Study On Fluid-structure Interaction Algorithms Based On Smoothed Point Interpolation Method Under The Framework Of Immersed Method

Fluid-structure interaction(FSI)problems are always associated with the inosculation and intersection of multi-branch disciplines,and have been deemed as one of the most typical mechanical problems in naval architecture and ocean engineering.Various complex FSI problems will be involved during the developments of new-type ships and marine engineering equipments such as vortex induced vibration of underwater risers,sloshing of tanks,and slamming of structures with high speed.Higher requirements for computational techniques and methods have been put forward when dealing with these problems.Arbitrary Lagrangian-Eulerian algorithm has been widely used for the solution of FSI problems.However,it needs to adjust or even regenerate the mesh when dealing with FSI problems with large deformation,rotational motion and contact phenomenon.This process is tedious and time-consuming,and the frequent adjustments of grids result in the degradation of grid quality and poor accuracy.Immersed boundary method(IBM)can avoid fluid mesh deformation resulting from moving boundary due to the utilization of non-body-fitted mesh,and has charted a new direction for solving complex FSI problems,which promotes the developments of immersed methods.Finite element method(FEM)is a popular solver to deal with the motion and deformation of solids under the framework of immersed method.However,the traditional FEM has poor continuity with compatible strain and low accuracy using low-order elements,which limits the application of simple triangular or tetrahedral elements.Based on the generalized gradient smoothing technique,smoothed point interpolation method(S-PIM)combines the advantages of FEM and meshless method,has overcome a series of problems that plagued the overly stiff FEM model over a long period of time,improved the computational performance of unstructured mesh significantly and shown very good performance for both linear and nonlinear problems in solid mechanics.Under the framework of immersed method,this dissertation couples S-PIM,which is based on linear background element,for largely deformable solids,and proposes novel coupling algorithms for different FSI problems.The main contents of this dissertation can be illustrated briefly as below:(1)Firstly,this dissertation introduces the construction schemes of smoothing domain in S-PIM,two types of nonlinear solid material models and detailed solution process for solids.Then immersed smoothed point interpolation method(IS-PIM)has been proposed by coupling S-PIM based on the framework of immersed method.Semi-implicit characteristic-based-splitting(CBS)algorithm is used to solve incompressible viscous fluid flow and the FSI force is calculated by introducing virtual fluid.Simple triangular elements are used to discretize two-dimensional fluid and solid field,and high-order interpolation schemes are employed to achieve the information exchange at the FSI interface.IS-PIM can avoid mesh regeneration under the framework of immersed method when dealing with complicated moving boundaries.The accuracy and efficiency of proposed method for large-deformation FSI problems has been verified by numerical examples.Then IS-PIM is applied to simulate flow control of cylinder with splitter plate,and the variation trends of drag coefficient and Strouhal number have been calculated with rigid and flexible as well as single and double splitter plates.The mechanism of flow control has been analyzed considering the inhibition effect for vortex generation and shedding.The characteristic of drag reduction has been compared with regrard to different forms of splitter plates.(2)On the basis of IS-PIM,immersed node-based partly smoothed interpolation method has been proposed by utilising node-based partly smoothed interpolation method(NPS-PIM)as solid solver.Combined overly-stiff FEM with overly-soft node-based S-PIM(NS-PIM),NPS-PIM can provide properly softened model stiffness based on partly gradient smoothing technique,which is very close to the stiffness of exact solution.Therefore,the accuracy of FSI model for large-deformation FSI problems has been improved.It should be noted that the displacement results will be significantly different with different solid model stiffness in FSI models when simulating FSI problems with severe solid distortion.However,the proposed immersed node-based partly smoothed interpolation method can still provide very close numerical results compared with reference solutions.(3)Given that CBS algorithm need solve pressure Poisson equation,be time-consuming and consume massive computing resources as a fluid solver,a copled lattice Boltzmann method(LBM)with S-PIM has been proposed by employing LBM as fluid solver,which possesses simple evolution equation and efficient computing performance.The computational time of LBM is much less than that of CBS,and the accuracy of LBM is also better than that of CBS in terms of simulating the problem of incompressible flow.Numerical examples show that the proposed coupling algorithm of LBM with S-PIM can effectively deal with complex moving boundary under the framework of immersed method,maintain numerical stability in a large range of fluid-solid mesh size ratio,and is simple with high efficiency.Under the same conditions,more accurate results can be obtained by the proposed method compared with the coupling algorithm of LBM with FEM.And the proposed method possesses the potential for large-scale computation.(4)In order to simulate violent FSI problems associated with overturning and breaking of free surface flow efficiently,a coupled smoothed particle hydrodynamics(SPH)method with S-PIM has been proposed by using SPH as fluid solver.Similar to virtual fluid in IS-PIM,the introduction of virtual particles covered by solid domain is beneficial to the imposition of FSI conditions.The improved coupling dynamic boundary conditions are used to treat solid wall condition and density regularization is used to improve the pressure results,which improves the stability of the pressure field.Numerical examples of dam-break,sloshing and water entry with high velocity have verified that the coupled SPH with S-PIM works well for FSI problems with large deformation of free surface and solids.