PFFT–QBEM for various boundary-value problems are studied and compared to those of the existing accelerated (lower- and higher-order) boundary element methods. To illustrate the usefulness of the PFFT–QBEM, it is applied to solve the initial boundary-value problem in the generation of three-dimensional nonlinear waves by a moving ship hull. The predicted wave profile and resistance on the ship are compared to available experimental measurements with satisfactory agreements.     

Crack–grain boundary interactions in zinc bicrystals

In polycrystalline materials that fail by transgranular cleavage, it is known that crystallographic misorientation of preferred fracture planes across grain boundaries can provide crack growth resistance; despite this, the micromechanisms associated with crack transmission across grain boundaries and their role in determining the overall fracture resistance are not well understood. Recent studies on diverse structural materials such as steels, aluminum alloys and intermetallics have shown a correlation between fracture resistance and the twist component of grain misorientation. However, the lack of control over the degree and type of misorientation in experimental studies, combined with a dearth of analytical and computational investigations that fully account for the three-dimensional nature of the problem, have precluded a systematic analysis of this phenomenon. In this study, this phenomenon was investigated through in situ crack propagation experiments across grain boundaries of controlled twist misorientation in zinc bicrystals. Extrinsic toughening mechanisms that activate upon crack stagnation at the grain boundary deter further crack propagation. The mechanical response and crack growth behavior were observed to be dependent on the twist angle, and several accommodation mechanisms such as twinning, strain localization and slip band blocking contribute to fracture resistance by competing with crack propagation. Three-dimensional finite element analyses incorporating crystal plasticity were performed on a stagnant crack at the grain boundary that provide insight into crack-tip stress and strain fields in the second grain. These analyses qualitatively capture the overall trends in mechanical response as well as strain localization around stagnant crack-tips.     

Wall effect on fluid–structure interactions of a tethered bluff body

Wind tunnel experiments have shown an unexplained amplification of the free motion of a tethered bluff body in a small wind tunnel relative to that in a large wind tunnel. The influence of wall proximity on fluid–structure interaction is explored using a compound pendulum motion in the plane orthogonal to a steady freestream with a doublet model for aerodynamic forces. Wall proximity amplifies a purely symmetric single degree of freedom oscillation with the addition of an out-of-phase force. The success of this simple level of simulation enables progress to develop metrics for unsteady wall interference in dynamic testing of tethered bluff bodies.     

Inelastic phonon interactions at solid–graphite interfaces

The presented model predicts thermal boundary conductance at interfaces where one material comprising the junction is characterized by high elastic anisotropy. In contrast to previous approaches, the current methodology accounts for contributions from inelastic scattering through consideration of multiple-phonon interactions. Inelastic contributions become significant as the temperature, as well as the degree of acoustic mismatch between the materials, increases. Inclusion of the inelastic interactions is necessary for a variety of interfacial systems including the metal–graphite boundary examined here. Improvement is shown over existing approaches that address only elastic scattering as both three- and four-phonon interactions significantly augment the transport.     

Topological boundary conditions in abelian Chern–Simons theory

We study topological boundary conditions in abelian Chern–Simons theory and line operators confined to such boundaries. From the mathematical point of view, their relationships are described by a certain 2-category associated to an even integer-valued symmetric bilinear form (the matrix of Chern–Simons couplings). We argue that boundary conditions correspond to Lagrangian subgroups in the finite abelian group classifying bulk line operators (the discriminant group). We describe properties of boundary line operators; in particular we compute the boundary associator. We also study codimension one defects (surface operators) in abelian Chern–Simons theories. As an application, we obtain a classification of such theories up to isomorphism, in general agreement with the work of Belov and Moore.     

Summation methods of Coulomb interactions in computer simulations of a system with one—dimensional periodic boundary conditions

The Ewald-type method, its modified version and the Lekner-type method for summing Coulomb interactions in a system periodic along one direction are presented and compared. Advantages and disadvantages of these methods are discussed, and the methods are tested in molecular dynamics simulations of acetone molecules confined to cylindrical silica pores.     

Anisotropic dynamic mass density for fluid–solid composites

By taking the low frequency limit of multiple-scattering theory, we obtain the dynamic effective mass density of fluid–solid composites with a two-dimensional rectangular lattice structure. The anisotropic mass density can be described by an angle-dependent dipole solution, to the leading-order of solid concentration. The angular dependence vanishes for the square lattice, but at high solid concentrations there is a structure-dependent factor that contributes to the leading-order solution. In all cases, Wood's formula is found to be accurately valid for the effective bulk modulus, independent of the structures. Numerical evaluations from the solutions are shown to be in excellent agreement with finite-element simulations.     

A coupled solid–fluid method for modelling subduction

We present a novel dynamic approach for solid–fluid coupling by joining two different numerical methods: the boundary-element method (BEM) and the finite element method (FEM). The FEM results describe the thermomechanical evolution of the solid while the fluid is solved with the BEM. The bidirectional feedback between the two domains evolves along a Lagrangian interface where the FEM domain is embedded inside the BEM domain. The feedback between the two codes is based on the calculation of a specific drag tensor for each boundary on finite element. The approach is presented here to solve the complex problem of the descent of a cold subducting oceanic plate into a hot fluid-like mantle. The coupling technique is shown to maintain the proper energy dissipation caused by the important secondary induced mantle flow induced by the lateral migrating of the subducting plate. We show how the method can be successfully applied for modelling the feedback between deformation of the oceanic plate and the induced mantle flow. We find that the mantle flow drag is singular at the edge of the retreating plate causing a distinct hook shape. In nature, such hooks can be observed at the northern end of the Tonga trench and at the southern perimeter, of the South American trench.     

On the effect of boundary conditions on I–V characteristics of HTSC tunnel junctions

The pairing potential distribution over the thickness of superconducting CuO₂ layers in cuprate HTSCs is determined within the Ginzburg–Landau (GL) theory using the microscopic justification of this theory by Gor’kov. It is found that the pairing potential in them is significantly suppressed due to the effect of non-superconducting interlayers, which results in a decrease in the critical temperature of these superconductors. The temperature dependences of the effective energy gap and current–voltage (I–V) characteristic of tunnel junctions of the “break junction” type made of these superconductors are calculated.     

Density functional theory of vapor to liquid heterogeneous nucleation: Lennard–Jones fluid on solid substrate

Density functional theory has been applied to investigate the vapor to liquid heterogeneous nucleation on a flat solid surface, by invoking a model free energy density functional along with an exponential density model. The effects of supersaturation of the vapor and the strength of the solid-fluid interaction on the nucleation barrier have been investigated for Lennard–Jones fluid with 12–6 fluid–fluid and 9–3 solid–fluid interaction model. The spinodal decomposition of vapor has been observed at higher supersaturation or at higher strength of the solid–fluid interaction. The shape, density profile and the free energy of formation of droplets of any arbitrary size have been obtained in this work.