Staggered Discontinuous Galerkin Method for Fluid-structure Interaction

• Other Authors: Cheung, Siu Wun (author.)
• Format: Others
• Language: English; Chinese
• Published: 2016
• Online Access: http://repository.lib.cuhk.edu.hk/en/item/cuhk-1292315

流固耦合(fluid-structre interaction)是模擬可動結構與周圍的流體相互作⽤的數學模型，是許多⼯程設計問題的關鍵。由Peskin[35]於1972年研發的浸⼊邊界法 (immersed boundary method)是其中⼀種流⾏的流固耦合求解⽅法。浸⼊邊界法起初⽤於⼼臟瓣膜⾎流的數值逼近，後來成功地引伸到其他應⽤。在浸⼊邊界法中，固體施予流體的⼒項包含狄拉克 函數，此項在伽遼⾦(Galerkin)⽅法中可以⾃然地處理。此外，浸⼊邊界法的其中⼀個誤差來源是容積流失，透過加強推動拉格朗⽇標記點的流體速度的無散條件，此誤差可被改善[39]。 === 最近，[9]提出⼀種新的交錯網格間斷伽遼⾦ (staggered discontinuous Galerkin)⽅法⽤作解決不可壓縮流體的納維－斯托克斯⽅程(incompressible Navier-Stokes equations)。此⽅法提供許多良好性質，包括局部及整體守恆、最佳收斂速度以及局部後處理帶來的超收斂速度。此外，⼀種新穎的分拆對流項及擴散項的⽅法，加強了能量守恆性質。故此，結合交錯網格間斷伽遼⾦⽅法為浸⼊邊界法提供更有效的數值解。 === 本⽂會探討交錯網格間斷伽遼⾦⽅法及浸⼊邊界法的結合⽅法，研究此⽅法的穩定性質，並以數值實驗結果驗證。此外，本⽂亦會提供此⽅法在流固耦合範疇的基準問題上的表現。 === Fluid-structure interaction is the key of design in many engineering problems. It models the interaction of movable structures and the surrounding fluid flow. A popular approach for fluid-structure interaction is the immersed boundary (IB) method, which was first proposed by Peskin [35] in 1972 for the numerical approximation of blood flow around the heart valves. The IB method has been successfully extended to other applications. In the IB method, the source term which represents the effects of the force exerted by the immersed structure on the fluid involves a Dirac delta function, which can be dealt with naturally in a variational way in Galerkin methods. One source of the numerical error of IB method is that the lack of volume conservation, which can be resolved by improving the divergence-free property of the interpolated velocity field which drives the Lagrangian markers [39]. === Recently, a new class of staggered discontinuous Galerkin (SDG) methods for approximations of the incompressible Navier-Stokes equations is proposed [9], which provides many good properties, namely local and global conservations, optimal convergence and superconvergence through the use of a local postprocessing technique. Furthermore, energy stability is enhanced by a novel splitting of the convection term and the diffusion term. It is therefore natural to combine the SDG method with the IB method, in order to provide better approximations for the IB method. === In this thesis, we will investigate the staggered discontinuous Galerkin imimersed boundary method. We will look into the stability of the method and some results of numerical experiments to support our analysis. We will also see some performance in some benchmark problems in fluid-structure interaction using the new method. === Cheung, Siu Wun. === Thesis M.Phil. Chinese University of Hong Kong 2016. === Includes bibliographical references (leaves ). === Abstracts also in Chinese. === Title from PDF title page (viewed on …). === Detailed summary in vernacular field only. === Detailed summary in vernacular field only. === Detailed summary in vernacular field only.