Finite Element Methods in Incompressible, Adiabatic, and Compressible Flows
Finite Element Methods in Incompressible, Adiabatic, and Compressible Flows
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不可压缩、绝热和可压缩流动的有限元方法
DOI：
10.1007/978-4-431-55450-9
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
M. Kawahara
中科院分区：
文献类型：
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作者：
M. Kawahara
德克萨斯大学奥斯汀分校副校长John Tinsley Oden教授在2013年东京的演讲中表示，计算力学是，或者至少应该是，除了理论和观察之外，科学和工程的第三大支柱。计算力学的剖析由数学模型、计算模型和实际计算组成。这本书涵盖了广泛的分析流体流动，利用数学和计算模型的不可压缩，绝热和可压缩的流动。这本书也涉及到一些实际的计算。根据质量、动量和能量守恒原理，建立了流体流场的数学模型。在可压缩流动分析中，控制方程组可以直接用密度、速度和能量场变量求解。在不可压缩流动分析中，场变量是速度和压力。通过引入绝热流动的概念，可以求解以密度和速度或速度和压力为场变量的大范围无热传导的流体流动。有限元法是工程中应用最广泛的计算方法之一。这本书的中心目的是介绍数学基础和有限元法在不可压缩，绝热和可压缩流动领域的综合理论。由于流动特性与固体材料的流动特性有很大的不同，因此计算技术也不同。基于气泡函数法、改进的平衡张量扩散率（IBTD）法、流线迎风Petrov-Galerkin（SUPG）法和特征线法，以及简单的欧拉法和两步法，给出了精确形式的有限元方法。特别是，这本书的一个关键特点是提供绝热流动的分析，可以解决不可压缩流动使用非混合插值。v
Professor John Tinsley Oden, a professor and vice-president of the University of Texas at Austin, in his 2013 speech in Tokyo suggested that computational mechanics is, or at least should be, the third pillar of science and engineering, in addition to theory and observation. The anatomy of computational mechanics consists of the mathematical model, the computational model, and the actual computation. This book covers a wide range of analyses of fluid flows, which make use of the mathematical and computational models of incompressible, adiabatic, and compressible flows. The book also touches on some actual computations. The mathematical models in the fluid flow field are established based on the conservation principles of mass, momentum, and energy. In the compressible flow analyses, the governing equation system can be solved directly with field variables of density, velocity, and energy. In the incompressible flow analyses, the field variables are velocity and pressure. By introducing the concept of the adiabatic flows, a wide range of fluid flows without heat conduction can be solved, for which the field variables are density and velocity, or velocity and pressure. The finite element method is one of the most widely used computational methods in engineering. The central aim of this book is to introduce mathematical foundations and comprehensive theories of the finite element method in the field of incompressible, adiabatic, and compressible flows. Because flow characteristics are considerably different from those of solid materials, the computational techniques are also different. The finite element method is presented in its precise form based on the bubble function method, the improved balancing tensor diffusivity (IBTD) method, stream-line upwind Petrov–Galerkin (SUPG) method, and the characteristic method in addition to simple Euler and two-step methods. In particular, one key feature of this book is to provide the analysis of adiabatic flows that can solve incompressible flows using non-mixed interpolation. v