An immersed boundary method for simulating the interfacial flows with soluble surfactant

• Main Authors: Chen, Kuan-Yu, 陳冠羽
• Other Authors: Lai, Ming-Chih
• Format: Others
• Language: en_US
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/18396050553755005142

博士 === 國立交通大學 === 應用數學系所 === 102 === In the first part of this thesis, we provide a simplified one-dimensional analysis and two-dimensional numerical experiments to predict that the overall accuracy for the pressure problem or indicator function in immersed boundary calculations is first-order accurate in L1 norm, half-order accurate in L2 norm, but has O(1) error in L∞ norm. We also discuss the accuracy for another type of source terms for solving Poisson problems with singular conditions on the interface. In the second part, we consider the surfactant, which is an amphiphilic molecular, under multi-phase fluids. These particles usually favor the presence in the fluid interface, and they may couple with the surfactant soluble in one of bulk domains through adsorption and desorption processes. This type of problem needs to solve partial differential equations in deformable interfaces or complex domains. Thus, it is important to accurately solve coupled surface-bulk convection-diffusion equations especially when the interface is moving. We first rewrite the original bulk concentration equation in an irregular domain (soluble region) into a regular computational domain via the usage of the indicator function, which is described in previous part, so that the concentration flux across the interface due to adsorption and desorption processes can be termed as a singular source in the modified equation. Based on the immersed boundary formulation, we then develop a new conservative scheme for solving this coupled surface-bulk concentration equations which the total surfactant mass is conserved in discrete sense. A series of numerical tests has been conducted to validate the present scheme. As an application, we extend our previous work to the soluble case and investigate the effect of solubility on drop deformations.