Browsing by Author "Ong, Kian Chuan"

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A simple projection method for the coupled Navier-Stokes and Darcy flows
(2019-02-01)
Lai, Ming-Chih
;
Shiue, Ming-Cheng
;
Ong, Kian Chuan
;
應用數學系
;
Department of Applied Mathematics
The flow through both an incompressible fluid region and a porous medium occurs in a wide range of applications encompassing industrial processes and geological phenomena. Recently, the fluid transport phenomena across the interface between the distinct regions have received increasing attention both from the mathematical and the numerical points of view. The primary objective of the present study lies in the development of a simple and efficient method for the computations of coupled Navier-Stokes and Darcy flows with complex interface conditions. A finite difference projection method is developed within a staggered grid framework to solve the coupled system in a segregated manner using primitive variables. Numerical simulations are carried out to demonstrate the order of convergence and its capability. The proposed method renders the versatility in solving the coupled system, and it is readily extendible to multi-physics fluid flows and turbulent flows for a broad range of applications.
An immersed boundary projection method for simulating the inextensible vesicle dynamics
(2020-05-01)
Ong, Kian Chuan
;
Lai, Ming-Chih
;
應用數學系
;
Department of Applied Mathematics
We develop an immersed boundary projection method (IBPM) based on an unconditionally energy stable scheme to simulate the vesicle dynamics in a viscous fluid. Utilizing the block LU decomposition of the algebraic system, a novel fractional step algorithm is introduced by decoupling all solution variables, including the fluid velocity, fluid pressure, and the elastic tension. In contrast to previous works, the present method preserves both the fluid incompressibility and the interface inextensibility at a discrete level simultaneously. In conjunction with an implicit discretization of the bending force, the present method alleviates the time-step restriction, so the numerical stability is assured by non-increasing total discrete energy during the simulation. The numerical algorithm takes a linearithmic complexity by using preconditioned GMRES and FFT-based solvers. The grid convergence studies confirm the solution variables exhibit first-order convergence rate in L-2-norm. We demonstrate the numerical results of the vesicle dynamics in a quiescent fluid, Poiseuille flow, and shear flow, which are congruent with the results in the literature. (C) 2020 Elsevier Inc. All rights reserved.
Convergence of the MAC Scheme for the Stokes/Darcy Coupling Problem
(2018-08-01)
Shiue, Ming-Cheng
;
Ong, Kian Chuan
;
Lai, Ming-Chih
;
應用數學系
;
Department of Applied Mathematics
In this paper, we extend the MAC scheme for Stokes problem to the Stokes/Darcy coupling problem. The interface conditions between two separate regions are discretized and well-incorporated into the MAC grid setting. We first perform the stability analysis of the scheme for the velocity in both Stokes and Darcy regions and establish the stability for the pressure in both regions by considering an analogue of discrete divergence problem. Following the similar analysis on stability, we perform the error estimates for the velocity and the pressure in both regions. The theoretical results show the first-order convergence of the scheme in discrete L-2 norms for both velocity and the pressure in both regions. Moreover, in fluid region, the first-order convergence for the x-derivative of velocity component u and the y-derivative of velocity component v is also obtained in discrete L-2 norms. However, numerical tests show one order better for the velocity in Stokes region and the pressure in Darcy region.
UNCONDITIONALLY ENERGY STABLE SCHEMES FOR THE INEXTENSIBLE INTERFACE PROBLEM WITH BENDING
(2019-01-01)
Lai, Ming-Chih
;
Ong, Kian Chuan
;
應用數學系
;
Department of Applied Mathematics
In this paper, we develop unconditionally energy stable schemes to solve the inextensible interface problem with bending. The fundamental problem is formulated by the immersed boundary method where the nonstationary Stokes equations are considered, with the elastic tension and bending forces expressed in terms of Dirac delta function along the interface. The elastic tension is one of the solution variables which plays the role of Lagrange multiplier to enforce the inextensibility of the interface. Both the backward Euler and Crank-Nicolson methods are introduced and it can be proved that the total energy, i.e., kinetic energy and bending energy, is discretely bounded. The numerical results show that both schemes are unconditionally energy stable without any time-step restriction. The backward Euler scheme is also applied to study the dynamics of vesicles suspended in a shear flow.