應用有限體積法於非線性結構體之流固耦合計算

Abstract

本篇研究主要是採用非結構性網格有限體積法來計算結構體力學及流固耦合之模擬分析。在計算結構體力學中，透過有限體積法，先將固體力學之統御方程式予以積分，並離散整理可得一聯立方程組，再利用虛擬時間之預測修正法進行求解，對於控制體積的選取則是採用以節點為中心的Cell-Vertex method，該法已證實能有效求解於此類問題，而求解之模型分別為一三維懸臂樑及平板承受一外力，以觀察結構體之位移變化並和理論解作一比較。在流固耦合計算中，主要是探討一矩形阻塊後方之二維水平非線性彈性結構體，當流體流經阻塊便會產生不穩定之渦流因而使結構體上下擺動，此擺動現象對於流場區域之計算網格會因而擠壓變形，故在處理此方面之問題需搭配空間守恆定理來滿足其體積守恆，在控制體積選取的部分，流場區域則是採用將控制體積取在網格中心之Cell-Centered method，此和結構體有所不同。在流力計算中，對流項則是採用上風法和中央差分法混和之高階方法，計算部分則是採用先預測再修正之PISO法則。最後觀察流場之速度、壓力變化及結構體之位移大小並利用快速傅立葉轉換求得擺動頻率和理論解作一比較。

A new unstructured-grid finite-volume method is developed for the structural dynamics and fluid-structure interaction. In structural calculations, the governing equations are discretized using the finite-volume method to obtain a system of ordinary differential equations. These system of ODEs are solved by a virtual time method using predictor-corrector methods. Which control volume is chosen by cell-vertex method. It has been shown that the method is advantage in this problem. The method is tested for three dimensional cantilever and plate. The results are in good agreement with theoretical analysis in terms of displacements and natural frequencies. In fluid-structure interaction, it tests that a two dimensional horizontal plate is placed behind a rectangular block. The vortices caused by the flow over the block result in vibration of the plate. Due to the vibration of the structure, moving grids are employed in flow calculations. Which control volume is chosen by cell-centred method that is difference from the structural calculations. By incorporating the space conservation concept, the mass is conserved in each cell with moving grids. The equations are discretized also using the finite-volume method. The convection term is approximated by a hybrid scheme which mixes the central and upwind differences. The coupling between the momentum and continuity equations is tackled using the predictor-corrector method of the PISO algorithm. Finally, to observe that the vibration of the structure which using Fast Fourier Transfer to get the frequency compared with theoretical solutions and the vortex flow of the fluid is clearly delineated in the interaction.