《Multiphysics Modeling With Finite Element Method》

作者:William B. J. Zimmerman

      随着科学和工程的的发展，使用有限元法来求偏微分方程组的数值解拥有非常广阔的前景，数值分析工具甚至可以让一个数值计算初学者将物理、力学、化学、生物等相关学科的物理场耦合起来求解。当然，科研人员也必须清楚的了解数学建模时的局限和困难，毕竟只有正确的数学模型才能更真实的反映实际过程。

本书介绍了使用Comsol Multiphysics来进行数值计算的方法和心得，Comsol Multiphysics软件的功能强大，可以用来求解多连通域上的高度耦合，高度非线性系统，甚至极其复杂的边界条件和初始值。

本书的第一部分中，初学者可以了解如何逐步的建立一个复杂模型并检验它正确与否。第二部分介绍了进阶的分析技巧，最后一部分通过各个方面的实例，详细演示了软件在各种问题中的应用。

作为有限元方法模拟的补充，本书使用了最新版本的Comsol Multiphysics， 包含了很多新的进展，例如包括相变的多相流，等离子体动力学，电磁水动力学，微流体混合以及腐蚀。 另外，对于level set method计算多相流最主要的进步就是确保了相位守恒。

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《Multiphysics Modeling With Finite Element Method》内 容：

• Comsol Multiphysics介绍
• Comsol Multiphysics 和数值分析基础
• 有限元法求解PDE的发展
• 多物理场
• 扩展多物理场
• 非线性动力学以及线性系统分析
• 几何体变换: 连续性及移动边界
• 耦合变量: 反问题, 线性积分, 积分方程,以及积分 - 微分方程
• 使用Level Set Method 的多相流模型
• 包含相变的自由表面流模型 - 三相流
• 沟槽微流道的牛顿混合
• 电动流体
• 通过Fokker-Planck方程的等离子体模拟
• 无镀膜钢材的裂缝腐蚀
• 直流微装置磁水动力学的数值模拟
• 附录: Comsol Multiphysics结合MATLAB的向量积分法则

Finite element methods for approximating partial differential equations that arise in science and engineering analysis find widespread application. Numerical analysis tools make the solutions of coupled physics, mechanics, chemistry, and even biology accessible to the novice modeler. Nevertheless, modelers must be aware of the limitations and difficulties in developing numerical models that faithfully represent the system they are modeling.

This textbook introduces the intellectual framework for modeling with Comsol Multiphysics, a package which has unique features in representing multiply linked domains with complex geometry, highly coupled and nonlinear equation systems, and arbitrarily complicated boundary, auxiliary, and initial conditions. But with this modeling power comes great opportunities and great perils.

Progressively, in the first part of the book the novice modeler develops an understanding of how to build up complicated models piecemeal and test them modularly. The second part of the book introduces advanced analysis techniques. The final part of the book deals with case studies in a broad range of application areas including nonlinear pattern formation, thin film dynamics and heterogeneous catalysis, composite and effective media for heat, mass, conductivity, and dispersion, population balances, tomography, multiphase flow, electrokinetic, microfluidic networks, plasma dynamics, and corrosion chemistry.

As a revision of Process Modeling and Simulation with Finite Element Methods, this book uses the very latest features of Comsol Multiphysics. There are new case studies on multiphase flow with phase change, plasma dynamics, electromagnetohydrodynamics, microfluidic mixing, and corrosion. In addition, major improvements to the level set method for multiphase flow to ensure phase conservation is introduced.

Contents

• Introduction to Comsol Multiphysics
• Comsol Multiphysics and the Basics of Numerical Analysis
• Analyzing Evolution Equations by the Finite Element Method
• Multiphysics
• Extended Multiphysics
• Nonlinear Dynamics and Linear System Analysis
• Changing Geometry: Continuation and Moving Boundaries
• Coupling Variables Revisited: Inverse Problems, Line Integrals, Integral Equations, and Integro-Differential Equations
• Modeling of Multi-Phase Flow Using the Level Set Method
• Modeling of Free Surface Flow Problems with Phase Change - Three Phase Flows
• Newtonian Mixing in Grooved Microchannels
• Electrokinetic Flow
• Plasma Simulations Via the Fokker-Planck Equation
• Crevice Corrosion of Steel Under a Disbonded Coating
• Numerical Simulation of a Magnetohydrodynamic DC Microdevice
• Appendix: Vector Calculus Fundamentals in Comsol Multiphysics with MATLAB