Iterative Coupling Procedure Research Articles

Sequential Coupling Shows Minor Effects of Fluid Dynamics on Myocardial Deformation in a Realistic Whole-Heart Model.

Background: The human heart is a masterpiece of the highest complexity coordinating multi-physics aspects on a multi-scale range. Thus, modeling the cardiac function in silico to reproduce physiological characteristics and diseases remains challenging. Especially the complex simulation of the blood's hemodynamics and its interaction with the myocardial tissue requires a high accuracy of the underlying computational models and solvers. These demanding aspects make whole-heart fully-coupled simulations computationally highly expensive and call for simpler but still accurate models. While the mechanical deformation during the heart cycle drives the blood flow, less is known about the feedback of the blood flow onto the myocardial tissue.Methods and Results: To solve the fluid-structure interaction problem, we suggest a cycle-to-cycle coupling of the structural deformation and the fluid dynamics. In a first step, the displacement of the endocardial wall in the mechanical simulation serves as a unidirectional boundary condition for the fluid simulation. After a complete heart cycle of fluid simulation, a spatially resolved pressure factor (PF) is extracted and returned to the next iteration of the solid mechanical simulation, closing the loop of the iterative coupling procedure. All simulations were performed on an individualized whole heart geometry. The effect of the sequential coupling was assessed by global measures such as the change in deformation and—as an example of diagnostically relevant information—the particle residence time. The mechanical displacement was up to 2 mm after the first iteration. In the second iteration, the deviation was in the sub-millimeter range, implying that already one iteration of the proposed cycle-to-cycle coupling is sufficient to converge to a coupled limit cycle.Conclusion: Cycle-to-cycle coupling between cardiac mechanics and fluid dynamics can be a promising approach to account for fluid-structure interaction with low computational effort. In an individualized healthy whole-heart model, one iteration sufficed to obtain converged and physiologically plausible results.

Nonlinear analysis of interacting saturated porous and elastic media by time-domain FEM/BEM iterative coupling procedures

This work deals with the coupling of the Finite Element Method (FEM) and the Boundary Element Method (BEM) to model interacting saturated porous and sealed elastic media. In this coupled analysis, the porodynamic subdomains of the model are discretised by the FEM, and the elastodynamic interacting subdomains are discretised by the BEM. Nonlinearities may be considered within the FEM subdomains. An iterative coupling approach is adopted, which leads to an efficient and easy to implement formulation, enabling the FEM and BEM modules to be handled separately. The iterative coupling methodology allows nonlinear analyses to be carried out quite directly, considering a single iterative loop for all iterative computations. It also permits independent discretisations to be straightforwardly applied for each subdomain of the model, taking into account simple interpolation/extrapolation procedures on common interfaces. Optimal relaxation parameters are considered to speed up the convergence of the iterative coupling analysis. At the end of the manuscript, numerical examples are presented, illustrating the performance of the proposed formulation.

Structural control of the floating breakwaters by implementation of tuned liquid column damper

The growing maritime activities have led offshore engineers to the application of floating breakwaters to protect coastlines from erosion and to provide a layer of support to ports in the case of strong wave actions. In these applications, minimizing the floating part responses to wave-induced excitations as one of the most critical operational characteristics would be a key factor. In this article, the structural responses of the floating breakwaters are studied through modeling and simulation. To mitigate the floating part wave-induced vibrations, an attached tuned liquid column damper is integrated into the simulation. In the first stage, the numerical model of the floating breakwater system containing the floating body and the mooring system is created. Then, by proposing an iterative coupling procedure, the joint tuned liquid column damper-floating breakwater model is developed. Several rigorous study cases are defined to evaluate the effect of tuned liquid column damper on controlling the floating body unwanted vibrations. In this application, the Airy wave theory and the Joint North Sea Wave Observation Project wave spectrum are used for wave excitations. In order to evaluate the effect of tuned liquid column damper on floating breakwaters, some design parameters like floating body motions and mooring system-mobilized tensile stresses are evaluated. The simulations are conducted in both the time domain and the frequency domain for cases with and without tuned liquid column damper. The rain flow counting method is applied to perform the mooring system fatigue analysis. The study results clearly proved that implementation of tuned liquid column damper would mitigate the floating body responses compared to the original floating breakwater system. In addition, it is indicated that the fatigue-induced failure risks in tuned liquid column damper-floating breakwater mooring system is decreased that would reduce the procurement costs and increase the operational safety of the floating breakwater system.

Iterative coupling procedure applied to the transient response of dynamic soil-structure systems

This paper proposes a methodology to obtain the transient response of structural system interacting with soil-foundation schemes supported by viscoelastic soils. The structure and soil are divided into sub-systems. The time domain solution for each subsystem is formulated by an appropriated methodology. The equations of motion of structure are solved by Newmark integration algorithm. The transient response of the soil is obtained by a convolution integral. The convolution integral uses transient impulse response of viscoelastic soils. Newmark and convolution algorithms are formulated as input and output schemes, which, in turn, are plugged to the time stepping iterative algorithm. The scheme is applied to vertical response of a dynamical system interacting with a massless foundation laying on a soil modelled as a three-dimensional homogeneous viscoelastic half-space. For two distinct external forces, the resulting coupled displacements, interface forces, errors and number of iterations within each time step are provided.

A CFD-supported dynamic system-level model of a sodium-cooled billboard-type receiver for central tower CSP applications

This work focusses on the dynamic modeling of a sodium-cooled billboard-type receiver, as adopted in the reference plant of this study, the Jemalong Solar Thermal Station, in Australia. A detailed system-level thermal-fluid-dynamic model is developed in the OpenModelica framework, with the aim to predict the receiver behavior during transients, as well as its performance upon reaching steady-state conditions. The model solves the conjugate heat transfer problem relating conduction in the receiver pipes to the internal flow of sodium. The convective losses from the irradiated face of the receiver, due to the external flow of air, are calculated using empirical correlation available in literature for flat-plates and then carefully evaluated using 3D Computational Fluid Dynamics (CFD), which allows taking into account the actual geometry of the receiver. The CFD results, considering different wind speeds and highlighting the cavity-like effects of the receiver geometry under consideration, are first compared with those obtained from empirical correlations available in the literature for vertical plates in the case of uniform temperature distribution on the absorber pipes, showing significant differences. Then an iterative coupling procedure with the system-level model of the same receiver is proposed, which facilitates handling of the more realistic case of a non-uniform temperature distribution. Finally, we present and discuss the successful benchmark in a simple case of the system-level model against another model from the literature, its preliminary validation against experimental data, and first applications to a fast start-up/passing cloud/shut-down transient and to a whole-day simulation with controls.

An efficient multi-time step FEM–SFEM iterative coupling procedure for elastic–acoustic interaction problems

An iterative coupling methodology between the finite element method (FEM) and the spectral finite element method (SFEM) for the modeling of coupled elastic–acoustic problems in the time domain is presented here. Since the iterative coupling procedure allows the use of a nonconforming mesh at the interface between the subdomains, the difference in the element sizes concerning the FEM and SFEM is handled in a straightforward and efficient manner, thereby retaining all the advantages of the SFEM. By means of the HHT time integration method, controllable numerical damping can be introduced in one of the subdomains, increasing the robustness of the method and improving the accuracy of the results; besides, independent time step sizes can be considered within each subdomain, resulting in a more efficient algorithm. In this work, a modification in the subcycling procedure is proposed, ensuring not only an efficient and accurate methodology but also avoiding the computation of a relaxation parameter. Numerical simulations are presented in order to illustrate the accuracy and potential of the proposed methodology.

On the Application of Acoustic Analogies in the Numerical Simulation of Human Phonation Process

This paper deals with the numerical simulation of the flow induced sound as generated in the human phonation process. The two-dimensional fluid-structure interaction problem is modeled with the aid of linear elastic problem coupled to the incompressible Navier-Stokes equations in the arbitrary Lagrangian-Eulerian form. For calculation of sound sources and its propagation the Lighthill acoustic analogy is used. This approach is compared to the Perturbed Convective Wave Equation method. All partial differential equations, describing the elastic body motion, the fluid flow and the acoustics, are solved by applying the finite element method. In order to overcome numerical instabilities in the Navier-Stokes equations arising due to high Reynolds numbers, the modified streamline-upwind/Petrov-Galerkin stabilization is used. The implemented iterative coupling procedure is described. Numerical results are presented.

Elastodynamic analysis by a frequency-domain FEM-BEM iterative coupling procedure

This paper presents a coupled FEM-BEM strategy for the numerical analysis of elastodynamic problems where infinite-domain models and complex heterogeneous media are involved, rendering a configuration in which neither the Finite Element Method (FEM) nor the Boundary Element Method (BEM) is most appropriate for the numerical analysis. In this case, the coupling of these methodologies is recommended, allowing exploring their respective advantages. Here, frequency domain analyses are focused and an iterative FEM-BEM coupling technique is considered. In this iterative coupling, each sub-domain of the model is solved separately, and the variables at the common interfaces are iteratively updated, until convergence is achieved. A relaxation parameter is introduced into the coupling algorithm and an expression for its optimal value is deduced. The iterative FEM-BEM coupling technique allows independent discretizations to be efficiently employed for both finite and boundary element methods, without any requirement of matching nodes at the common interfaces. In addition, it leads to smaller and better-conditioned systems of equations (different solvers, suitable for each sub-domain, may be employed), which do not need to be treated (inverted, triangularized etc.) at each iterative step, providing an accurate and efficient methodology.

Frequency domain analysis of interacting acoustic–elastodynamic models taking into account optimized iterative coupling of different numerical methods

In this work, interacting acoustic–elastodynamic models are analyzed by means of an optimized iterative coupling algorithm. In this iterative coupling procedure, each acoustic/elastodynamic sub-domain of the model is solved independently, and the variables at the common interfaces of the sub-domains are successively renewed, until convergence is achieved. A relaxation parameter is introduced in order to ensure and/or speed up the convergence of the iterative analysis, and an expression to compute optimal values for the relaxation parameter is presented. Several numerical methods are considered to discretize the acoustic and elastodynamic sub-domains of the coupled model, and the performance of these different methodologies, in the coupled analysis, is discussed. In this context, the boundary element method and the method of fundamental solutions are applied to model the acoustic sub-domains, whereas the finite element method, the collocation method and the meshless local Petrov–Galerkin method are applied to model the elastodynamic sub-domains. Independent discretizations of the acoustic/elastodynamic sub-domains are allowed, being no matching nodes required along the common interfaces. At the end of the paper, numerical examples are presented, illustrating the performance and potentialities of the adopted procedures.

Iterative dynamic analysis of linear and nonlinear fully saturated porous media considering edge-based smoothed meshfree techniques

In this work, smoothed meshfree methods are firstly applied to numerically analyze nonlinear pore-dynamic models. A weakened weak formulation based on the edges of triangular cells obtained by a Delaunay triangulation is considered here, framing the so-called edge-based smoothed domains. The meshfree shape functions are computed by the radial point interpolation method considering the T6-scheme for the shape function support domains. Enhanced procedures to compute the mass, compressibility and coupling matrices of the pore-dynamic model are discussed, which are consistent with the computation of the stiffness and permeability matrices (as well as internal force vectors, in case of nonlinear analyses) of the edge-based smoothed domain formulation and that consider finer local integration techniques at lower computational costs, rendering more accurate and efficient procedures. Two numerical formulations are considered here to analyze the time-domain nonlinear coupled system of equations that arises once the spatial discretization is accomplished: the standard Newmark/Newton–Raphson method and an alternative iterative coupling approach. In this iterative approach, each phase of the coupled problem is treated separately, uncoupling the governing equations of the model; thus, smaller and better conditioned systems of equations are obtained, rendering more attractive techniques. A relaxation parameter is introduced in order to improve the efficiency of the iterative coupling procedure and an expression to compute optimal values for the relaxation parameter is discussed. At the end of the paper, numerical examples are presented, illustrating the effectiveness and potentialities of the proposed methodologies.

Frequency domain analysis of acoustic wave propagation in heterogeneous media considering iterative coupling procedures between the method of fundamental solutions and Kansa's method

SUMMARYAcoustic wave propagation in heterogeneous media is a topic of significant interest in many areas of science and engineering, including aeroacoustics and sound propagation in oceans. In the present work, numerical frequency domain models based on the joint use of the method of fundamental solutions and of the radial basis function collocation method (also known as Kansa's method) are discussed. In this context, the method of fundamental solutions is used to model the homogeneous part of the propagation domain, while Kansa's method is employed to model the presence of heterogeneities. The coupling between the two parts of the propagation domain is performed iteratively, allowing independent spatial discretization between the different subdomains of the model (i.e. matching collocation points at common surfaces are not necessary). Additionally, an optimised algorithm, based on the use of a varying relaxation parameter, is employed to speed up and/or to ensure the convergence of the iterative coupling process. At the end of the paper, numerical results illustrate the applicability and potentialities of the proposed formulations. Copyright © 2011 John Wiley & Sons, Ltd.

A Hybrid Finite‐Difference and Analytic Element Groundwater Model

Regional finite-difference models tend to have large cell sizes, often on the order of 1-2 km on a side. Although the regional flow patterns in deeper formations may be adequately represented by such a model, the intricate surface water and groundwater interactions in the shallower layers are not. Several stream reaches and nearby wells may occur in a single cell, precluding any meaningful modeling of the surface water and groundwater interactions between the individual features. We propose to replace the upper MODFLOW layer or layers, in which the surface water and groundwater interactions occur, by an analytic element model (GFLOW) that does not employ a model grid; instead, it represents wells and surface waters directly by the use of point-sinks and line-sinks. For many practical cases it suffices to provide GFLOW with the vertical leakage rates calculated in the original coarse MODFLOW model in order to obtain a good representation of surface water and groundwater interactions. However, when the combined transmissivities in the deeper (MODFLOW) layers dominate, the accuracy of the GFLOW solution diminishes. For those cases, an iterative coupling procedure, whereby the leakages between the GFLOW and MODFLOW model are updated, appreciably improves the overall solution, albeit at considerable computational cost. The coupled GFLOW-MODFLOW model is applicable to relatively large areas, in many cases to the entire model domain, thus forming an attractive alternative to local grid refinement or inset models.

Numerical modelling of acoustic–elastodynamic coupled problems by stabilized boundary element techniques

In this work, an efficient, flexible, accurate and stable algorithm to numerically model interacting acoustic–elastodynamic sub-domains is described. Stabilized time-domain boundary element techniques are considered to discretize each sub-domain of the model and proper numerical expressions on acoustic–elastodynamic interfaces are presented. Moreover, stabilized iterative coupling procedures are adopted and different time and space sub-domain discretizations are allowed, improving the robustness and versatility of the methodology. At the end of the paper, numerical results are presented, illustrating the potentialities of the proposed formulation.

Numerical study of hemodynamics and wall mechanics in distal end-to-side anastomoses of bypass grafts

The development and progress of distal anastomotic intimal hyperplasia seems to be promoted by altered flow conditions and intramural stress distributions at the region of the artery–graft junction of vascular bypass configurations. From clinical observations, it is known that intimal hyperplasia preferentially occurs at outflow anastomoses of prosthetic bypass grafts. In order to gain a deeper insight into post-operative disease processes, and subsequently, to contribute to the development of improved vascular reconstructions with respect to long term patency rates, detailed studies are required. In context with in vivo experiments, this study was designed to analyze the flow dynamics and wall mechanics in anatomically correct bypass configurations related to two different surgical techniques and resulting geometries (conventional geometry and Miller-cuff). The influence of geometric conditions and of different compliance of synthetic graft, the host artery and the interposed venous cuff on the hemodynamic behavior and on the wall stresses are investigated. The flow studies apply the time-dependent, three-dimensional Navier–Stokes equations describing the motion of an incompressible Newtonian fluid. The vessel walls are described by a geometrically non-linear shell structure. In an iterative coupling procedure, the two problems are solved by means of the finite element method. The numerical results demonstrate non-physiological flow patterns in the anastomotic region. Strongly skewed axial velocity profiles and high secondary velocities occur downstream the artery–graft junction. On the artery floor opposite the junction, flow separation and zones of recirculation are found. The wall mechanical studies show that increased compliance mismatch leads to increased intramural stresses, and thus, may have a proliferative influence on suture line hyperplasia, as it is observed in the in vivo study.

Coupling dynamic models of climate and vegetation

AbstractNumerous studies have underscored the importance of terrestrial ecosystems as an integral component of the Earth's climate system. This realization has already led to efforts to link simple equilibrium vegetation models with Atmospheric General Circulation Models through iterative coupling procedures. While these linked models have pointed to several possible climate–vegetation feedback mechanisms, they have been limited by two shortcomings: (i) they only consider the equilibrium response of vegetation to shifting climatic conditions and therefore cannot be used to explore transient interactions between climate and vegetation; and (ii) the representations of vegetation processes and land‐atmosphere exchange processes are still treated by two separate models and, as a result, may contain physical or ecological inconsistencies.Here we present, as a proof concept, a more tightly integrated framework for simulating global climate and vegetation interactions. The prototype coupled model consists of the GENESIS (version 2) Atmospheric General Circulation Model and the IBIS (version 1) Dynamic Global Vegetation Model. The two models are directly coupled through a common treatment of land surface and ecophysiological processes, which is used to calculate the energy, water, carbon, and momentum fluxes between vegetation, soils, and the atmosphere. On one side of the interface, GENESIS simulates the physics and general circulation of the atmosphere. On the other side, IBIS predicts transient changes in the vegetation structure through changes in the carbon balance and competition among plants within terrestrial ecosystems.As an initial test of this modelling framework, we perform a 30 year simulation in which the coupled model is supplied with modern CO2concentrations, observed ocean temperatures, and modern insolation. In this exploratory study, we run the GENESIS atmospheric model at relatively coarse horizontal resolution (4.5° latitude by 7.5° longitude) and IBIS at moderate resolution (2° latitude by 2° longitude). We initialize the models with globally uniform climatic conditions and the modern distribution of potential vegetation cover. While the simulation does not fully reach equilibrium by the end of the run, several general features of the coupled model behaviour emerge.We compare the results of the coupled model against the observed patterns of modern climate. The model correctly simulates the basic zonal distribution of temperature and precipitation, but several important regional biases remain. In particular, there is a significant warm bias in the high northern latitudes, and cooler than observed conditions over the Himalayas, central South America, and north‐central Africa. In terms of precipitation, the model simulates drier than observed conditions in much of South America, equatorial Africa and Indonesia, with wetter than observed conditions in northern Africa and China.Comparing the model results against observed patterns of vegetation cover shows that the general placement of forests and grasslands is roughly captured by the model. In addition, the model simulates a roughly correct separation of evergreen and deciduous forests in the tropical, temperate and boreal zones. However, the general patterns of global vegetation cover are only approximately correct: there are still significant regional biases in the simulation. In particular, forest cover is not simulated correctly in large portions of central Canada and southern South America, and grasslands extend too far into northern Africa.These preliminary results demonstrate the feasibility of coupling climate models with fully dynamic representations of the terrestrial biosphere. Continued development of fully coupled climate‐vegetation models will facilitate the exploration of a broad range of global change issues, including the potential role of vegetation feedbacks within the climate system, and the impact of climate variability and transient climate change on the terrestrial biosphere.

Coupling dynamic models of climate and vegetation

Numerous studies have underscored the importance of terrestrial ecosystems as an integral component of the Earth's climate system. This realization has already led to efforts to link simple equilibrium vegetation models with Atmospheric General Circulation Models through iterative coupling procedures. While these linked models have pointed to several possible climate–vegetation feedback mechanisms, they have been limited by two shortcomings: (i) they only consider the equilibrium response of vegetation to shifting climatic conditions and therefore cannot be used to explore transient interactions between climate and vegetation; and (ii) the representations of vegetation processes and land-atmosphere exchange processes are still treated by two separate models and, as a result, may contain physical or ecological inconsistencies. Here we present, as a proof concept, a more tightly integrated framework for simulating global climate and vegetation interactions. The prototype coupled model consists of the GENESIS (version 2) Atmospheric General Circulation Model and the IBIS (version 1) Dynamic Global Vegetation Model. The two models are directly coupled through a common treatment of land surface and ecophysiological processes, which is used to calculate the energy, water, carbon, and momentum fluxes between vegetation, soils, and the atmosphere. On one side of the interface, GENESIS simulates the physics and general circulation of the atmosphere. On the other side, IBIS predicts transient changes in the vegetation structure through changes in the carbon balance and competition among plants within terrestrial ecosystems. As an initial test of this modelling framework, we perform a 30 year simulation in which the coupled model is supplied with modern CO2 concentrations, observed ocean temperatures, and modern insolation. In this exploratory study, we run the GENESIS atmospheric model at relatively coarse horizontal resolution (4.5° latitude by 7.5° longitude) and IBIS at moderate resolution (2° latitude by 2° longitude). We initialize the models with globally uniform climatic conditions and the modern distribution of potential vegetation cover. While the simulation does not fully reach equilibrium by the end of the run, several general features of the coupled model behaviour emerge. We compare the results of the coupled model against the observed patterns of modern climate. The model correctly simulates the basic zonal distribution of temperature and precipitation, but several important regional biases remain. In particular, there is a significant warm bias in the high northern latitudes, and cooler than observed conditions over the Himalayas, central South America, and north-central Africa. In terms of precipitation, the model simulates drier than observed conditions in much of South America, equatorial Africa and Indonesia, with wetter than observed conditions in northern Africa and China. Comparing the model results against observed patterns of vegetation cover shows that the general placement of forests and grasslands is roughly captured by the model. In addition, the model simulates a roughly correct separation of evergreen and deciduous forests in the tropical, temperate and boreal zones. However, the general patterns of global vegetation cover are only approximately correct: there are still significant regional biases in the simulation. In particular, forest cover is not simulated correctly in large portions of central Canada and southern South America, and grasslands extend too far into northern Africa. These preliminary results demonstrate the feasibility of coupling climate models with fully dynamic representations of the terrestrial biosphere. Continued development of fully coupled climate-vegetation models will facilitate the exploration of a broad range of global change issues, including the potential role of vegetation feedbacks within the climate system, and the impact of climate variability and transient climate change on the terrestrial biosphere.

Two‐dimensional transport model for variably saturated porous media with major ion chemistry

We present the development and demonstrate the use of the two‐dimensional finite element code UNSATCHEM‐2D for modeling major ion equilibrium and kinetic nonequilibrium chemistry in variably saturated porous media. The model is intended for prediction of major ion chemistry and water and solute fluxes for soils under transient conditions. Since the solution chemistry in the unsaturated zone is significantly influenced by variations in water content, temperature, and CO2 concentrations in the soil gas, all these variables are also calculated by the model. The major variables of the chemical system are Ca, Mg, Na, K, SO4, Cl, NO3, alkalinity, and CO2. The model accounts for equilibrium chemical reactions between these components such as complexation, cation exchange, and precipitation‐dissolution. For the precipitation‐dissolution of calcite and dissolution of dolomite, either equilibrium or multicomponent kinetic expressions are used which include both forward and back reactions. Other dissolution‐precipitation reactions considered include gypsum, hydromagnesite, and nesquehonite. Since the ionic strength of soil solutions can often reach high values, both modified Debye‐Hückel and Pitzer expressions were incorporated into the model to calculate single ion activities. The need for an iterative coupling procedure between the solute transport and chemical modules is demonstrated with an example which considers root water uptake and irrigation using moderately saline water. The utility of the model is further illustrated with two‐dimensional simulations with surface and subsurface irrigation from a line source.