中大機構典藏-NCU Institutional Repository-提供博碩士論文、考古題、期刊論文、研究計畫等下載:Item 987654321/82899
English  |  正體中文  |  简体中文  |  全文筆數/總筆數 : 69561/69561 (100%)
造訪人次 : 23214208      線上人數 : 248
RC Version 7.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.
搜尋範圍 查詢小技巧:
  • 您可在西文檢索詞彙前後加上"雙引號",以獲取較精準的檢索結果
  • 若欲以作者姓名搜尋,建議至進階搜尋限定作者欄位,可獲得較完整資料
  • 進階搜尋


    請使用永久網址來引用或連結此文件: http://ir.lib.ncu.edu.tw/handle/987654321/82899


    題名: 模擬自由落體動力行為的接近不可壓縮直接施力沉浸邊界法;A Nearly Incompressible Direct Forcing Immersed Boundary Method for Simulating the Dynamics of Freely Falling Solid Balls
    作者: 陳詩柔;Chen, Shi-Rou
    貢獻者: 數學系
    關鍵詞: 不可壓縮納維-斯托克斯方程式;流固耦合;人工壓縮法;直接施力法;沉浸邊界法;沉澱作用;incompressible Navier-Stokes equations;fluid-solid interaction;artificial compressibility method;direct forcing method;immersed boundary method;sedimentation
    日期: 2020-01-08
    上傳時間: 2020-06-05 17:41:22 (UTC+8)
    出版者: 國立中央大學
    摘要: 本文主要實現一種接近不可壓縮直接施力的沉浸邊界法,用以求解流體和固體耦合問題,並模擬二維空間中圓形自由落體的動力行為。此方法結合了人工壓縮法、直接施力沉浸邊界法和一種預測校正程序,並整合一個碰撞模型。首先我們使用懲罰技術來弱化納維-斯托克斯方程組中的不可壓縮條件,然後引入一個僅分布在固體範圍上的虛擬力,並將其加入流體的動量方程式中,以期符合沉浸固體的無滑動邊界條件。對於時間變數的離散,我們引用二階向後差分公式離散方程組中的時間變量,改進了cite{C}一文中的時間精度,並使用一個時間二階的泰勒近似逼近非線性對流項。關於空間變數的離散,我們在交錯的笛卡爾網格上使用二階中央差分法進行速度場與壓力場的空間變數離散。在實現該接近不可壓縮直接施力的沉浸邊界法時,我們運用一種用預測校正方法,並在該程序中導入一個碰撞模型來模擬固體間碰撞所引發的排斥力。最後,我們經由一系列的二維自由落體模擬實驗來驗證此方法所具有的合理效能。;The aim of this thesis is to realize a nearly incompressible direct forcing
    immersed boundary method for solving fluid-solid intersection problems
    and simulating the dynamics of freely falling solid balls in two-dimensional space.
    This approach combines the artificial compressibility method and
    the direct-forcing immersed boundary method with
    a prediction-correction process, and also integrated with a collision model.
    In this thesis, we first employ the penalty technique to weaken
    the incompressibility condition in the incompressible Navier-Stokes equations.
    Then we introduce a virtual force which is distributed on the solid object region
    and appended to the fluid momentum equation to fulfill
    the no-slip boundary condition at the immersed solid boundary.
    For the time-discretization, we employ the second-order backward difference to discretize
    the time variable, which improves the time accuracy of the method considered in \cite{C},
    and we approximate the nonlinear convection term by using a second-order Taylor formula.
    For the space-discretization, we use the second-order central difference
    over the staggered Cartesian grid for the velocity and pressure fields.
    The nearly incompressible direct forcing immersed boundary method is implemented
    in a prediction-correction way.
    In that process, we also integrate a collision model into the method to mimic
    the repulsion force arising from body-body or body-wall collisions
    in the fluid-solid interaction process.
    Finally, a series of numerical experiments of freely falling solid balls
    in two-dimensional space are performed to illustrate the effectiveness of the method.
    顯示於類別:[數學研究所] 博碩士論文

    文件中的檔案:

    檔案 描述 大小格式瀏覽次數
    index.html0KbHTML24檢視/開啟


    在NCUIR中所有的資料項目都受到原著作權保護.

    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 ©   - 回饋  - 隱私權政策聲明