Stable Numerical Schemes For Fluids Structures And Their Interactions PDF Download

This thesis is dedicated to developing numerical methods to solve fluid-structure interaction (FSI) problems. FSI features in a vast range of physical systems and has a wide application in engineering. The work of this thesis is focused on the partitioned methods, mostly due to their features of modularity, robustness and reliability. In a partitioned approach, separate solvers are used for the fluid and structural sub-problem domains and a coupling method is devised to account for their mutual interaction. Moreover, the thesis is focused on FSI problems with strong added-mass effect, which are more challenging to solve numerically. For such FSI problems, normally an implicit partitioned method is used which enforces the coupling conditions on the interface through coupling iterations between the fluid and structural solvers. However, these methods are computationally expensive. In this work we follow a semi-implicit approach to develop stable, efficient and accurate numerical methods for FSI problems. In these methods, the fluid pressure term is segregated and strongly coupled to the structure via coupling iterations. However, the remaining fluid terms and the geometrical nonlinearities are treated explicitly. Strong coupling of the fluid pressure term provides for the stability of the method in FSI problems with strong added-mass effect, while loose coupling of the remaining terms reduces the computational cost of the simulations. The work of this thesis could be divided into three major parts. In the first part, we have developed a simple, efficient and robust semi-implicit coupling method for FSI problems with strong added-mass effect. The proposed method is simple and modular. An extensive set of numerical tests were carried out and the results were compared both to literature data (numerical and experimental), as well as domestic results obtained by using a fully-implicit coupling method. Results showed that the proposed method considerably reduces the computational cost of the simulations without degrading the stability or accuracy of the solution. Moreover, the robustness of the method is demonstrated through numerical tests. Furthermore, we have tried to further analyze the semi-implicit methods in order to gain a better understanding of several unaddressed issues concerning different aspects of these methods. The second major part of this thesis is focused on the temporal accuracy of the semi-implicit coupling methods for FSI problems. The semi-implicit methods in the literature appear to be only first-order in time. Most semi-implicit methods rely on using a projection method for the fluid equations, while extending the temporal accuracy of the projection methods is not straightforward. Moreover, mesh-conforming FSI solution methods require solving the ALE form of the Navier-Stokes equations on a moving mesh, which does not necessarily preserve the order of accuracy of the method on a fixed grid. Furthermore, if the FSI coupling technique is not properly designed, the second-order accuracy for the coupled problem is not guaranteed, even though each sub-problem possessed such accuracy. In this work, we have proposed a second-order time accurate semi-implicit method for FSI problems and demonstrated its second-order accuracy through rigorous numerical tests. The last major part of this thesis is concerned with computational efficiency and parallel scalability of the developed methods for numerical solution of complex FSI problems on massively-parallel supercomputers. We have presented a scalable parallel framework for partitioned solution of FSI problems through multi-code coupling. Two instances of our in-house software is used to solve the fluid and structural sub-problems. The communication between the single-physics solvers are carried out using an external coupling library. Parallel efficiency and scalability of the coupled framework is demonstrated in solving practical FSI test cases.