Browsing by Author "Hsu, Shih-Hsuan"

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A coupled grid based particle and implicit boundary integral method for two-phase flows with insoluble surfactant
(2019-10-15)
Hsu, Shih-Hsuan
;
Chu, Jay
;
Lai, Ming-Chih
;
Tsai, Richard
;
應用數學系
We develop a coupled grid based particle and implicit boundary integral method for simulation of three-dimensional interfacial flows with the presence of insoluble surfactant. The grid based particle method (GBPM, Leung and Zhao [20]) tracks the interface by the projection of the neighboring Eulerian grid points and does not require stitching of parameterizations nor body fitted moving meshes. Using this GBPM to represent the interface, the surfactant equation defined on the interface is discretized naturally following a new volumetric constant-along-surface-normal extension approach (Chu and Tsai [4]). We first examine the proposed scheme to solve the convection-diffusion equation for the problems with available analytical solutions. The numerical results demonstrate secondorder accuracy of the scheme. We then perform a series of simulations for interfacial flows with insoluble surfactant. The numerical results agree well with the theory, and are comparable with other numerical works in literature. (C) 2019 Elsevier Inc. All rights reserved.
A coupled immersed interface and grid based particle method for three-dimensional electrohydrodynamic simulations
(2019-12-01)
Hsu, Shih-Hsuan
;
Hu, Wei-Fan
;
Lai, Ming-Chih
;
應用數學系
;
Department of Applied Mathematics
In the present work, we propose a coupled immersed interface and grid based particle method to solve two-phase electrohydrodynamic problems in three dimensions. The problem considers a leaky dielectric (weakly conducting) droplet immersed in another leaky dielectric fluid under electric field where the non-homogeneous droplet surface charge effect is taken into account. Due to the mismatch of electrical properties between two fluids, the electric potential satisfying Laplace equation with jump conditions across the droplet surface is coupled with the conservation equation for the surface charge density. Consequently, we first develop a three-dimensional augmented immersed interface method (IIM) which incorporates some known jump conditions naturally along the normal direction and check the desired accuracy. Here, the grid based particle method (GBPM) is used to track the interface by the projection of the neighboring Eulerian grid points so no requirement for stitching of parameterizations nor body fitted moving meshes. Within the leaky dielectric framework, the electric stress can be treated as an interfacial force so that both the surface tension and electric force can be formulated in a unified continuum force in the Navier-Stokes equations. A series of numerical tests have been carefully conducted to illustrate the accuracy and applicability of the present method to simulate droplet electrohydrodynamics. In particular, we investigate the droplet equilibrium dynamics under weak and strong electric fields in detail. It is interesting to find out a chaotic tumbling motion with irregular rotating modes which we believe that is the first numerical verification to the recent experiments. (C) 2019 Elsevier Inc. All rights reserved.
An Immersed Boundary Method for Simulating Interfacial Flows with Insoluble Surfactant in Three Dimensions
(2018-03-01)
Seol, Yunchang
;
Hsu, Shih-Hsuan
;
Lai, Ming-Chih
;
應用數學系
;
Department of Applied Mathematics
In this paper, an immersed boundary (IB) method for simulating the interfacial flows with insoluble surfactant in three dimensions is developed. We consider a doubly periodic interface separating two fluids where the surfactant exists only along the evolving interface. An equi-arclength parametrization is introduced in order to track the moving interface and maintain good Lagrangian meshes, so stable computations can be performed without remeshing. This surface mesh-control technique is done by adding two artificial tangential velocity components into the Lagrangian marker velocity so that the Lagrangian markers can be equi-arclength distributed during the time evolution. As a result, the surfactant equation on the interface must be modified based on the new parametrization. A conservative scheme for solving the modified surfactant equation has been developed and proved to satisfy the total surfactant mass exactly in discrete level. A series of numerical experiments consisting of the validation of Lagrangian mesh control technique, the convergence study, the study of self-healing dynamics, and the simulations of two-layer fluids under Couette flow have been conducted to test our present numerical scheme.