本論文結合沉浸邊界法(IBM)和D3Q27多鬆弛時間晶格波茲曼法(LBM)，以模擬流固耦合問題。流場採用晶格波茲曼法求解，彈性結構則採用非線性運動方程建模。為驗證 LBM求解器，本論文模擬了層流壓力驅動管流；為驗證IBM-LBM求解器，模擬了distorted relaxing balloon所引起的流動。為了確保模擬穩定性和體積守恆，本論文共測試了三種方法，並發現使用split-forcing並以半隱式的方法計算時，模擬更加穩定與準確。最後，本論文模擬了壓力驅動流中水平夾鉗的可伸長纖維，並呈現可伸長性的影響。為了加速模擬，使用 CUDA 通過 GPU實現平行計算。

In this thesis, diffusive immersed boundary method and D3Q27 MRT lattice Boltzmann method are integrated to model the interaction between fluid and elastic solid structures. The Navier-Stokes equation is solved using the lattice Boltzmann method, while the elastic structure is modeled by nonlinear equation of motion. To validate the LBM solver, laminar pressure-driven channel flow is simulated, while flow induced by distorted relaxing balloon is simulated to verify the hybrid IB-LBM solver. To ensure the stability and the volume conservation problem, three schemes are tested. It is found that the method using split-forcing of Guo et al. with semi-implicit coupling performs more stably and accurately. Finally, a horizontally clamped
extensible filament in Poiseuille channel flow was simulated, and the effects of extensibility is shown. To accelerate the simulation, parallel computation via GPU is implemented using CUDA. With some modifications, extension of the established FSI solver to 3D environment is readily feasible as long as the structural equation of motion is generalized to a 2D surface.

Contents


1 Introduction 1
1.1 Introduction 1
1.2 Motivation and Objective 7
2 Methodology 8
2.1 Mathematical formulations 8
2.1.1 Fluid field 8
2.1.2 Dynamics of a flexible structure 8
2.1.3 Diffusive immersed boundary method 9
2.2 Numerical Method 10
2.2.1 Discrezation of elastic force 10
2.2.2 Lattice Boltzmann Method 11
2.2.3 Discrete IB-LBM 14
2.2.4 Overall procedure 18
2.3 Parallelization 18
3 Numerical Simulations and Results 21
3.1 Validation of Numerical Methods 21
3.1.1 Poiseuille Channel flow 21

3.1.2 Flow induced by distorted relaxing balloon 22
3.2 Horizontally clamped extensible filament in Poiseuille channel flow 34
4 Conclusion Future work 41
4.1 The conclusion 41
4.2 Future work 41

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