Browsing by Author "Shiue, Ming-Cheng"

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A simple projection method for the coupled Navier-Stokes and Darcy flows
(2019-02-01)
Lai, Ming-Chih
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Shiue, Ming-Cheng
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Ong, Kian Chuan
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應用數學系
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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 initial boundary value problem for one-dimensional shallow water magnetohydrodynamics in the solar tachocline
(2013-01-01)
Shiue, Ming-Cheng
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土木工程學系
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應用數學系
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Department of Civil Engineering
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Department of Applied Mathematics
In this article we investigate the shallow water magnetohydrodynamic equations in space dimension one with Dirichlet boundary conditions only for the velocity. This model has been proposed to study the phenomena in the solar tachocline. In this article, the local well-posedness in time of the model is proven by constructing the approximate solutions and showing the strong convergence of the approximate solutions. (C) 2012 Elsevier Ltd. All rights reserved.
Boundary Conditions for Limited Area Models Based on the Shallow Water Equations
(2013-09-01)
Bousquet, Arthur
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Petcu, Madalina
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Shiue, Ming-Cheng
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Temam, Roger
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Tribbia, Joseph
A new set of boundary conditions has been derived by rigorous methods for the shallow water equations in a limited domain. The aim of this article is to present these boundary conditions and to report on numerical simulations which have been performed using these boundary conditions. The new boundary conditions which are mildly dissipative let the waves move freely inside and outside the domain. The problems considered include a one-dimensional shallow water system with two layers of fluids and a two-dimensional inviscid shallow water system in a rectangle.
Convergence of the MAC Scheme for the Stokes/Darcy Coupling Problem
(2018-08-01)
Shiue, Ming-Cheng
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Ong, Kian Chuan
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Lai, Ming-Chih
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應用數學系
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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.
Interior penalty discontinuous Galerkin methods with implicit time-integration techniques for nonlinear parabolic equations
(2013-07-01)
Song, Lunji
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Gie, Gung-Min
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Shiue, Ming-Cheng
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應用數學系
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Department of Applied Mathematics
We prove existence and numerical stability of numerical solutions of three fully discrete interior penalty discontinuous Galerkin methods for solving nonlinear parabolic equations. Under some appropriate regularity conditions, we give the l2(H1) and l(L2) error estimates of the fully discrete symmetric interior penalty discontinuous Galerkinscheme with the implicit -schemes in time, which include backward Euler and CrankNicolson finite difference approximations. Our estimates are optimal with respect to the mesh size h. The theoretical results are confirmed by some numerical experiments. (c) 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013
On mathematical analysis of synchronization to bidirectionally coupled Kuramoto oscillators
(2020-12-01)
Chen, Shih-Hsin
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Hsia, Chun-Hsiung
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Shiue, Ming-Cheng
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應用數學系
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Department of Applied Mathematics
This article is concerned about the synchronization problem of the bidirectionally coupled Kuramoto model. In this model, each oscillator only interacts with the oscillators with adjacent labeling numbers. Namely, the oscillator theta(i) only interacts with theta(i+1) and theta(i-1). In real applications, this is a typical setting of concatenation connection. We first prove the global convergence of frequency synchronization for the identical oscillators. Also, we present two results of phase synchronization for the identical case in relatively wide initial configuration regimes. In the case that the coupling strength is sufficiently large (equivalent to the difference of the natural frequencies is sufficiently small), we show that for non-identical oscillators within a suitable initial configuration regime, the bidirectionally coupled Kuramoto model achieves a frequency synchronization. The supportive numerical simulations are presented as well. (C) 2020 Elsevier Ltd. All rights reserved.
On the Asymptotic Stability Analysis and the Existence of Time-Periodic Solutions of the Primitive Equations
(2013)
Hsia, Chun-Hsiung
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Shiue, Ming-Cheng
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應用數學系
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Department of Applied Mathematics
In this article, we prove an asymptotic stability criterion for the solutions of primitive equations defined on a three-dimensional finite cylindrical domain with time-dependent forcing terms. Under a suitable smallness assumption on the nontrivial forcing terms, we obtain the existence of the time periodic solution for the primitive equations. Moreover, this time-periodic solution is asymptotically stable in L-2 sense.
On the long-time stability of a temporal discretization scheme for the three dimensional viscous primitive equations
(2018-05-01)
Hsia, Chun-Hsiung
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Shiue, Ming-Cheng
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應用數學系
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Department of Applied Mathematics
In this article, a semi-discretized Euler scheme to solve the three dimensional viscous primitive equations is studied. Based on suitable assumptions on the initial data and forcing terms, the long-time stability of the proposed scheme is proven by showing that the norm (in space variables) of the solutions is bounded at each time step when the time step satisfies certain smallness condition.
On time periodic solutions, asymptotic stability and bifurcations of Navier-Stokes equations
(2017-02)
Hsia, Chun-Hsiung
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Jung, Chang-Yeol
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Thien Binh Nguyen
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Shiue, Ming-Cheng
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應用數學系
In this article, we investigate the time periodic solutions for two-dimensional Navier-Stokes equations with nontrivial time periodic force terms. Under the time periodic assumption of the force term, the existence of time periodic solutions for two-dimensional Navier-Stokes equations has received extensive attention from many authors. With the smallness assumption of the time periodic force, we show that there exists only one time periodic solution and this time periodic solution is globally asymptotically stable in the sense. Without smallness assumption of the force term, there is no stability analysis theory addressed. It is expected that when the amplitude of the force term is increasing, the time periodic solution is no longer asymptotically stable. In the last part of the article, we use numerical experiments to study the bifurcation of the time periodic solutions when the amplitude of the force is increasing. Extrapolating to the heating of the earth by the sun, the bifurcation diagram hints that when the earth receives a relatively small amount of solar energy regularly, the time periodic fluid patterns are asymptotically stable; while/when the earth receives too much solar energy even though in a time periodic way, the time periodic pattern of the fluid motions will lose its stability.
Self-gravitational Force Calculation of High-order Accuracy for Infinitesimally Thin Gaseous Disks
(2019-06-01)
Wang, Hsiang-Hsu
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Shiue, Ming-Cheng
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Wu, Rui-Zhu
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Yen, Chien-Chang
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應用數學系
Self-gravitational force calculation for infinitesimally thin disks is important for studies on the evolution of galactic and protoplanetary disks. Although high-order methods have been developed for hydrodynamic and magnetohydrodynamic equations, high-order improvement is desirable for solving self-gravitational forces for thin disks. In this work, we present a new numerical algorithm that is of linear complexity and of high-order accuracy. This approach is fast since the force calculation is associated with a convolution form, and the fast calculation can be achieved using Fast Fourier Transform. The nice properties, such as the finite supports and smoothness, of basis spline functions are exploited to stably interpolate a surface density and to achieve a high-order accuracy in forces. Moreover, if the mass distribution of interest is exclusively confined within a calculation domain, the method does not require artificial boundary values to be specified before the force calculation. To validate the proposed algorithm, a series of numerical tests, ranging from first- to third-order implementations, are performed, and the results are compared with analytic expressions derived for third-and fourth-order generalized Maclaurin disks. We conclude that the improvement on the numerical accuracy is significant with the order of the method, with only little increase of the complexity of the method.
Some DG schemes for the Stokes-Darcy problem using P1/P1 element
(2019-09-01)
Zhou, Guanyu
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Kashiwabara, Takahito
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Oikawa, Issei
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Chung, Eric
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Shiue, Ming-Cheng
We propose two new DG schemes based on the penalty and Nitsche's methods respectively for the Stokes-Darcy problem, where we adopt the P1/P1 elements for both the Stokes and Darcy's velocity/pressure. The well-posedness and a-priori estimates for the discrete solutions are established. The convergence order is elucidated by the numerical experiments.
Time-periodic solutions of the primitive equations of large-scale moist atmosphere: existence and stability
(2015-09-02)
Hsia, Chun-Hsiung
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Shiue, Ming-Cheng
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數學建模與科學計算所(含中心)
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Graduate Program of Mathematical Modeling and Scientific Computing, Department of Applied Mathematics
This article is devoted to the study of the asymptotic stability of the three-dimensional viscous primitive equations for large-scale moist atmosphere in the pressure coordinate system. An asymptotic stability criterion for the solutions of such model with time-dependent forcing terms is obtained. In particular, under the assumptions that the associated forces are both time-periodic and small (in a suitable sense), we obtain the existence of the time-periodic solution for the primitive equations of large-scale moist atmosphere. Moreover, this time-periodic solution is asymptotically stable in L-2 sense.