Visualizing multiphysics,fluid-structure interaction phenomena in intracranial aneurysms

This work presents recent advances in visualizing multi-physics, fluid-structure interaction (FSI) phenomena in cerebral aneurysms. Realistic FSI simulations produce very large and complex data sets, yielding the need for parallel data processing and visualization. Here we present our efforts to develop an interactive visualization tool which enables the visualization of such FSI simulation data. Specifically, we present a ParaView–NekTar interface that couples the ParaView visualization engine with NekTar’s parallel libraries, which are employed for the calculation of derived fields in both the fluid and solid domains with spectral accuracy. This interface allows the flexibility of independently choosing the resolution for visualizing both the volume data and the surface data from each of the solid and fluid domains, which significantly facilitates the visualization of complex structures under large deformations. The animation of the fluid and structure data is synchronized in time, while the ParaView–NekTar interface enables the visualization of different fields to be superimposed, e.g. fluid jet and structural stress, to better understand the interactions in this multi-physics environment. Such visualizations are key towards elucidating important biophysical interactions in health and disease, as well as disseminating the insight gained from our simulations and further engaging the medical community in this effort of bringing computational science to the bedside.     

Shape design optimization of stationary fluid-structure interaction problems with large displacements and turbulence

This paper presents general and efficient methods for analysis and gradient based shape optimization of systems characterized as strongly coupled stationary fluid-structure interaction (FSI) problems. The incompressible fluid flow can be laminar or turbulent and is described using the Reynolds-averaged Navier-Stokes equations (RANS) together with the algebraic Baldwin–Lomax turbulence model. The structure may exhibit large displacements due to the interaction with the fluid domain, resulting in geometrically nonlinear structural behaviour and nonlinear interface coupling conditions. The problem is discretized using Galerkin and Streamline-Upwind/Petrov–Galerkin finite element methods, and the resulting nonlinear equations are solved using Newtons method. Due to the large displacements of the structure, an efficient update algorithm for the fluid mesh must be applied, leading to the use of an approximate Jacobian matrix in the solution routine. Expressions for Design Sensitivity Analysis (DSA) are derived using the direct differentiation approach, and the use of an inexact Jacobian matrix in the analysis leads to an iterative but very efficient scheme for DSA. The potential of gradient based shape optimization of fluid flow and FSI problems is illustrated by several examples.     

Application of Navier–Stokes simulations for aeroelastic stability assessment in transonic regime

Aeroelastic stability analyses in transonic regime require the adoption of accurate aerodynamic models, such as those based on Euler or Navier–Stokes equations, to model the physics associated with shock waves. To transfer the application of this type of analyses from academy to industry, it is necessary to verify if the technology is mature enough to be implemented without using specialised pieces of software. This paper presents a numerical strategy for solving aeroelastic fluid–structure interactions (FSI) stability problems using partitioned procedures based on the adoption of “black-box” CFD software for the solution of the flow field. The paper focuses on three elements: the outline of a numerical test procedure based on linearised reduced order models (ROMs) to quickly locate instability points; a novel interface scheme with a high degree of flexibility, to adapt to structural models initially not developed for FSI interactions; fast, reliable and easy to use CFD grid deformation schemes. The purpose is to show how robustness of results and ease of use can be achieved with limited efforts.     

A strong coupling partitioned approach for fluid-structure interaction with free surfaces

Fluid-structure interaction (FSI) problems are of great relevance to many fields in engineering and applied sciences. One wide spread and complex FSI-subclass is the category that studies the instationary behavior of incompressible viscous flows and thin-walled structures exhibiting large deformations. Free surfaces often present an essential additional challenge for this class of problems. Prominent application areas are fluid sloshing in tanks and numerable problems in offshore engineering and naval architecture. Especially when partitioned strong coupling schemes are used in order to solve the coupled FSI problem the design of an appropriate overall computational approach including free surface effects is not trivial. In this paper a new so-called partitioned implicit free surface approach is introduced and embedded into a strong coupling FSI solver. For complex problem classes this approach is combined with the general elevation equation that is closed through a dimensionally reduced pseudo-structural approach. The presented approach shows the same stability properties as a full implicit approach but is by far more efficient—especially in the partitioned coupled case.     

Immersed boundary method and lattice Boltzmann method coupled FSI simulation of mitral leaflet flow

Coupling the immersed boundary (IB) method and the lattice Boltzmann (LB) method might be a promising approach to simulate fluid-structure interaction (FSI) problems with flexible structures and moving boundaries. To investigate the possibility for future IB-LB coupled simulations of the heart flow dynamics, an IB-LB coupling scheme suitable for rapid boundary motion and large pressure gradient FSI is proposed, and the mitral valve jet flow considering the interaction of leaflets and fluid is simulated. After analyzing the respective concepts, formulae and advantages of the IB and LB methods, we first explain the coupling strategy and detailed implementation procedures, and then verify the effectiveness and second-order accuracy of the scheme by simulating a benchmark case, the relaxation of a stretched membrane immersed in fluid. After that, the diastolic filling jet flow between mitral leaflets in a simplified 2D left heart model is simulated. The model consists of the simplified transmitral passage of the heart and two curvilinear leaflets. In the simulation, the atrial and ventricular pressure histories of normal human are specified as boundary conditions, and the leaflets are treated as fibers that interact with the fluid to define their deformations and movements. The resulting opening and closing movements of the leaflets and the flow patterns of the filling jet are qualitatively reasonable and compare well with existing numerical and measured data. It is shown that this IB-LB coupling method is feasible for treating flexible boundary FSI problems with rapid boundary motion and large pressure gradient, the results of the mitral leaflet flow are valuable for understanding the transmitral FSI dynamics, and it is possible to simulate the more realistic 3D heart flow by the scheme in the future.     

Fluid–shell structure interaction analysis by coupled particle and finite element method

This paper presents a coupled particle and finite element method for fluid–shell structure interaction analysis. The Moving Particle Semi-Implicit (MPS) method is used to analyze fluid flow and the MITC4 shell element is used in the FEM analysis of the structure. This paper considers partitioned coupling between the fluid and structural solvers. In order to satisfy compatibility in the employed partitioned coupling scheme, the Neumann–Dirichlet condition is applied to both the fluid and the structure. A symplectic time integration scheme is used to preserve energy when analyzing the shell structure. If the frequencies of the shell analysis are much higher than those of the MPS fluid solver, its time integration scheme is sub-cycled. When the presented coupling scheme was applied to simulate the sloshing phenomenon in an elastic thin shell structure, fluid fragmentation and large structural deformations were observed.     

Large-scale fluid–structure interaction simulation of viscoplastic and fracturing thin-shells subjected to shocks and detonations

The fluid–structure interaction simulation of shock- and detonation-loaded thin-walled structures requires numerical methods that can cope with large deformations as well as local topology changes. We present a robust level-set-based approach that integrates a Lagrangian thin-shell finite element solver with fracture and fragmentation capabilities and an Eulerian Cartesian fluid solver with optional dynamic mesh adaptation. As computational applications, we consider the plastic deformation of a copper plate impacted by a strong piston-induced pressure wave inside a water pipe; and the induction of large plastic deformations and rupture of thin aluminum tubes due to the passage of ethylene–oxygen detonations.     

Performance of a new partitioned procedure versus a monolithic procedure in fluid–structure interaction

Fluid–structure interaction (FSI) can be simulated in a monolithic way by solving the flow and structural equations simultaneously and in a partitioned way with separate solvers for the flow equations and the structural equations. A partitioned quasi-Newton technique which solves the coupled problem through nonlinear equations corresponding to the interface position is presented and its performance is compared with a monolithic Newton algorithm. Various structural configurations with an incompressible fluid are solved, and the ratio of the time for the partitioned simulation, when convergence is reached, to the time for the monolithic simulation is found to be between 1/2 and 4. However, in this comparison of the partitioned and monolithic simulations, the flow and structural equations have been solved with a direct sparse solver in full Newton–Raphson iterations, only relatively small problems have been solved and this ratio would likely change if large industrial problems were considered or if other solution strategies were used.     

Interaction of flexible multibody systems with fluids analyzed by means of smoothed particle hydrodynamics

The present work deals with a computational approach to fluid-structure interaction (FSI) problems by coupling of flexible multibody system dynamics and fluid dynamics. Since the methods for the numerical modeling are well known, both for the structural and the fluid part, the focus of this work lies on the coupling formalism. Moreover, the applicability of the presented approach to arbitrary geometries and high structural stiffness is studied, as well as an easy model setup. No restriction should be made on the topology of the structure or the complexity of motion.For the fluid part a meshless method, known as smoothed particle hydrodynamics (SPH) is applied, which fulfills the above requirements. While an explicit time integration scheme in SPH provides a fast simulation of the fluid dynamics, advanced methods from flexible multibody dynamics provide a variety of benefits for the simulation of the solid part. Amongst these are specialized structural finite elements for both small and large deformation bodies, joints, stable implicit time-integration schemes, and model reduction techniques.A rule for the interaction between fluids and structures is derived from imposing a distributed potential over boundary segments of the structures, which the fluid particles respond to. The work is concluded by illustrative examples, demonstrating the successful coupling of flexible multibody systems with fluids.     

A robust solution procedure for hyperelastic solids with large boundary deformation

Compressible Mooney–Rivlin theory has been used to model hyperelastic solids, such as rubber and porous polymers, and more recently for the modeling of soft tissues for biomedical tissues, undergoing large elastic deformations. We propose a solution procedure for Lagrangian finite element discretization of a static nonlinear compressible Mooney–Rivlin hyperelastic solid. We consider the case in which the boundary condition is a large prescribed deformation, so that mesh tangling becomes an obstacle for straightforward algorithms. Our solution procedure involves a largely geometric procedure to untangle the mesh: solution of a sequence of linear systems to obtain initial guesses for interior nodal positions for which no element is inverted. After the mesh is untangled, we take Newton iterations to converge to a mechanical equilibrium. The Newton iterations are safeguarded by a line search similar to one used in optimization. Our computational results indicate that the algorithm is up to 70 times faster than a straightforward Newton continuation procedure and is also more robust (i.e., able to tolerate much larger deformations). For a few extremely large deformations, the deformed mesh could only be computed through the use of an expensive Newton continuation method while using a tight convergence tolerance and taking very small steps.     

Conserving energy and momentum in nonlinear dynamics: A simple implicit time integration scheme

We focus on a simple implicit time integration scheme for the transient response solution of structures when large deformations and long time durations are considered. Our aim is to have a practical method of implicit time integration for analyses in which the widely used Newmark time integration procedure is not conserving energy and momentum, and is unstable. The method of time integration discussed in this paper is performing well and is a good candidate for practical analyses.     

Fluid–structure interaction for non-conforming interfaces based on a dual mortar formulation

In the present work the problem of fluid–structure interaction (FSI) with independently space discretized fluid and structure fields is addressed in the context of finite elements. To be able to deal with non-conforming meshes at the fluid–structure interface, we propose the integration of a dual mortar method into the general FSI framework. This method has lately been used successfully to impose interface constraints in other contexts such as finite deformation contact. The main focus is set on monolithic coupling algorithms for FSI here. In these cases the dual mortar approach allows for the elimination of the additional Lagrange multiplier degrees of freedom from the global system by condensation. The resulting system matrices have the same block structure as their counterparts for the conforming case and permit the same numerical treatment. Partitioned Dirichlet–Neumann coupling is also considered briefly and it is shown that the dual mortar approach permits a numerically efficient mapping between fluid and structure quantities at the interface.Numerical examples demonstrate the efficiency and robustness of the proposed method. We present results for a variety of different element formulations for the fluid and the structure field, indicating that the proposed method is not limited to any specific formulation. Furthermore, the applicability of state-of-the-art iterative solvers is considered and the convergence behavior is shown to be comparable to standard simulations with conforming discretizations at the interface.     

Numerical simulation of the fluid–structure interaction between air blast waves and free-standing plates

A numerical method is used to compute the flow field corresponding to blast waves of different incident profiles propagating in air and impinging on free-standing plates. The method is suitable for the consideration of compressibility effects in the fluid and their influence on the plate dynamics. The history of the pressure experienced by the plate is extracted from numerical simulations for arbitrary blast strengths and plate masses and used to infer the impulse per unit area transmitted to the plate. The numerical results complement some recent analytical solutions in the intermediate range of plate masses and arbitrary blast intensities where exact solutions are not available. The resulting beneficial effect of the fluid–structure interaction (FSI) in reducing transmitted impulse in the presence of compressibility effects is discussed. In particular, it is shown that in order to take advantage of the impulse reduction provided by the FSI effect, large plate displacements are required which, in effect, may limit the practical applicability of exploiting FSI effects in the design of blast-mitigating systems.     

Three-dimensional fluid-structure coupling in transient analysis

The numerical simulation of nonlinear, transient fluid-structure interactions (FSI) is a current area of concern by researchers in various fields, including the field of nuclear reactor safety. This paper primarily discusses the formulation used in an algorithm that couples three-dimensional hydrodynamic and structural domains. Here, both the fluid and structure are discretized using finite elements. The semi-discretized equations of motion are solved using an explicit temporal integrator.Coupling is accomplished by satisfying interface mechanics. The structure imposes kinematic constraints to the moving fluid boundary, and the fluid in turn provides an external loading on the structure. At each interface node, normals are computed from the nodal basis functions of only the hydrodynamic nodes. By defining the interface normal in this manner, it becomes independent of the type of structural boundary (i.e. shell, plate, continuum, etc.) and thus makes this aspect of the coupling independent of the structure type. A penalty type gap-impact element is developed to model the impact region between the fluid and structure.Results for several problems are presented and these include a comparison between analytical results for a FSI problem and numerical predictions.     

Increasing solution stability for finite-element modeling of elasto-plastic shell response

The present article introduces a highly efficient numerical simulation strategy for the analysis of elasto-plastic shell structures. An isoparametric Finite Element, based on a Finite Rotation Reissner–Mindlin shell theory in isoparametric formulation, is enhanced by a Layered Approach for a realistic simulation of nonlinear material behaviour. A general material model including isotropic hardening effects is embedded into each material point. A new, highly accurate integration scheme is combined with consistently linearized constitutive relations in order to achieve quadratic rate of convergence. A global Riks–Wempner–Wessels iteration scheme enhanced by a linear Line-Search procedure was used to trace arbitrary deformation paths. Numerical examples show the efficiency of the present concept.     

A general iterative sparse linear solver and its parallelization for interval Newton methods

Interval Newton/Generalized Bisection methods reliably find all numerical solutions within a given domain. Both computational complexity analysis and numerical experiments have shown that solving the corresponding interval linear system generated by interval Newton's methods can be computationally expensive (especially when the nonlinear system is large). In applications, many large-scale nonlinear systems of equations result in sparse interval jacobian matrices. In this paper, we first propose a general indexed storage scheme to store sparse interval matrices We then present an iterative interval linear solver that utilizes the proposed index storage scheme It is expected that the newly proposed general interval iterative sparse linear solver will improve the overall performance for interval Newton/Generalized bisection methods when the jacobian matrices are sparse. In section 1, we briefly review interval Newton's methods. In Section 2, we review some currently used storage schemes for sparse systems. In Section 3, we introduce a new index scheme to store general sparse matrices. In Section 4, we present both sequential and parallel algorithms to evaluate a general sparse Jacobian matrix. In Section 5, we present both sequential and parallel algorithms to solve the corresponding interval linear system by the all-row preconditioned scheme. Conclusions and future work are discussed in Section 6.     

Numerical solution of potential flow equations with a predictor-corrector finite difference method

We develop a numerical solution algorithm of the nonlinear potential flow equations with the nonlinear free surface boundary condition.A finite difference method with a predictor-corrector method is applied to solve the nonlinear potential flow equations in a two-dimensional (2D) tank.The irregular tank is mapped onto a fixed square domain with rectangular cells through a proper mapping function.A staggered mesh system is adopted in a 2D tank to capture the wave elevation of the transient fluid.The finite difference method with a predictor-corrector scheme is applied to discretize the nonlinear dynamic boundary condition and nonlinear kinematic boundary condition.We present the numerical results of wave elevations from small to large amplitude waves with free oscillation motion,and the numerical solutions of wave elevation with horizontal excited motion.The beating period and the nonlinear phenomenon are very clear.The numerical solutions agree well with the analytical solutions and previously published results.     

Evolutionary topology optimization of elastoplastic structures

We have recently proposed in (Fritzen et al., Int J Numer Methods Eng 106(6):430–453, 2016) an evolutionary topology optimization model for the design of multiscale elastoplastic structures, which is in general independent of the applied material law. Facing the variability of the final design for minor parameter changes when dealing with plastic structural designs, we further improve the robustness and the effectiveness of the BESO optimization procedure in this work by introducing a damping scheme on sensitivity numbers and by progressively reducing the sensitivity filtering radius. The damping scheme constraining the variance of the sensitivity numbers stabilizes the topological evolution process in particular for dissipative structural designs. By setting initially a large filter radius value and reducing it gradually, the emergence of the redundant structural branches, which are to be eliminated afterwards and are the main reasons deteriorating the design process, could be avoided. The robustness and the effectiveness of the improved model has been validated by means of benchmark numerical examples of conventional homogeneous structures.