發展一適用於結構體力學之隱性有限體積法及應用於流固耦合計

Abstract

本文研究主要為發展一個隱性非結構性網格有限體積法，應用於計算結構力 學並與流體力學結合來探討流固耦合之問題。在計算結構體力學中，透過有限體 積法，將方程式離散後整理成一代數方程式，求解方式採用高斯疊代求解。並且 和虛擬時間法下的預測修正解法做比較，比較兩者計算所需的CPU 時間和疊代次 數，其中又以虛擬時間預測修正解法有較快之收斂速度和較少的疊代次數。此方 法能有效的運用在典型的二維懸臂樑和固定樑問題，且分析之結果為結構體的位 移量、以及應力分佈。在流固耦合問題中，一水平矩形彈性平板位於流場中，阻 塊會使流場產生渦流，彈性平板受到流場所產生的渦流造成壓力差和剪應力影響 產生變形，結構體產生變形後又會使流場產生變化，更進一步產生更大的渦流和 高壓及低壓區，而結構體在這影響下又會產生更劇烈的變化。

Development of implicit unstructured-grid finite-volume method for the structural dynamics used in fluid-structure interaction calculation. In structural calculations, the governing equations are discretized using the finite-volume method to obtain a system of algebraic equations. These system of algebraic equations are solved by Gauss-Seidel iteration. Compared with the predictor-corrector scheme with the virtual time method. Calculate the required CPU time and number of iterations , Incorporating the predictor-corrector scheme with the virtual time method, less number of iterations and faster convergence rates are obtained. The methods are tested for cantilever and built-in beams. The results are displacements and stress. In the tests of fluid-structure interaction. The case is a horizontal elasticity plate is placed in flow field. The vortices caused by the flow over the block result in vibration of the plate. Vortex caused by the pressure difference and shear stress. Elastic plate deformed by the pressure difference and shear stress.