2021-08-012024-05-18https://scholars.lib.ntu.edu.tw/handle/123456789/696532摘要：流、固耦合問題，一直以來都是工程與科學領域中極重要且具挑戰性的困難研究主題。隨著電腦硬體的進步，流、固耦合問題的數值模擬受到越來越廣泛的注意。本研究將在非交錯網格的架構下，利用有限差分發展一新型具準確性且有效率的計算流體力學程式，並將其應用於求解流、固耦合問題。整體的分析架構將在正交的卡式座標下，將不可壓縮Navier-Stokes方程式分解成相互耦合的Euler、Helmholtz及投影方程來求解流場與壓力場。針對Euler方程，將採用高階組合緊致差分(combined compact difference)格式及具辛(symplecticity)性質的六階Runge-Kutta時間積分法，來分別離散Euler方程中的一階空間與時間導數項，以期在經長時間計算後仍可獲得精確的答案。另外，將採用高階緊致的格式來求解Helmholtz跟壓力PPE方程。自由液面的追蹤將採用等位函數方法，另外複雜外型固體的處理將採用沉浸邊界法來處理。本研究計畫將結合這兩種方法，以期有效地求解同時涉及自由液面、複雜外型物體以及該物體允許隨時間移動的流場問題。所發展的程式將執行在單張及多張GPU晶片上，以期得以大幅地減少計算的時間。最後，本研究計畫所發展的平行計算數值模擬工具將用來求解三維真實流、固耦合問題，並將與流場量測結果做一詳盡的比較以檢驗其正確性。經由本研究計畫執行所開發的在GPU晶片上的高度平行計算程式，未來應可做為求解大型工業流場問題的有利工具。<br> Abstract: It is now well accepted that the fluid-structure interaction (FSI) problem is academically and practically important in science and engineering communities and it poses a major challenging research topic. With the ever-improving computing hardware, numerical simulation of FSI problem has drawn much more attention. In this proposal, an accurate and effective finite difference code for solving FSI problems will be developed by incorporating the level set (LS) and immersed boundary (IB) methods. The proposed finite difference scheme will be developed in 3D Cartesian grid system, on which all the primitive variables are stored on non-staggered grids for avoiding coding complexity. The incompressible Navier-Stokes equations are fractionally split into the steps involving inviscid Euler, Helmholtz, and projection equations, which are coupled to each other. The high-order upwinding combined compact difference (UCCD) scheme developed in three-point grid stencil is used to approximate the first-order spatial derivative terms. The sixth-order symplectic Runge-Kutta (SRK6) integrator is employed to approximate the temporal derivative term in the inviscid Euler equation so as to numerically retain the embedded Hamiltonian structure and to get a long-time accurate solution. Moreover, the proposed high-order compact difference scheme will be employed to solve the Helmholtz and PPE equations. The level set method will be employed to accurately track time-varying free surface. As for the immersed boundary method, it will be employed to deal with complex geometry and solid body moving with the flow. These two methods will be combined to effectively solve the flow problems with complex geometry, free surface, and moving solid simultaneously. For the sake of efficiency, all the calculations will be performed on multiple GPU cards in order to accelerate computing considerably. The major goal of this proposal is to solve the three-dimensional realistic FSI problems. The simulated results will be compared with the available experimental data in the literature. Through this 2-year project, we expect to get an in-house developed highly effective parallelized computer program and it will be applied to solve some very large-sized industrial flow problems.等位函數法沉浸邊界法CUDACPU/GPU流固耦合Level set methodImmersed boundary methodFinite differenceCPU/GPUFluid-structure interaction