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Numerical Simulation of Moving Contact Lines with Surfactant by Immersed Boundary Method

Communications in Computational Physics 2010年第9期8卷 735-757页

作者： Ming-Chih Lai Yu-Hau Tseng Huaxiong Huang Center of Mathematical Modeling and Scientific Computing Department of Applied Mathematics National Chiao Tung University1001Ta Hsueh RoadHsinchu 300Taiwan Department of Mathematics and Statistics York UniversityTorontoOntarioM3J 1P3Canada

In this paper,we present an immersed boundary method for simulating moving contact lines with *** governing equations are the incompressible Navier-Stokes equations with the usual mixture of Eulerian fluid variables and Lagrangian interfacial *** immersed boundary force has two components:one from the nonhomogeneous surface tension determined by the distribution of surfactant along the fluid interface,and the other from unbalanced Young’s force at the moving contact *** artificial tangential velocity has been added to the Lagrangian markers to ensure that the markers are uniformly distributed at all *** corresponding modified surfactant equation is solved in a way such that the total surfactant mass is *** experiments including convergence analysis are carefully *** effect of the surfactant on the motion of hydrophilic and hydrophobic drops are investigated in detail.

关键词： Immersed boundary method interfacial flow Navier-Stokes equations surfactant moving contact line hydrophilic drop hydrophobic drop wetting

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Numerical Method of Fabric Dynamics Using Front Tracking and Spring Model

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Communications in Computational Physics 2013年第10期14卷 1228-1251页

作者： Yan Li I-Liang Chern Joung-Dong Kim Xiaolin Li Department of Applied Mathematics and Statistics Stony Brook UniversityStony BrookNY 11794-3600USA Department of Applied Mathematics Center of Mathematical Modeling and Scientific ComputingNational Chiao Tung UniversityHsin Chu300Taiwan Department of Mathematics National Taiwan UniversityTaipei106Taiwan National Center for Theoretical Sciences Taipei OfficeTaipei106Taiwan

We use front tracking data structures and functions to model the dynamic evolution of fabric *** represent the fabric surface by a triangulated mesh with preset equilibrium side *** stretching and wrinkling of the surface are modeled by the mass-spring *** external driving force is added to the fabric motion through the"Impulse method"which computes the velocity of the point mass by superposition of *** mass-spring system is a nonlinear ODE *** by the numerical and computational analysis,we show that the spring system has an upper bound of the eigen *** analyzed the system by considering two spring models and we proved in one case that all eigenvalues are imaginary and there exists an upper bound for the *** upper bound plays an important role in determining the numerical stability and accuracy of the ODE *** on this analysis,we analyzed the numerical accuracy and stability of the nonlinear spring mass system for fabric surface and its tangential and normal *** used the fourth order Runge-Kutta method to solve the ODE system and showed that the time step is linearly dependent on the mesh size for the system.

关键词： Front tracking spring model eigen frequency

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Phase-field-based lattice Boltzmann method for containerless freezing

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Physical Review E 2024年第3期110卷 035301页

作者： Jiangxu Huang Lei Wang Zhenhua Chai Baochang Shi School of Mathematics and Statistics School of Mathematics and Physics Institute of Interdisciplinary Research for Mathematics and Applied Science Hubei Key Laboratory of Engineering Modeling and Scientific Computing

In this paper we first propose a phase-field model for the containerless freezing problems, in which the volume expansion or shrinkage of the liquid caused by the density change during the phase change process is considered by adding a mass source term to the continuum equation. Then a phase-field-based lattice Boltzmann (LB) method is further developed to simulate solid-liquid phase change phenomena in multiphase systems. We test the developed LB method by the problem of conduction-induced freezing in a semi-infinite space, the three-phase Stefan problem, and the droplet solidification on a cold surface, and the numerical results are in agreement with the analytical and experimental solutions. In addition, the LB method is also used to study the rising bubbles with solidification. The results of the present method not only accurately capture the effect of bubbles on the solidification process, but also are in agreement with the previous work. Finally, a parametric study is carried out to examine the influences of some physical parameters on the sessile droplet solidification, and it is found that the time of droplet solidification increases with the increase of droplet volume and contact angle.

关键词： Drops & bubbles Liquid-solid phase transition

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A class of nonsymmetric preconditioners for saddle point problems

A class of nonsymmetric preconditioners for saddle point pro...

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作者： Botchev, Mike A. Golub, Gene H. Department of Applied Mathematics University of Twente P.O. Box 217 7500 AE Enschede Netherlands Scientific Computing and Computational Mathematics Program Stanford University Stanford CA 94305-9025

For the iterative solution of saddle point problems, a nonsymmetric preconditioner is studied which, with respect to the upper-left block of the system matrix, can be seen as a variant of SSOR. An idealized situation where SSOR is taken with respect to the skew-symmetric part plus the diagonal part of the upper-left block is analyzed in detail. Since action of the preconditioner involves solution of a Schur complement system, an inexact form of the preconditioner can be of interest. This results in an inner-outer iterative process. Numerical experiments with solution of linearized Navier-Stokes equations demonstrate the efficiency of the new preconditioner, especially when the upper-left block is far from symmetric. © 2006 Society for Industrial and applied mathematics.

关键词： Problem solving

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The TSTT mesh interface

The TSTT mesh interface

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44th AIAA Aerospace Sciences Meeting 2006

作者： Ollivier-Gooch, Carl Chand, Kyle Dahlgren, Tamara Diachin, Lori Freitag Fix, Brian Kraftcheck, Jason Xiaolin, Li Seol, E. Seegyoung Shephard, Mark S. Tautges, Timothy Trease, Harold Advanced Numerical Simulation Laboratory University of British Columbia Center for Applied Scientific Computing Lawrence Livermore National Laboratory Dept. of Applied Mathematics and Statistics SUNY Stonybrook Parallel Computing Sciences Sandia National Laboratories Scientific Computation Research Center Rensselaer Polytechnic Institute Pacific Northwest National Laboratory

ISBN: (纸本)1563478072

PDE-based numerical simulation applications commonly use basic software infrastructure to manage mesh, geometry, and discretization data. The commonality of this infrastructure implies the software is theoretically amenable to re-use. However, the traditional reliance on library-based implementations of these functionalities hampers experimentation with different software instances that provide similar functionality. This is especially true for meshing and geometry libraries where applications often directly access the underlying data structures, which can be quite different from implementation to implementation. Thus, using different libraries interchangeably or interoperably for this functionality has proven difficult at best and has hampered the wide spread use of advanced meshing and geometry tools developed by the research community. To address these issues, the Terascale Simulation Tools and Technologies center is working to develop standard interfaces to enable the creation of interoperable and interchangeable simulation tools. In this paper, we focus on a language-and data-structure-independent interface supporting query and modification of mesh data conforming to a general abstract data model. We describe the model and interface, and provide programming "best practices" recommendations based on early experience implementing and using the interface.

关键词： Software engineering

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Optimal Control of PDEs under Uncertainty 1

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丛书名： SpringerBriefs in mathematics

1000年

作者： Jesús Martínez-Frutos Francisco Periago Esparza

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Extension of Leap Condition in Approximate Stochastic Simulation Algorithms of Biological Networks with 2nd and 3rd order Taylor Expansion 2nd

Extension of Leap Condition in Approximate Stochastic Simul...

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2nd International Conference on mathematics and its Applications in Science and Engineering, ICMASE 2021

作者： Demirbüken, Saliha Purutçuoğlu, Vilda Scientific Computing Institute of Applied Mathematics Middle East Technical University Ankara Turkey Department of Mathematics Faculty of Science Gebze Technical University Kocaeli Turkey Department of Statistics Faculty of Arts and Sciences Middle East Technical University Ankara Turkey

ISBN: (纸本)9783030964009

The approximate stochastic simulation algorithms are the alternative methods to simulate the complex biological systems with a loss in accuracy by acquiring from computational demand. These methods depend on the leap condition. Here, the study aims to construct an actual and close confidence interval for the parameter denoting the number of simultaneously reaction in the system, by expanding the leap condition and the hazard function by second and third order Taylor expansion in the same time. To reach the goal, we use the poisson τ -leap and approximate Gillespie algorithm. Moreover, we derive the maximum likelihood estimators (MLE) and the method of moment estimators (MME) of the simulation parameters and construct confidence interval estimators at a given significance level α for these extended version of algorithms. Finally, we theoretically present that the obtained k can generate more narrower results [1–5, 7, 10]. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Method of moments

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∈-subgradient algorithms for bilevel convex optimization

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Inverse Problems 2017年第5期33卷

作者： Helou, Elias S. Simões, Lucas E.A. Department of Applied Mathematics and Statistics Institute of Mathematical Sciences and Computation USP São Carlos Brazil Institute of Mathematics Statistics and Scientific Computing UNICAMP Campinas Brazil

This paper introduces and studies the convergence properties of a new class of explicit ∈-subgradient methods for the task of minimizing a convex function over a set of minimizers of another convex minimization problem. The general algorithm specializes to some important cases, such as first-order methods applied to a varying objective function, which have computationally cheap iterations. We present numerical experimentation concerning certain applications where the theoretical framework encompasses efficient algorithmic techniques, enabling the use of the resulting methods to solve very large practical problems arising in tomographic image reconstruction. © 2017 IOP Publishing Ltd.

关键词： Convex optimization

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Wavelet-Like Block Incremental Unknowns for Numerical Computation of Anisotropic Parabolic Equations

Wavelet-Like Block Incremental Unknowns for Numerical Comput...

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Computer Science and Information Engineering, CSIE, WRI World Congress on FLAGGED

作者： Yu-Jiang Wu Ai-Li Yang Lun-Ji Song School of Mathematics and Statistics Lanzhou University Lanzhou China Institute of Scientific Computing and Applied Mathematics Indiana University Bloomington IN USA

For the anisotropic parabolic equations, we introduce a multilevel wavelet-like block incremental unknowns (WBIU) method and then, based on this new method, we construct a WBIU-type Crank-Nicholson scheme. The stability of this scheme is carefully studied. The numerical results show that the condition number of the coefficient matrix of the linear system correspond to this scheme is reduced efficiently for epsiv small, and these results also validate the stability of this new scheme.

关键词： Anisotropic magnetoresistance Equations mathematics statistics Stability Finite difference methods Computer science scientific computing Linear systems Discrete wavelet transforms

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Preconditioning techniques for reduced basis methods for parameterized elliptic partial differential equations

Preconditioning techniques for reduced basis methods for par...

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作者： Elman, Howard C. Forstall, Virginia Department of Computer Science Institute for Advanced Computer Studies University of Maryland College ParkMD20742 United States Applied Mathematics and Statistics and Scientific Computation Program University of Maryland College ParkMD20742 United States

The reduced basis methodology is an efficient approach to solve parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space, and an online step utilizes this approximation, the reduced basis, to solve a smaller reduced problem, which provides an accurate estimate of the solution. Traditionally, the reduced problem is solved using direct methods. However, the size of the reduced system needed to produce solutions of a given accuracy depends on the characteristics of the problem, and it may happen that the size is significantly smaller than that of the original discrete problem but large enough to make direct solution costly. In this scenario, it may be more effective to use iterative methods to solve the reduced problem. We construct preconditioners for reduced iterative methods which are derived from preconditioners for the full problem. This approach permits reduced basis methods to be practical for larger bases than direct methods allow. We illustrate the effectiveness of iterative methods for solving reduced problems by considering two examples, the steady-state diffusion and convection-diffusion-reaction equations. © 2015 Society for Industrial and applied mathematics.

关键词： Iterative methods

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