本文選題：邊界嵌入方法 + 動(dòng)邊界流動(dòng)��； 參考：《南京航空航天大學(xué)》2016年博士論文

【摘要】：動(dòng)邊界流動(dòng)問題,如魚類游動(dòng)、鳥類飛行、人體心臟血液流動(dòng)和軍用飛機(jī)的武器投放等,是流體力學(xué)研究中的熱點(diǎn)和難點(diǎn)。邊界嵌入(IB:Immersed Boundary)方法可以使用固定網(wǎng)格模擬這類問題,近些年來受到了廣泛的關(guān)注。本文對一種離散強(qiáng)制型有限體積IB方法展開研究,該方法本質(zhì)上是一種通過邊界附近解的近似形式,使得邊界附近節(jié)點(diǎn)上控制方程的有限體積離散形式封閉的數(shù)值方法。根據(jù)"邊界條件強(qiáng)制點(diǎn)"所處位置的不同,該方法又進(jìn)一步分為當(dāng)?shù)谼FD方法和有限體積HCIB方法。對當(dāng)?shù)谼FD方法來說,"邊界條件強(qiáng)制點(diǎn)"是解域外緊靠固壁邊界的網(wǎng)格節(jié)點(diǎn),對有限體積HCIB方法來說則是解域內(nèi)緊靠固壁的節(jié)點(diǎn)。論文的主要研究工作有如下幾個(gè)方面:(1)提出了不可壓粘性流動(dòng)模擬的有限體積HCIB方法�？臻g離散采用Garlerkin有限體積近似,采用結(jié)合了無滑移條件和簡化動(dòng)量方程的沿物面法向的二次多項(xiàng)式近似,確定邊界嵌入點(diǎn)上的壓強(qiáng)和速度,并將該方法推廣到三維復(fù)雜幾何外形動(dòng)邊界繞流問題的求解。與原始的有限差分HCIB相比,該方法不限于Cartesian網(wǎng)格,也適用于非結(jié)構(gòu)網(wǎng)格;如果流場中同時(shí)存在靜止和運(yùn)動(dòng)邊界,仍然可以對靜止邊界采用傳統(tǒng)的邊界協(xié)調(diào)網(wǎng)格。與當(dāng)?shù)谼FD方法相比,在處理薄物體繞流問題時(shí)不會出現(xiàn)多值點(diǎn)的情況,方法的實(shí)現(xiàn)要簡單得多。(2)提出了無粘可壓流動(dòng)模擬的有限體積HCIB方法�？臻g離散同樣采用Garlerkin有限體積近似。邊界嵌入點(diǎn)上的法向速度由結(jié)合了壁面無穿透條件的線性內(nèi)插決定,壓強(qiáng)由簡化的動(dòng)量方程確定,密度和切向速度則由等熵和等總焓關(guān)系分別確定。通過引入當(dāng)?shù)乇菊髯鴺?biāo)系,使這一方法推廣至三維變得非常簡單。與Cartesian Cut-cell方法相比,該方法不需要對單元作當(dāng)?shù)厍懈钐幚�。與Ghost-cell和當(dāng)?shù)谼FD方法相比,該方法可以避免繁瑣的多值點(diǎn)處理過程以及因外插導(dǎo)致的誤差增大。(3)針對當(dāng)?shù)谼FD方法,提出了混合重構(gòu)和附加質(zhì)量源/匯兩種改進(jìn)措施�；旌现貥�(gòu)中,在最靠近物面邊界的流體點(diǎn)上,通過當(dāng)?shù)谼FD解和沿物面法向二次多項(xiàng)式近似解的加權(quán)平均進(jìn)行解的重構(gòu),以實(shí)現(xiàn)該點(diǎn)上數(shù)值描述的平滑過渡。通過在連續(xù)方程中引入質(zhì)量源匯項(xiàng),提高當(dāng)?shù)谼FD方法動(dòng)邊界流動(dòng)模擬時(shí)的質(zhì)量守恒性,質(zhì)量源匯項(xiàng)的構(gòu)建通過計(jì)算被浸沒邊界分割的控制體固體部分上的通量得到。這兩種措施均能夠在不影響原始DFD方法空間精度和幾乎不增加計(jì)算量的前提下,有效地降低動(dòng)邊界流動(dòng)模擬結(jié)果中的數(shù)值振蕩。(4)針對流固耦合問題,發(fā)展了一種適用于模擬剛性和柔性物體的分區(qū)緊耦合方法,分析了緊耦合迭代的穩(wěn)定性和收斂性,并針對附加質(zhì)量效應(yīng)顯著的問題,提出了一種新型的適用于分區(qū)緊耦合策略的預(yù)估-校正方法以提高FSI的迭代效率。預(yù)估-校正方法中通過預(yù)估流固交界面處流體運(yùn)動(dòng)和固體運(yùn)動(dòng)的各種信息,減少校正過程所需的迭代步數(shù),達(dá)到提高緊耦合效率的目的。預(yù)估-校正方法的意義在于:其基本思想可以應(yīng)用到其他的SC-FSI求解器中,以提高耦合效率。采用本文的離散強(qiáng)制型有限體積IB方法求解流體方程,驗(yàn)證了其求解復(fù)雜流固耦合問題的可靠性。針對二維/三維、靜止/運(yùn)動(dòng)、剛性/柔性物體的繞流,本文開展了大量的數(shù)值實(shí)驗(yàn),并將計(jì)算結(jié)果與參考文獻(xiàn)的數(shù)值結(jié)果或?qū)嶒?yàn)數(shù)據(jù)進(jìn)行了比較,驗(yàn)證了所提出和發(fā)展的各種數(shù)值方法的準(zhǔn)確性和可靠性。
[Abstract]:The dynamic boundary flow problem, such as fishes swimming, bird flight, human heart blood flow and military aircraft weapon delivery, is a hot and difficult point in the study of fluid mechanics. The boundary embedding (IB:Immersed Boundary) method can use fixed grid to simulate such problems. In recent years, it has received extensive attention. This paper is a kind of discrete coercion. The finite volume IB method is studied. This method is essentially a numerical method of finite volume discretization of the control equations on the nodes near the boundary by the approximate form near the boundary, which is further divided into the local DFD method and the finite volume HCI according to the different position of the "boundary condition coercion". B method. For local DFD method, "boundary condition coercion point" is a grid node that is close to the solid wall boundary outside the solution. For the finite volume HCIB method, it is a node close to the solid wall in the solution. The main research work of this paper is as follows: (1) a finite volume HCIB method for the incompressible viscous flow simulation is proposed. By using the finite volume approximation of Garlerkin, the two polynomial approximation, which combines the non slip condition and the simplified momentum equation, is used to determine the pressure and velocity on the boundary embedded point, and the method is extended to the solution of the flow problem in the three-dimensional complex geometric contour. Compared with the original finite difference HCIB, the method is not limited. The Cartesian grid is also suitable for unstructured grids. If there is a static and moving boundary in the flow field, the traditional boundary coordination grid can still be used on the stationary boundary. Compared with the local DFD method, the implementation of the method is much simpler in dealing with the problem of flow around a thin object. (2) a non sticky method is proposed. The finite volume HCIB method for the pressure flow simulation. The spatial discretization is also used for the Garlerkin finite volume approximation. The normal velocity on the boundary embedded point is determined by the linear interpolation combined with the wall without penetration condition. The pressure is determined by the simplified momentum equation, and the density and tangent velocity are determined by the isentropic and equal total enthalpy relations. The local eigencoordinate system is very simple to extend this method to 3D. Compared with the Cartesian Cut-cell method, this method does not require local cutting processing. Compared with the Ghost-cell and local DFD methods, this method can avoid cumbersome multivalue processing and increase the error caused by extrapolation. (3) local DFD side Two improvement measures are proposed in the method of mixed reconstruction and additional mass source / sink. In the mixed reconstruction, the solution is reconstructed by the local DFD solution and the weighted average of the approximate two polynomial approximate solution at the fluid point near the boundary of the surface, so as to realize the smooth transition of the numerical description on this point. Source and sink terms, improve the mass conservation of the dynamic boundary flow simulation in the local DFD method. The construction of the quality source and sink is obtained by calculating the flux on the solid part of the controlled body divided by the immersed boundary. These two measures can effectively reduce the moving edge without affecting the spatial accuracy of the original DFD method and almost without increasing the amount of calculation. The numerical oscillation in the boundary flow simulation results. (4) for the fluid solid coupling problem, a zonal tight coupling method suitable for the rigid and flexible objects is developed, and the stability and convergence of the tightly coupled iteration are analyzed. A new method is proposed for the subarea tight coupling strategy for the problem of the significant additional mass effect. The correction method is used to improve the iterative efficiency of FSI. The prediction correction method can reduce the number of iterative steps required for the correction process by predicting the various information of fluid motion and solid motion at the fluid solid interface. The significance of the predictor correction method is that its basic idea can be applied to other SC-FSI solutions. In order to improve the coupling efficiency, the discrete forced finite volume IB method in this paper is used to solve the fluid equation, and the reliability of the solution to the complex fluid solid coupling problem is verified. A large number of numerical experiments are carried out in this paper for two-dimensional / three-dimensional, static / motion, rigid / flexible body around the flow, and the calculation results are compared with the reference values. Compared with experimental data, the accuracy and reliability of various numerical methods proposed and developed are verified.

【學(xué)位授予單位】：南京航空航天大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：O241.82;O35

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