English  |  正體中文  |  简体中文  |  Items with full text/Total items : 69561/69561 (100%)
Visitors : 23053398      Online Users : 352
RC Version 7.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.
Scope Tips:
  • please add "double quotation mark" for query phrases to get precise results
  • please goto advance search for comprehansive author search
  • Adv. Search
    HomeLoginUploadHelpAboutAdminister Goto mobile version

    Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/72330

    Title: On Two Immersed Boundary Methods for Simulating the Dynamics of Fluid-Structure Interaction Problems
    Authors: 游承書;You,Cheng-Shu
    Contributors: 數學系
    Keywords: 不可壓縮納維爾-史托克方程;史托克方程;流構耦合;不可延展界面;固體粒子;沉浸邊界法;懲罰法;直接施力法;投影法;預測-修正;穩定性;incompressible Navier-Stokes equations;Stokes equations;fluid-structure interaction;inextensible interface;solid particle;immersed boundary method;penalty method;direct-forcing method;projection method;prediction-correction;stability
    Date: 2016-07-22
    Issue Date: 2016-10-13 14:48:03 (UTC+8)
    Publisher: 國立中央大學
    Abstract: 本文主要目的為發展高效率的沉浸邊界法用於模擬流構耦合的動力行為,內容可分為下列兩個部份:


    ;This thesis is devoted to developing efficient immersed boundary methods for simulating the dynamics
    of fluid-structure interaction problems. It is mainly divided into the following two parts:

    In the first part, we propose a novel penalty immersed boundary method for simulating the transient Stokes flow with an inextensible interface enclosing a suspended solid particle. The main idea of this approach relies on the penalty techniques by modifying the constitutive equation of Stokes flow to weaken the incompressibility condition, relating the surface divergence to the elastic tension $\sigma$ to relax the interface′s inextensibility, and connecting the particle surface-velocity with the particle surface force ${\mbf F}$ to regularize the particle′s rigid motion. The advantage of these regularized governing equations is that when they are discretized by the standard centered difference scheme on a staggered grid, the resulting linear system can easily be reduced by eliminating the unknowns $p_h$, $\sigma_h$ and ${\mbf F}_h$ directly, so that we just need to solve a smaller linear system of the velocity approximation ${\mbf u}_h$. This advantage is preserved and even enhanced when such an approach is applied to the transient Stokes flow with multiple compound vesicles. Moreover, this smaller linear system is symmetric and negative-definite, which enables us to use efficient linear solvers. Another important feature of the proposed method is that the discretization scheme is unconditionally stable in the sense that an appropriately defined energy functional associated with the discrete system is decreasing and hence bounded in time. We numerically test the accuracy and stability of the immersed boundary discretization scheme. The tank-treading and tumbling motions of inextensible interface with a suspended solid particle in the simple shear flow will be studied extensively. The simulation of the motion of multiple compound vesicles will be performed as well. Numerical results illustrate the superior performance of the proposed penalty immersed boundary method.

    In the second part, we propose a simple prediction-correction direct-forcing immersed boundary method, which is combined with the Choi-Moin projection method, for simulating the dynamics of fluid-solid interaction problems. The immersed solid object can be stationary or moving in the fluid with a prescribed velocity. As usual, an Eulerian description is used for the fluid dynamics, while the Lagrangian representation is employed for the immersed solid boundary. The proposed approach can be categorized as a discrete forcing method with a prediction-correction strategy, in which a virtual force of discrete type distributed on the whole solid body is introduced and added to the fluid momentum equations to accommodate the no-slip boundary condition at the immersed solid boundary. More specifically, based on the rate of moment changes of the solid body, the virtual force at the grid points can be first predicted by using the difference between the prescribed solid velocities and the computed velocities which are obtained by the Choi-Moin projection method for the incompressible Navier-Stokes equations without adding any virtual forcing term. Such predicted virtual force is then put into the momentum equations for the correction step to update the velocity field, pressure and virtual force. This prediction-correction procedure can be iterated to generate a more general method, if necessary. Numerical experiments of several benchmark problems are performed to illustrate the simplicity and high performance of the proposed prediction-correction approach. We find that our numerical results are in very good agreement with the previous works in the literature and in most cases, one correction step is good enough.
    Appears in Collections:[數學研究所] 博碩士論文

    Files in This Item:

    File Description SizeFormat

    All items in NCUIR are protected by copyright, with all rights reserved.

    社群 sharing

    ::: Copyright National Central University. | 國立中央大學圖書館版權所有 | 收藏本站 | 設為首頁 | 最佳瀏覽畫面: 1024*768 | 建站日期:8-24-2009 :::
    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library IR team Copyright ©   - Feedback  - 隱私權政策聲明