A 2D Spectral-Element Simulation Tool For Rigid-Body Motion in Viscous Incompressible Flow

剛體與流體耦合運動之二維寬頻元素模擬方法

陳立杰(Li-Chieh Chen) ； 黃美嬌(Mei-Jiau Huang)

《中國機械工程學刊》 36卷5期 (2015/10) Pp. 449-460

摘要

本文提出一求解流固雙向交互作用問題的數值模擬方法。在本方法中，整個流固系統被視為一種密度不均勻的不可壓縮流體，流固邊界上的無滑移邊界條件則由動量方程式中額外加入的懲罰力來強制。時間及空間離散方面分別使用一階混和隱性/顯性方法與寬頻元素法，並以分步驟法計算各力源項的作用。為了降低數值的不穩定性，我們特地設計分胞法來進行固體區域內的相關內差與積分，此分胞法並遵守動量守恆；也嘗試利用常見的平滑函數將介面的不連續性去除，並比較兩方法的優缺點。我們以通道中圓柱的自由落體運動為測試例，經與現有文獻比較，我們驗證了此數值工具的準確性與可靠性。文中針對方法中幾個重要的數值參數的影響力也有完整的探討。

並列摘要

We propose a simulation method for solving fluid-structure-interaction problems. In this method, the entire fluid-solid system is treated as an incompressible fluid with non-uniform density and the no-slip boundary condition at the rigid body surface is enforced by the penalization method, namely by adding a penalization force to the momentum equations in the solid region. The penalized equations are first discretized by a mixed explicit/implicit scheme in time and the spectral element method in space and then solved by a fractional step algorithm. In order to reduce the numerical instability, the flow density and the velocity are smoothed at the fluid-solid interface by using either a smoothing function or a momentum-conserved sub-cell method. The accuracy and validity of the solver are verified by comparing the simulation results of the sedimentation of a circular cylinder in a channel with data in literature. Important numerical parameters involved in this method are investigated thoroughly as well.

並列關鍵字

Fluid-structure interaction ； immersed boundary method ； spectral element method ； penalization method