A multi-solver quasi-Newton method for the partitioned simulation of fluid-structure interaction

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

Evaluation of a new implicit coupling algorithm for the partitioned fluid-structure interaction simulation of bileaflet mechanical heart valves

The movement of the leaflets of Bileaflet Mechanical Heart Valves (BMHVs) strongly interacts with the surrounding fluid motion and therefore it needs to be modeled through a Fluid-Structure Interaction (FSI) scheme with implicit coupling. Therefore, when using partitioned solvers, a subiteration loop within each time step is needed. The stability of such a scheme depends on the value of the under-relaxation factor. For the simulation of a BMHV, several methods can be used to find such an appropriate under-relaxation factor, like fixed under-relaxation or the dynamically changing Aitken Δ2 under-relaxation. Also, a stable scheme can be achieved with a newly developed algorithm which uses the Jacobian with the derivatives of the pressure and viscous moments acting on the leaflets with resprect to the angular accelerations of the leaflets. In this paper, this new algorithm is presented and compared to existing coupling schemes. It is shown through numerical experiments that our newly developed algorithm outperforms these existing coupling schemes

Evaluation of a new implicit coupling algorithm for the partitioned fluid-structure interaction simulation of bileaflet mechanical heart valves

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 Δ2 relaxation in the coupling iterations when the new positions of the leaflets are computed. Results show that dynamic Aitken Δ2 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 Δ2 relaxation. Thus, our newly developed FSI coupling scheme outperforms the existing coupling schemes

Optimization of a piezoelectric fan using fluid-structure interaction simulation

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

Coupling techniques for partitioned fluid-structure interaction simulations with black-box solvers

In partitioned simulations of fluid‐structure interaction, the flow and the displacement of the structure are calculated separately and coupling iterations between the flow solver and the structural solver are required to calculate the solution of the coupled problem if the interaction is strong. This work is a comparison of three coupling algorithms which use the flow solver and structural solver as a “black box”. Consequently, these algorithms are suitable for implementation in future versions of MpCCI. It is demonstrated that the algorithm of the interface quasi‐Newton technique with an approximation for the inverse of the Jacobian from a least‐squares model is straightforward and that this technique needs a relatively low number of coupling iterations in the simulation of an oscillating flexible beam and the propagation of a pressure wave in a flexible tube

Numerical analysis of the fluid-structure interaction in a membrane pump

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

Performance of partitioned procedures in fluid-structure interaction

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