A numerical study on the fluid compressibility effects in strongly coupled fluid–solid interaction problems

Interactions between an incompressible fluid passing through a flexible tube and the elastic wall is one of the strongly coupled fluid–solid interaction (FSI) problems frequently studied in the literature due to its research importance and wide range of applications. Although incompressible fluid is a prevalent model in many simulation studies, the assumption of incompressibility may not be appropriate in strongly coupled FSI problems. This paper narrowly aims to study the effect of the fluid compressibility on the wave propagation and fluid–solid interactions in a flexible tube. A partitioned FSI solver is used which employs a finite volume-based fluid solver. For the sake of comparison, both traditional incompressible (ico) and weakly compressible (wco) fluid models are used in an Arbitrary Lagrangian–Eulerian (ALE) formulation and a PISO-like algorithm is used to solve the unsteady flow equations on a collocated mesh. The solid part is modeled as a simple hyperelastic material obeying the St-Venant constitutive relation. Computational results show that not only use of the weakly compressible fluid model makes the FSI solver in this case more efficient, but also the incompressible fluid model may produce largely unrealistic computational results. Therefore, the use of the weakly compressible fluid model is suggested for strongly coupled FSI problems involving seemingly incompressible fluids such as water especially in cases where wave propagation in the solid plays an important role.

     

Parametric study of fluid–solid interaction for single-particle dissipative particle dynamics model

In this paper, a parametric study of fluid–solid interaction for single-particle dissipative particle dynamics (DPD) model is conducted to describe the hydrodynamic interactions in a large range of particle sizes. To successfully reproduce the hydrodynamics for different particle sizes, and overcome the problem that effective radius of solid sphere does not match its real radius, the cut-off radius and conservative force coefficient of single-particle DPD model have been modified. The cut-off radius and conservative force coefficient are related to the drag force and radial distribution function, so that, for each particle size, they can be determined by DPD simulations. Through numerical fitting, two empirical formulas as a function of spherical radius are developed to calculate the cut-off radius and conservative force coefficient. Numerical results indicate that the single-particle DPD model is, indeed, capable of capturing low Reynolds number hydrodynamic interactions for different particle sizes by selecting these model parameters reasonably. Specifically, the model can not only insure that drag force and torque are quantitatively consistent with theoretical results, but also guarantee the effective radius matches well its real radius. In addition, the shear dissipative force is the major part of drag force and should not be ignored. This study will help to improve the application range of single-particle DPD model to make it suitable for different particle sizes and provide parameter guidance for studying fluid–solid interaction using single-particle DPD model.     

Modeling accidental-type fluid–structure interaction problems with the SPH method

This paper presents the validation aspects of a unified numerical framework based on SPH formulation and devoted to the modeling of fluid–structure interaction problems involving large motion of the fluid and large deformation with a possible failure of the structure. The fluid domain is modeled according to an updated Lagrangian formulation. The solid domain (3D and shell models) uses the total Lagrangian formulation. The fluid–structure interaction is treated via a unilateral contact algorithm adapted to SPH context. The SPH framework is verified on academic test cases and validated by simulating an experiment involving the reservoir leakage.     

Simulation of multibody systems with the use of coupling techniques: a case study

Simulation coupling (or cosimulation) techniques provide a framework for the analysis of decomposed dynamical systems with the use of independent numerical procedures for decomposed subsystems. These methods are often seen as very promising because they enable the utilization of the existing software for subsystem analysis and usually are easy to parallelize, and run in a distributed environment. For example, in the domain of multibody systems dynamics, a general setup for “Gluing Algorithms” was proposed by Wang et al. It was intended to provide a basis for multilevel distributed simulation environments. The authors presented an example where Newton’s method was used to synchronize the responses of subsystem simulators.     

A Lagrangian meshless finite element method applied to fluid–structure interaction problems

A method is presented for the solution of the incompressible fluid flow equations using a Lagrangian formulation. The interpolation functions are those used in the meshless finite element method and the time integration is introduced in a semi-implicit way by a fractional step method. Classical stabilization terms used in the momentum equations are unnecessary due to the lack of convective terms in the Lagrangian formulation. Furthermore, the Lagrangian formulation simplifies the connections with fixed or moving solid structures, thus providing a very easy way to solve fluid–structure interaction problems.     

Accelerating solid–fluid interaction based on the immersed boundary method on multicore and GPU architectures

This work proposes several approaches to accelerate the solid–fluid interaction through the use of the Immersed Boundary method on multicore and GPU architectures. Different optimizations on both architectures have been proposed, focusing on memory management and workload mapping. We have chosen two different test scenarios which consist of single-solid and multiple-solid simulations. The performance analysis has been carried out on an intensive set of test cases to analyze the proposed optimizations using multiple CPUs (2) and GPUs (4). An effective performance is obtained for single-solid executions using one CPU (Intel Xeon E5520) achieving a speedup peak equal to 5.5. It is reached a higher benefit on multiple solids obtaining a top speedup of approximately 5.9 and 9 using one CPU (8 cores) and two CPUs (16 cores), respectively. On GPU (Kepler K20c) architecture, two different approaches are presented as the best alternative: one for single-solid executions and one for multiple-solid executions. The best approach obtained for one solid executions achieves a speedup of approximately 17 with respect the sequential counterpart. In contrast, for multiple-solid executions the benefit is much higher, being this type of problems much more suitable for GPU and reaching a peak speedup of 68, 115 and 162 using 1, 2 and 4 GPUs, respectively.     

On the adjoint-consistent formulation of interface conditions in goal-oriented error estimation and adaptivity for fluid–structure interaction

The numerical solution of fluid–structure-interaction problems poses a paradox in that most of the computational resources are consumed by the subsystem of least practical interest, viz., the fluid. Goal-oriented adaptive discretization methods provide a paradigm to bypass this paradox. Based on the solution of a dual problem, the contribution of local residuals to the error in a specific goal functional is estimated, and only the regions that yield a dominant contribution are refined. In the present work, we address a fundamental complication in the application of goal-oriented adaptivity to fluid–structure-interaction problems, namely, that the treatment of the interface conditions has nontrivial consequences for the properties of the dual problem. In the context of a linearized model problem, we consider two equivalent discretizations differing only on the formulation of the interface coupling terms. By means of an adjoint consistency analysis, we show that only one of these discretizations is adjoint consistent. Numerical experiments convey that the two discretizations behave very differently for the dual problem, and that the adjoint-consistent discretization yields more reliable error estimates. Based on the adjoint-consistent discretization, we finally present some h- and hp-adaptive results, confirming that tremendous savings in computational cost can be realized through the use of goal-oriented refinement strategies. The numerical experiments illustrate that the goal-oriented approach effectively equilibrates the error contributions of the fluid and structure subsystems, which is imperative for efficiently resolving the coupled fluid–structure-interaction problem, and which cannot be accomplished by uniform or residual-based refinement strategies.     

Coupling of mesoscale and microscale models—an approach to simulate scale interaction

Atmospheric flow and pollutant dispersion over built-up areas are affected by phenomena occurring at different scales. Hence, scale interactions should also be considered in the mathematical modelling of atmospheric flow and pollutant dispersion. In this paper a method is presented to couple prognostic mesoscale and microscale flow models. Results from mesoscale simulations are used to generate the initial state and boundary conditions for microscale simulations. The method comprises a three-dimensional interpolation scheme and a vertical adjustment of the interpolated quantities in the surface layer based on similarity theory. The method is applied to couple the microscale model MIMO with the mesoscale model MEMO.The coupled system MEMO–MIMO is applied to simulate the local scale flow for an industrial area in southwestern Germany. Model results are presented and compared with available measurements.     

Multi-solver algorithms for the partitioned simulation of fluid–structure interaction

In partitioned fluid–structure interaction simulations, the flow equations and the structural equations are solved separately. As a result, a coupling algorithm is needed to enforce the equilibrium on the fluid–structure interface in cases with strong interaction. This coupling algorithm performs coupling iterations between the solver of the flow equations and the solver of the structural equations. Current coupling algorithms couple one flow solver with one structural solver. Here, a new class of multi-solver quasi-Newton coupling algorithms for unsteady fluid–structure interaction simulations is presented. More than one flow solver and more than one structural solver are used for a single simulation. The numerical experiments demonstrate that the duration of a simulation decreases as the number of solvers is increased.     

Topology optimization for fluid–thermal interaction problems under constant input power

This paper deals with density-based topology optimization considering fluid and thermal interactions, in which the Navier–Stokes and heat transport equations are coupled. We particularly focus on designing heat exchangers. In the engineering context, heat exchangers are designed while considering a certain amount of input power. Therefore it is important to maximize the performance of a heat exchanger under a constant input power. In this paper we propose a way to control the input power by introducing an extra integral equation. To be more precise, in the fluid analysis, the inlet pressure is determined by solving the extra integral equation together with the Navier–Stokes equation. By doing this we can keep the inlet power constant even when the flow channels are changed in the optimization process. Consequently, the system of equations of the fluid field takes an integrodifferential form. On the other hand, in the heat transport analysis, a single governing equation is defined for simultaneously modeling both the solid and fluid parts. The design variable is a fluid fraction whose distribution represents the topology of the solid and fluid domains. When designing heat exchangers, two different heat conditions are considered in the formulation of the optimization problems, namely temperature-dependent and temperature-independent heat sources. Through the numerical examples for designing flow channels in a heat exchanger, it is shown that distinct topologies can be obtained according to the input power and the heat source conditions.     

Recent development of fluid–structure interaction capabilities in the ADINA system

The ADINA system has been developed in recent years into a complete system for the analysis of solid, fluid and coupled problems. Fluid flows can be modeled as Navier–Stokes incompressible, slightly compressible and fully compressible flows. They can also be modeled as porous medium flows. Structures can be modeled as 2D/3D solids, beams or shells. The response of the structure can be linear or nonlinear, and can also include contact effects. The fluid and structure can be coupled through their interface (FSI), porous media (PFSI) or thermal materials (TFSI). Both iterative and direct solution procedures can be used for solving the fully coupled system. These capabilities, together with the extensive boundary conditions and material models, and the user-friendly graphical system for pre- and post-processing (AUI), make the ADINA system a powerful tool for engineers and researchers.     

On the robustness and optimality of algebraic multilevel methods for reaction–diffusion type problems

This paper is on preconditioners for reaction–diffusion problems that are both, uniform with respect to the reaction–diffusion coefficients, and optimal in terms of computational complexity. The considered preconditioners belong to the class of so-called algebraic multilevel iteration (AMLI) methods, which are based on a multilevel block factorization and polynomial stabilization. The main focus of this work is on the construction and on the analysis of a hierarchical splitting of the conforming finite element space of piecewise linear functions that allows to meet the optimality conditions for the related AMLI preconditioner in case of second-order elliptic problems with non-vanishing zero-order term. The finite element method (FEM) then leads to a system of linear equations with a system matrix that is a weighted sum of stiffness and mass matrices. Bounds for the constant \(\gamma \) in the strengthened Cauchy–Bunyakowski–Schwarz inequality are computed for both mass and stiffness matrices in case of a general \(m\) -refinement. Moreover, an additive preconditioner is presented for the pivot blocks that arise in the course of the multilevel block factorization. Its optimality is proven for the case \(m=3\) . Together with the estimates for \(\gamma \) this shows that the construction of a uniformly convergent AMLI method with optimal complexity is possible (for \(m \ge 3\) ). Finally, we discuss the practical application of this preconditioning technique in the context of time-periodic parabolic optimal control problems.     

Comparison of X–T and X–X co-simulation techniques applied on railway dynamics

Multibody System Dynamics - Co-simulation techniques start to be of high interest when building a vehicle–track–soil model dedicated to ground-borne vibrations’ assessment. If...     

On the space–time of optimal, approximate and streaming algorithms for synopsis construction problems

Synopses construction algorithms have been found to be of interest in query optimization, approximate query answering and mining, and over the last few years several good synopsis construction algorithms have been proposed. These algorithms have mostly focused on the running time of the synopsis construction vis-a-vis the synopsis quality. However the space complexity of synopsis construction algorithms has not been investigated as thoroughly. Many of the optimum synopsis construction algorithms are expensive in space. For some of these algorithms the space required to construct the synopsis is significantly larger than the space required to store the input. These algorithms rely on the fact that they require a smaller “working space” and most of the data can be resident on disc. The large space complexity of synopsis construction algorithms is a handicap in several scenarios. In the case of streaming algorithms, space is a fundamental constraint. In case of offline optimal or approximate algorithms, a better space complexity often makes these algorithms much more attractive by allowing them to run in main memory and not use disc, or alternately allows us to scale to significantly larger problems without running out of space. In this paper, we propose a simple and general technique that reduces space complexity of synopsis construction algorithms. As a consequence we show that the notion of “working space” proposed in these contexts is redundant. This technique can be easily applied to many existing algorithms for synopsis construction problems. We demonstrate the performance benefits of our proposal through experiments on real-life and synthetic data. We believe that our algorithm also generalizes to a broader range of dynamic programs beyond synopsis construction. Sudipto Guha’s research supported in part by an Alfred P. Sloan Research Fellowship and by NSF Awards CCF-0430376, CCF-0644119.A preliminary version of the paper appeared as “Space efficiency in synopsis construction algorithms”, VLDB Conference 2005, Trondheim, [19].     

A fully discrete scheme for the pressure–stress formulation of the time-domain fluid–structure interaction problem

We propose an implicit Newmark method for the time integration of the pressure–stress formulation of a fluid–structure interaction problem. The space Galerkin discretization is based on the Arnold–Falk–Winther mixed finite element method with weak symmetry in the solid and the usual Lagrange finite element method in the acoustic medium. We prove that the resulting fully discrete scheme is well-posed and uniformly stable with respect to the discretization parameters and Poisson ratio, and we provide asymptotic error estimates. Finally, we present numerical tests to confirm the asymptotic error estimates predicted by the theory.     

Structural analysis of the intervertebral discs adjacent to an interbody fusion using multibody dynamics and finite element cosimulation

This work describes a methodology for the dynamic and structural analysis of complex (bio)mechanical systems that joins both multibody dynamics and finite element domains, in a synergetic way, through a cosimulation procedure that takes benefit of the advantages of each numerical formulation. To accomplish this goal, a cosimulation module is developed based on the gluing algorithm X-X, which is the key element responsible for the management of the information flux between the two software packages (each using its own mathematical formulation and code). The X-X algorithm uses for each cosimulated structure multiple pairs of reference points whose kinematics are solved by the multibody module and prescribed, as initial data, to the finite element counterpart. The finite element module, by its turn, solves the structural problem imposed by the prescribed kinematics, calculates the resulting generalized loads applied over the reference points and return these loads back to the multibody module that uses them to solve the dynamic problem and to calculate new reference kinematics to prescribe to the finite element module in the next time step. The proposed method is applied to study the cervical spine dynamics in a pathologic situation in which an intersomatic fusion is simulated to confirm its potential advantages. Taking into account the proposed simulation scenario, a cervical spine multibody model that includes the rigid vertebrae, the facet joints’ and spinous processes’ contacts, ligaments and the finite element models of the intervertebral discs, and their surrogates is developed. The proposed model is simulated for extension in a forward dynamics perspective.     

Two-dimensional simulation of fluid–structure interaction using lattice-Boltzmann methods

The development of flow instabilities due to high Reynolds number flow in artificial heart-value geometries inducing high strain rates and stresses often leads to hemolysis and related highly undesired effects. Geometric and functional optimization of artificial heart valves is therefore mandatory. In addition to experimental work in this field it is meanwhile possible to obtain increasing insight into flow dynamics by computer simulation of refined model problems. Here we present two-dimensional simulation results of the coupled fluid–structure problem defined by a model geometry of an artificial heart value with moving leaflets exposed to a channel flow driven by transient boundary conditions representing a physiologically relevant regime. A modified lattice-Boltzmann approach is used to solve the coupled problem.     

An hp finite element adaptive scheme to solve the Laplace model for fluid–solid vibrations

In this paper we introduce an hp finite element method to solve a two-dimensional fluid–structure spectral problem. This problem arises from the computation of the vibration modes of a bundle of parallel tubes immersed in an incompressible fluid. We prove the convergence of the method and a priori error estimates for the eigenfunctions and the eigenvalues. We define an a posteriori error estimator of the residual type which can be computed locally from the approximate eigenpair. We show its reliability and efficiency by proving that the estimator is equivalent to the energy norm of the error up to higher order terms, the equivalence constant of the efficiency estimate being suboptimal in that it depends on the polynomial degree. We present an hp adaptive algorithm and several numerical tests which show the performance of the scheme, including some numerical evidence of exponential convergence.     

Thermal interactions in nanoscale fluid flow: molecular dynamics simulations with solid–liquid interfaces

Molecular dynamics (MD) simulations of nano-scale flows typically utilize fixed lattice crystal interactions between the fluid and stationary wall molecules. This approach cannot properly model interactions and thermal exchange at the wall–fluid interface. We present a new interactive thermal wall model that can properly simulate the flow and heat transfer in nano-scale channels. The new model utilizes fluid molecules freely interacting with the thermally oscillating wall molecules, which are connected to the lattice positions with “bonds”. Thermostats are applied separately to each layer of the walls to keep the wall temperature constant, while temperature of the fluid is sustained without the application of a thermostat. Two-dimensional MD simulation results for shear driven nano-channel flow shows parabolic temperature distribution within the domain, induced by viscous heating due to a constant shear rate. As a result of the Kapitza resistance, temperature profiles exhibit jumps at the fluid–wall interface. Time dependent simulation results for freezing of liquid argon in a nano-channel are also presented.