In this paper, a validation of a recently developed fluid-structure interaction (FSI) coupling algorithm to simulate numerically the dynamics of an aortic bileaflet mechanical heart valve (BMHV) is performed. This validation is done by comparing the numerical simulation results with in vitro experiments. For the in vitro experiments, the leaflet kinematics and flow fields are obtained via the particle image velocimetry (PIV) technique. Subsequently, the same case is numerically simulated by the coupling algorithm and the resulting leaflet kinematics and flow fields are obtained. Finally, the results are compared, revealing great similarity in leaflet motion and flow fields between the numerical simulation and the experimental test. Therefore, it is concluded that the developed algorithm is able to capture very accurately all the major leaflet kinematics and dynamics and can be used to study and optimize the design of BMHVs.

The aim of this study was to reconcile some of our own previous work and the work of others to generate a physiologically realistic numerical simulation environment that allows to virtually assess the performance of BMHVs. The model incorporates: (i) a left ventricular deformable model to generate a physiological inflow to the aortic valve; (ii) a patient-specific aortic geometry (root, arch and descending aorta); (iii) physiological pressure and flow boundary conditions. We particularly studied the influence of downstream geometry, valve size and orientation on leaflet kinematics and functional indices used in clinical routine. Compared to the straight tube geometry, the patient-specific aorta leads to a significant asynchronous movement of the valve, especially during the closing of the valve. The anterior leaflet starts to close first, impacts the casing at the closed position and remains in this position. At the same time, the posterior leaflet impacts the pivoting mechanisms at the fully open position. At the end of systole, this leaflet subsequently accelerates to the closed position, impacting the casing with an angular velocity of approximately −477 rad/s. The valve size greatly influences the transvalvular pressure gradient (TPG), but does not change the overall leaflet kinematics. This is in contrast to changes in valve orientation, where changing valve orientation induces large differences in leaflet kinematics, but the TPG remains approximately the same.

SUMMARYIn this paper, the influence of the upstream boundary condition in the numerical simulation of an aortic bileaflet mechanical heart valve (BMHV) is studied. Three three‐dimensional cases with different upstream boundary conditions are compared. The first case consists of a rigid straight tube with a velocity profile at its inlet. In the second case, the upstream geometry is a contracting left ventricle (LV), positioned symmetrically with respect to the valve. In the last case, the LV is positioned asymmetrical with respect to the valve. The cases are used to simulate the same three‐dimensional BMHV. The change in time of the LV volume is calculated such that the flow rate through the valve is identical in each case. The opening dynamics of the BMHV are modelled using fluid–structure interaction. The simulations show that differences occur in the leaflet movement of the three cases. In particular, with the asymmetric LV, one of the leaflets impacts the blocking mechanism at its open position with a 34% higher velocity than when using the velocity profile, and with an 88% higher velocity than in the symmetric LV case. Therefore, when simulating such an impact, the upstream boundary condition needs to be chosen carefully. Copyright © 2012 John Wiley & Sons, Ltd.

In the past 60 years, the replacement of the aortic valve by a prosthesis has become a routine treatment for severe aortic valve failure. Several valve prostheses have been developed of which the bileaflet mechanical heart valves (BMHVs) are widely preferred. However, current BMHVs still induce thromboembolism, among other undesired side effects, which is believed to be due to non-physiological flow generated by the leaflets. Insights into the dynamics of a BMHV can be provided by numerical methods. In this study, the dynamics of the BMHV are calculated by a strong fluid-structure interaction (FSI) coupling algorithm and the aortic BMHV is simulated under realistic, patient-specific boundary conditions. Upstream of the valve, a model of the left ventricle is constructed. The geometry downstream of the valve consists of a patient-specific aorta with patient-specific flow rates and physiological pressure profiles at its endings. To the best of our knowledge, this is the first 3D numerical simulation of an aortic BMHV that combines upstream and downstream anatomical boundary conditions with a strongly coupled solution of the valve leaflet movement. The results give insights into realistic flow fields and leaflet kinematics. Clinical performance parameters are calculated, such as the amount of back flow and the drop in flow potential energy.

One of the major challenges in the design of Bileaflet Mechanical Heart Valves (BMHVs) is reduction of the blood damage generated by non-physiological blood flow. Numerical simulations provide relevant insights into the (fluid) dynamics of the BMHV and are used for design optimisation. In this paper, a strong coupling algorithm for the partitioned Fluid-Structure Interaction (FSI) simulation of a BMHV is presented. The convergence of the coupling iterations between the flow solver and the leaflet motion solver is accelerated by using a numerically calculated Jacobian with the derivatives of the pressure and viscous moments acting on the leaflets with respect to the leaflet accelerations. The developed algorithm is used to simulate the dynamics of a 3D BMHV in three different geometries, allowing an analysis of the solution process. Moreover, the leaflet kinematics and the general flow field are discussed, with special focus on the shear stresses on the valve leaflets.

The numerical simulation of Bileaflet Mechanical Heart Valves (BMHVs) has gained strong interest in the last years, as a design and optimisation tool. In this paper, a strong coupling algorithm for the partitioned fluidstructure interaction simulation of a BMHV is presented. The convergence of the coupling iterations between the flow solver and the leaflet motion solver is accelerated by using the Jacobian with the derivatives of the pressure and viscous moments acting on the leaflets with respect to the leaflet accelerations. This Jacobian is numerically calculated from the coupling iterations. An error analysis is done to derive a criterion for the selection of useable coupling iterations. The algorithm is successfully tested for two 3D cases of a BMHV and a comparison is made with existing coupling schemes. It is observed that the developed coupling scheme outperforms these existing schemes in needed coupling iterations per time step and CPU time.

In previous work of the authors, Fourier stability analyses have been performed of Gauss–Seidel iterations between the flow solver and the structural solver in a partitioned fluid-structure interaction simulation. These analyses of the flow in an elastic tube demonstrated that only a number of Fourier modes in the error on the interface displacement are unstable. Moreover, the modes with a low wave number are most unstable and these modes can be resolved on a coarser grid. Therefore, a new class of quasi-Newton methods with more than one grid level is introduced. Numerical experiments show a significant reduction in run time.

The diffusion factor of Rodgers (1978) for impellers of centrifugal compressors, which is an adapted version of the diffusion factor of Lieblein et al. (1953) for axial cascades with decelerating flow, is slightly adapted for impellers of radial fans. The relation between the impeller efficiency and the diffusion factor is determined from numerical analysis of 31 impeller configurations. These are variants of the impellers of 2 built radial fans by varying the blade shape and the blade number. The numerical technique is validated by comparison with the measured performance of the two built fans. Recommendations on optimal values of the diffusion factor are formulated, with a similar limiting value DF=0.6 as for axial cascades.

In this article, we present a fluid-structure interaction algorithm accounting for the mutual interaction between two rigid bodies. The algorithm was used to perform a numerical simulation of mitral valve (MV) dynamics during diastolic filling. In numerical simulations of intraventricular flow and MV motion, the asymmetry of the leaflets is often neglected. In this study the MV was rendered as two rigid, asymmetric leaflets. The 2D simulations incorporated the dynamic interaction of blood flow and leaflet motion and an imposed subject-specific, transient left ventricular wall movement obtained from ultrasound recordings. By including the full Jacobian matrix in the algorithm, the speed of the simulation was enhanced by more than 20% compared to using a diagonal Jacobian matrix. Furthermore, our results indicate that important features of the flow field may not be predicted by the use of symmetric leaflets or in the absence of an adequate model for the left atrium.

We present a newly developed Fluid-Structure Interaction coupling algorithm to simulate Bileaflet Mechanical Heart Valves dynamics in a partitioned way. The coupling iterations between the flow solver and the leaflet motion solver are accelerated by using the Jacobian with the derivatives of the pressure and viscous moments acting on the leaflets with respect to the leaflet acceleration. This Jacobian is used in the leaflet motion solver when new positions of the leaflets are computed during the coupling iterations. The Jacobian is numerically derived from the flow solver by applying leaflet perturbations. Instead of calculating this Jacobian every time step, the Jacobian is extrapolated from previous time steps and a recalculation of the Jacobian is only done when needed. The efficiency of our new algorithm is subsequently compared to existing algorithms which use fixed relaxation and dynamic Aitken Delta(2) relaxation in the coupling iterations when the new positions of the leaflets are computed. Results show that dynamic Aitken Delta(2) relaxation outperforms fixed relaxation. Moreover, during the opening phase of the valve, our new algorithm needs fewer subiterations per time step to achieve convergence than the method with Aitken Delta(2) relaxation. Thus, our newly developed FSI coupling scheme outperforms the existing coupling schemes.

Currently, the interaction between free surface flow and an elastic structure is simulated with monolithic codes which calculate the deformation of the structure and the liquid–gas flow simultaneously. In this work, this interaction is calculated in a partitioned way with a separate flow solver and a separate structural solver using the interface quasi-Newton algorithm with approximation for the inverse of the Jacobian from a least-squares model (IQN-ILS). The interaction between an elastic beam and a sloshing liquid in a rolling tank is calculated and the results agree well with experimental data. Subsequently, the impact of both a rigid cylinder and a flexible composite cylinder on a water surface is simulated to assess the effect of slamming on the components of certain wave-energy converters. The impact pressure on the bottom of the rigid cylinder is nearly twice as high as on the flexible cylinder, which emphasizes the need for fluid–structure interaction calculations in the design process of these wave-energy converters. For both the rolling tank simulations and the impact simulations, grid refinement is performed and the IQN-ILS algorithm requires the same number of iterations on each grid. The simulations on the coarse grid are also executed using Gauss-Seidel coupling iterations with Aitken relaxation which requires significantly more coupling iterations per time step.

In partitioned fluid-structure interaction simulations, the flow equations and the structural equations are solved separately. Consequently, the stresses and displacements on both sides of the fluid-structure interface are not automatically in equilibrium. Coupling techniques like Aitken relaxation and the Interface Block Quasi-Newton method with approximate Jacobians from Least-Squares models (IBQN-LS) enforce this equilibrium, even with black-box solvers. However, all existing coupling techniques use only one flow solver and one structural solver. To benefit from the large number of multi-core processors in modern clusters, a new Multi-Solver Interface Block Quasi-Newton (MS-IBQN-LS) algorithm has been developed. This algorithm uses more than one flow solver and structural solver, each running in parallel on a number of cores. One-dimensional and three-dimensional numerical experiments demonstrate that the run time of a simulation decreases as the number of solvers increases, albeit at a slower pace. Hence, the presented multi-solver algorithm accelerates fluid-structure interaction calculations by increasing the number of solvers, especially when the run time does not decrease further if more cores are used per solver.

In this paper, the heat transfer from a single heat fin to the air flow in the wake of a piezoelectric fan (piezofan) is optimised. Both the heat fin and the piezofan are positioned in a channel, which has a significant influence on the flow field. The design variable is the frequency of the voltage applied to the piezofan. The heat transfer for different excitation frequencies is calculated using unsteady fluid-structure interaction simulations. To obtain a modular simulation environment, the flow equations and the structural equations are solved separately. However, the equilibrium on the fluid-structure interface is not satisfied automatically in this partitioned approach. Therefore, the interface quasi-Newton technique with an approximation for the inverse of the Jacobian from a least-squares model (IQN-ILS) is used to perform coupling iterations between the flow solver and the structural solver in each time step. With the unsteady fluid-structure interaction model, a surrogate model is constructed. The optimization of the surrogate model yields a frequency close to the first eigenfrequency of the structure.

In this research, the fluid-structure interaction in a recently developed membrane pump is analysed. The governing equations for the laminar flow and for the deformation of the membrane are solved with two separate codes, which are coupled with the quasi-Newton technique with an approximation for the inverse of the Jacobian from a least-squares model. After the description of the model and the solution techniques, a detailed analysis of the flow field, the deformation of the structure and the stress in the membrane is presented. An energetic analysis of the pump is performed, and the pump's efficiency is calculated.

Partitioned simulations of fluid–structure interaction can be solved for the interface’s position with Newton–Raphson iterations but obtaining the exact Jacobian is impossible if the solvers are “black boxes”. It is demonstrated that only an approximate Jacobian is needed, as long as it describes the reaction to certain components of the error on the interface’s position. Based on this insight, a quasi-Newton coupling algorithm with an approximation for the inverse of the Jacobian (IQN-ILS) has been developed and compared with a monolithic solver in previous work. Here, IQN-ILS is compared with other partitioned schemes such as IBQN-LS, Aitken relaxation and Interface-GMRES(R).

In this chapter a short review will be given on stability issues for fluid-structure interaction (FSI) problems we encountered and studied in the last decade. Based on this, the ideas behind two implicit coupling algorithms, developed in the department, will be explained. The first algorithm is the Interface Quasi-Newton coupling method and the second is the Interface Artificial Compressibility coupling method. Most of the applications that are shown are in the biomechanical field. These are representative for more general strongly coupled problems with incompressible fluids and flexible structures.