A Jacobian‐free‐based IIM for incompressible flows involving moving interfaces with Dirichlet boundary conditions

In this paper, a finite difference marker‐and‐cell (MAC) scheme is presented for the steady Stokes equations with moving interfaces and Dirichlet boundary condition. The moving interfaces are represented by Lagrangian control points and their position is updated implicitly using a Jacobian‐free approach within each time step. The forces at the moving interfaces are calculated from the position of the interfaces and interpolated using cubic splines and then applied to the fluid through the related jump conditions. The proposed Jacobian‐free Newton–generalized minimum residual (GMRES) method avoids the need to form and store the matrix explicitly in the computation of the inverse of the Jacobian and betters numerical stability. The Stokes equations are discretized on a MAC grid via a second‐order finite difference scheme with the incorporation of jump contributions and the resulting saddle point system is solved by the conjugate gradient Uzawa‐type method. Numerical results demonstrate very well the accuracy and effectiveness of the proposed method. The present algorithm has been applied to solve incompressible Navier–Stokes flows with moving interfaces. Copyright © 2010 John Wiley & Sons, Ltd.     

Improved multi‐level Newton solvers for fully coupled multi‐physics problems

An algorithm is suggested to improve the efficiency of the multi‐level Newton method that is used to solve multi‐physics problems. It accounts for full coupling between the subsystems by using the direct differentiation method rather than error prone finite difference calculations and retains the advantage of greater flexibility over the tightly coupled approaches. Performance of the algorithm is demonstrated by solving a fluid–structure interaction problem. Copyright © 2003 John Wiley & Sons, Ltd.     

Modeling of flow‐induced sound in porous materials

The impact of flow on a structure plays a crucial part when considering structural behavior, for example, in aviation. As structural vibrations (also denominated as structural sound) propagate within a structure, sound radiation is a likely consequence. To reduce the emission of noise, the use of poroelastic material is investigated. The approach consists in applying a poroelastic layer on the surface submitted to flow, as such utilizing the damping properties of poroelastic material. To predict flow‐induced sound, a computational model has been developed to account for (1) flow‐induced sound immission into a structure; (2) sound propagation; and (3) possible resulting sound radiation. Consistent formulation of the interactions between the components—that is, flow, poroelastic material, elastic structure, and acoustic fluid—allows to apply different simulation techniques for each component and thus to exploit each method's advantages. The key aspect of this work is the formulation of the interface conditions to couple flow with poroelastic material. The proposed and implemented coupling conditions are studied. The given example shows a possible application and demonstrates the effectiveness of poroelastic material to reduce flow‐induced sound emission. Copyright © 2014 John Wiley & Sons, Ltd.     

Analysis of space mapping algorithms for application to partitioned fluid–structure interaction problems

Fluid–structure interactions (FSI) play a crucial role in many engineering fields. However, the computational cost associated with high‐fidelity aeroelastic models currently precludes their direct use in industry, especially for strong interactions. The strongly coupled segregated problem—that results from domain partitioning—can be interpreted as an optimization problem of a fluid–structure interface residual. Multi‐fidelity optimization techniques can therefore directly be applied to this problem in order to obtain the solution efficiently. In previous work, it is already shown that aggressive space mapping (ASM) can be used in this context. In this contribution, we extend the research towards the use of space mapping for FSI simulations. We investigate the performance of two other approaches, generalized space mapping and output space mapping, by application to both compressible and incompressible 2D problems. Moreover, an analysis of the influence of the applied low‐fidelity model on the achievable speedup is presented. The results indicate that output space mapping is a viable alternative to ASM when applied in the context of solver coupling for partitioned FSI, showing similar performance as ASM and resulting in reductions in computational cost up to 50% with respect to the reference quasi‐Newton method. Copyright © 2015 John Wiley & Sons, Ltd.     

Coupled adjoint‐based sensitivities in large‐displacement fluid‐structure interaction using algorithmic differentiation

A methodology for the calculation of gradients with respect to design parameters in general fluid‐structure interaction problems is presented. It is based on fixed‐point iterations on the adjoint variables of the coupled system using algorithmic differentiation. This removes the need for the construction of the analytic Jacobian for the coupled physical problem, which is the usual limitation for the computation of adjoints in most realistic applications. The formulation is shown to be amenable to partitioned solution methods for the adjoint equations. It also poses no restrictions to the nonlinear physics in either the fluid or structural field, other than the existence of a converged solution to the primal problem from which to compute the adjoints. We demonstrate the applicability of this procedure and the accuracy of the computed gradients on coupled problems involving viscous flows with geometrical and material nonlinearities in the structural domain.     

Robin‐Neumann transmission conditions for fluid‐structure coupling: Embedded boundary implementation and parameter analysis

Partitioned procedures are appealing for solving complex fluid‐structure interaction (FSI) problems, as they allow existing computational fluid dynamics (CFD) and computational structural dynamics algorithms and solvers to be combined and reused. However, for problems involving incompressible flow and strong added‐mass effect (eg, heavy fluid and slender structure), partitioned procedures suffer from numerical instability, which typically requires additional subiterations between the fluid and structural solvers, hence significantly increasing the computational cost. This paper investigates the use of Robin‐Neumann transmission conditions to mitigate the above instability issue. Firstly, an embedded Robin boundary method is presented in the context of projection‐based incompressible CFD and finite element–based computational structural dynamics. The method utilizes operator splitting and a modified ghost fluid method to enforce the Robin transmission condition on fluid‐structure interfaces embedded in structured non–body‐conforming CFD grids. The method is demonstrated and verified using the Turek and Hron benchmark problem, which involves a slender beam undergoing large transient deformation in an unsteady vortex‐dominated channel flow. Secondly, this paper investigates the effect of the combination parameter in the Robin transmission condition, ie, α_f, on numerical stability and solution accuracy. This paper presents a numerical study using the Turek and Hron benchmark problem and an analytical study using a simplified FSI model featuring an Euler‐Bernoulli beam interacting with a two‐dimensional incompressible inviscid flow. Both studies reveal a trade‐off between stability and accuracy: smaller values of α_f tend to improve numerical stability, yet deteriorate the accuracy of the partitioned solution. Using the simplified FSI model, the critical value of α_f that optimizes this trade‐off is derived and discussed.     

Quasi‐Static Single‐Component Hybrid Simulation of a Composite Structure with Multi‐Axis Control

This paper presents a quasi‐static hybrid simulation performed on a single component structure. Hybrid simulation is a substructural technique, where a structure is divided into two sections: a numerical section of the main structure and a physical experiment of the remainder. In previous cases, hybrid simulation has typically been applied to structures with a simple connection between the numerical model and physical test, e.g. civil engineering structures. In this paper, the method is applied to a composite structure, where the boundary is more complex i.e. 3 degrees of freedom. In order to evaluate the validity of the method, the results are compared to a test of the emulated structure – referred to here as the reference test. It was found that the error introduced by compliance in the load train was significant. Digital image correlation was for this reason implemented in the hybrid simulation communication loop to compensate for this source of error. Furthermore, the accuracy of the hybrid simulation was improved by compensating for communication delay. The test showed high correspondence between the hybrid simulation and the reference test in terms of overall deflection as well as displacements and rotation in the shared boundary.     

Generalized Robin–Neumann explicit coupling schemes for incompressible fluid‐structure interaction: Stability analysis and numerics

We introduce a new class of explicit coupling schemes for the numerical solution of fluid‐structure interaction problems involving a viscous incompressible fluid and an elastic structure. These methods generalize the arguments reported in [Comput. Methods Appl. Mech. Engrg., 267:566–593, 2013, Numer. Math., 123(1):21–65, 2013] to the case of the coupling with thick‐walled structures. The basic idea lies in the derivation of an intrinsic interface Robin consistency at the space semi‐discrete level, using a lumped‐mass approximation in the structure. The fluid–solid splitting is then performed through appropriate extrapolations of the solid velocity and stress on the interface. Based on these methods, a new, parameter‐free, Robin–Neumann iterative procedure is also proposed for the partitioned solution of implicit coupling. A priori energy estimates, guaranteeing the stability of the schemes and the convergence of the iterative procedure, are established within a representative linear setting. The accuracy and performance of the methods are illustrated in several numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.     

Improved Morphology and Performance of Solution‐Processed Metal‐Oxide Thin‐Film Transistors Due to a Polymer Based Interface Modifier

The influence of a polymer interface modifier on the performance of solution‐processed indium‐based metal‐oxide (MO) thin‐film transistors (TFTs) is investigated. We use the polymer ethoxylated polyethylenimine (PEIE). Compared to a reference sample this modification enhances the mobility by a factor of four, clearly reduces the contact and the sheet resistance, and decreases the charge carrier activation energy by about 20%. The improved electrical performance originates from both a reduced contact and a reduced sheet resistance of the TFTs. The molecular dipole of PEIE reduces the work function of the electrodes. Adversely the dipole enhances the off current and the trap density at the semiconductor/dielectric interface for bottom‐contact transistors with small channel length. The substrate becomes highly polar with a PEIE‐treatment. Accordingly, topographical studies of bottom‐contact TFTs show a very similar MO film morphology on the electrodes and in the channel for modified TFTs, whereas in the untreated samples the film has a higher roughness on the electrodes than in the channel. TFTs in top‐contact configuration with the polymer interface layer at the dielectric/semiconductor interface also show higher mobility compared to the reference MOTFTs which displays that the improved performance is due to the improved morphology of the MO film.     

Interface dynamic stiffness matrix approach for three‐dimensional transient multi‐region boundary element analysis

A novel substructuring method is developed for the coupling of boundary element and finite element subdomains in order to model three‐dimensional multi‐region elastodynamic problems in the time domain. The proposed procedure is based on the interface stiffness matrix approach for static multi‐region problems using variational principles together with the concept of Duhamel integrals. Unit impulses are applied at the boundary of each region in order to evaluate the impulse response matrices of the Duhamel (convolution) integrals. Although the method is not restricted to a special discretization technique, the regions are discretized using the boundary element method combined with the convolution quadrature method. This results in a time‐domain methodology with the advantages of performing computations in the Laplace domain, which produces very accurate and stable results as verified on test examples. In addition, the assembly of the boundary element regions and the coupling to finite elements are greatly simplified and more efficient. Finally, practical applications in the area of soil–structure interaction and tunneling problems are shown. Copyright © 2009 John Wiley & Sons, Ltd.     

A monolithic,mortar‐based interface coupling and solution scheme for finite element simulations of lithium‐ion cells

This work introduces a novel, mortar‐based coupling scheme for electrode‐electrolyte interfaces in 3‐dimensional finite element models for lithium‐ion cells and similar electrochemical systems. The coupling scheme incorporates the widely applied Butler‐Volmer charge transfer kinetics, but conceptually also works for other interface equations. Unlike conventional approaches, the coupling scheme allows flexible mesh generation for the electrode and electrolyte phases with nonmatching meshes at electrode‐electrolyte interfaces. As a result, the desired spatial mesh resolution in each phase and the resulting computational effort can be easily controlled, leading to improved efficiency. All governing equations are solved in a monolithic fashion as a holistic, unified system of linear equations for computational robustness and performance reasons. Consistency and optimal convergence behavior of the coupling scheme are demonstrated in elementary numerical tests, and the discharge of two different realistic lithium‐ion cells, each consisting of an anode, a cathode, and an electrolyte, is also simulated. One of the two cells involves about 1.35 million degrees of freedom and very complex microstructural geometries obtained from X‐ray tomography data. For validation purposes, characteristic numerical results from the literature are reproduced, and the coupling scheme is shown to require considerably fewer degrees of freedom than a standard discretization with matching interface meshes to achieve a similar level of accuracy.     

Interface current method for multi‐region neutron diffusion problems

This paper presents an interface current method for solving multi‐region neutron diffusion problems using multi‐dimensional Green's functions. The method is based on evaluation of the net currents at each interface. The unknown interface currents are expanded in terms of eigenfunctions. The orthogonality condition of the eigenfunctions is employed in order to transform these equations to an algebraic system. Numerical examples are provided at the end of the paper to demonstrate the validity of the method, and for comparison with the more established finite difference method. Copyright © 2003 John Wiley & Sons, Ltd.     

Two‐fluid model with interface sharpening

Two‐fluid models are applicable for simulations of all types of two‐phase flows ranging from separated flows with large characteristic interfacial length scales to highly dispersed flows with very small characteristic interfacial length scales. The main drawback of the two‐fluid model, when used for simulations of stratified flows, is the numerical diffusion of the interface. Stratified flows can be easily and more accurately solved with interface tracking methods; however, these methods are limited to the flows, that do not develop into dispersed types of flows. The present paper describes a new approach, where the advantage of the two‐fluid model is combined with the conservative level set method for interface tracking. The advection step of the volume fraction transport equation is followed by the interface sharpening, which preserves the thickness of the interface during the simulation. The proposed two‐fluid model with interface sharpening was found to be more accurate than the existing two‐fluid models. The mixed flow with both: stratified and dispersed flow, is simulated with the coupled model in this paper. In the coupled model, the dispersed two‐fluid model and two‐fluid model with interface sharpening are used locally, depending on the parameter which recognizes the flow regime. Copyright © 2010 John Wiley & Sons, Ltd.     

Capillary Force‐Driven,Hierarchical Co‐Assembly of Dandelion‐Like Peptide Microstructures

The wetting and drying of drops on flexible fibers occurs ubiquitously in nature, and the capillary force underlying this phenomenon has motivated our great interest in learning how to direct supramolecular self‐assembly. Here, the hierarchical co‐assembly of two aromatic peptides, diphenylalanine (FF) and ferrocene‐diphenylalanine (Fc‐FF), is reported via sequential, combinatorial assembly. The resulting dandelion‐like microstructures have highly complex architectures, where FF microtube arrays serve as the scapes and the Fc‐FF nanofibers serve as the flower heads. Homogeneous FF microtubes with diameters tailored between 1 and 9 μm and wall thickness ranging from 70 to 950 nm are initially formed by controlling the degree of supersaturation of the FF and the water content. Once the FF microtubes are formed, the growth of the dandelion‐like microstructures is then driven by the capillary force, derived from the wetting and drying of the Fc‐FF solution on the FF microtubes. This simple and ingenious strategy offers many opportunities to develop new and creative methods for controlling the hierarchical self‐assembly of peptides and thus building highly complex nano and microstructures.     

Two‐scale diffusion–deformation coupling model for material deterioration involving micro‐crack propagation

In this paper, we introduce a two‐scale diffusion–deformation coupled model that represents the aging material deterioration of two‐phase materials involving micro‐crack propagations. The mathematical homogenization method is applied to relate the micro‐ and macroscopic field variables, and a weak coupling solution method is employed to solve the two‐way coupling phenomena between the diffusion of scalar fields and the deformation of quasi‐brittle solids. The macroscopic mechanical behavior represented by the derived two‐scale two‐way coupled model reveals material nonlinearity due to micro‐scale cracking induced by the scalar‐field‐induced deformation, which can be simulated by the finite cover method. After verifying the fundamental validity of the proposed model and the analysis method, we perform a simple numerical example to demonstrate their ability to predict aging material deterioration. Copyright © 2010 John Wiley & Sons, Ltd.     

Finite‐volume stress analysis in multi‐material linear elastic body

Correct calculation of stresses at the interface of bonded or otherwise joined materials plays a significant role in many applications. It is therefore important that traction at the material interface is calculated as accurately as possible. This paper describes procedures that can be employed to achieve this goal by using centre‐based finite‐volume method. Total traction at the interface is calculated by decomposing it into normal and tangential components, both being calculated at each side of the interface, and applying the continuity assumption. The way in which the traction approximation is achieved depends on calculation of tangential gradient of displacement at the interface. To this end, three different methods are proposed and validated against problems with known solutions. It was shown that all methods can be successfully used to simulate problems with multi‐material domains, with the procedure based on finite area method being most accurate. Copyright © 2012 John Wiley & Sons, Ltd.     

Interface handling for three‐dimensional higher‐order XFEM‐computations in fluid–structure interaction

Three‐dimensional higher‐order eXtended finite element method (XFEM)‐computations still pose challenging computational geometry problems especially for moving interfaces. This paper provides a method for the localization of a higher‐order interface finite element (FE) mesh in an underlying three‐dimensional higher‐order FE mesh. Additionally, it demonstrates, how a subtetrahedralization of an intersected element can be obtained, which preserves the possibly curved interface and allows therefore exact numerical integration. The proposed interface algorithm collects initially a set of possibly intersecting elements by comparing their ‘eXtended axis‐aligned bounding boxes’. The intersection method is applied to a highly reduced number of intersection candidates. The resulting linearized interface is used as input for an elementwise constrained Delaunay tetrahedralization, which computes an appropriate subdivision for each intersected element. The curved interface is recovered from the linearized interface in the last step. The output comprises triangular integration cells representing the interface and tetrahedral integration cells for each intersected element. Application of the interface algorithm currently concentrates on fluid–structure interaction problems on low‐order and higher‐order FE meshes, which may be composed of any arbitrary element types such as hexahedra, tetrahedra, wedges, etc. Nevertheless, other XFEM‐problems with explicitly given interfaces or discontinuities may be tackled in addition. Multiple structures and interfaces per intersected element can be handled without any additional difficulties. Several parallelization strategies exist depending on the desired domain decomposition approach. Numerical test cases including various geometrical exceptions demonstrate the accuracy, robustness and efficiency of the interface handling. Copyright © 2009 John Wiley & Sons, Ltd.     

A computational framework for scale‐bridging in multi‐scale simulations

A computational framework for scale‐bridging in multi‐scale simulations is presented. The framework enables seamless combination of at‐scale models into highly dynamic hierarchies to build a multi‐scale model. Its centerpiece is formulated as a standalone module capable of fully asynchronous operation. We assess its feasibility and performance for a two‐scale model applied to two challenging test problems from impact physics. We find that the computational cost associated with using the framework may, as expected, become substantial. However, the framework has the ability of effortlessly combining at‐scale models to render complex multi‐scale models. The main source of the computational inefficiency of the framework is related to poor load balancing of the lower‐scale model evaluation We demonstrate that the load balancing can be efficiently addressed by recourse to conventional load‐balancing strategies. Copyright © 2016 John Wiley & Sons, Ltd.     

Lamellarly Stacking Porous N,P Co‐Doped Mo2C/C Nanosheets as High Performance Anode for Lithium‐Ion Batteries

Layered stacking and highly porous N, P co‐doped Mo₂C/C nanosheets are prepared from a stable Mo‐enhanced hydrogel. The hydrogel is formed through the ultrafast cross‐linking of phosphomolybdic acid and chitosan. During the reduction of the composite hydrogel framework under inert gas protection, highly porous N and P co‐doped carbon nanosheets are produced with the in situ formation of ultrafine Mo₂C nanoparticles highly distributed throughout the nanosheets which are entangled via a hierarchical lamellar infrastructure. This unique architecture of the N, P co‐doped Mo₂C/C nanosheets tremendously promote the electrochemical activity and operate stability with high specific capacity and extremely stable cycling. In particular, this versatile synthetic strategy can also be extended to other polyoxometalate (such as phosphotungstic acid) to provide greater opportunities for the controlled fabrication of novel hierarchical nanostructures for next‐generation high performance energy storage applications.