数值模拟概述-英文翻译

数值模拟概述

无功流量的范围包括广泛的现象，如火焰、爆炸、化学激光器、地球的大气层、恒星和超新星，甚至宇宙的早期阶段，基本粒子相互作用。这些现象之间即使基础方程的一般形式都非常相似，但其身体有着惊人的差异。因此，为这些现象仔细考虑系统程序而建立的的数值模式也很相似。最明显得现象和主要分歧是在规模、输入数据、数学逼近的过程中出现代表不同的物理贡献，以及这些过程的耦合强度。

例如，在火焰和爆炸中，有一个化学反应之间的紧密耦合，热释放后，与流体相互作用，让所有的过程必须同时考虑。在地球的高层大气，这是一个以电离等离子体中性风为背景，流体动力学、化学反应中的电离气体和弱耦合。这些反应以中性气体发生的运动为背景提供的。太阳的大气层是高度离子化，在光子以及离子和中性原子的物种的反应中，所有字段都存在电磁强度。A型拉超新星爆炸产生耦合热核反应的一系列强烈的元素，通过元素发生周期核火焰和爆炸。这类型的反应，主要是物理过程，以及过程的程度和类型之间的耦合系统大幅改变这些。有时反应基本上是从流体流动分离，有时辐射是重要的，有时扩散运输的影响是重要的。这些是非常不同的制度，尽管，它们一般都是动态和不稳定。

对一些术语的评论

在这本书中模型、仿真、算法、数值计算等词语是重复使用的。虽然这些词语似乎很容易理解和使用在普通的谈话中，但是其技术的使用是混乱和不准确的。对于不同的个人和研究界，这些词语有不同的，有时是重叠的意义。为了打击这种技术，“巴别塔”的定义的硬性提出只会增加更多的混乱。在这里，相反，在这本书中我们讨论了在这方面所有关键的细微差别，然后尝试使用一致的条款。

一般意义上的模型建立比一般意义上的模拟仿真广泛得多。仿真试图模仿一个系统的动态行为，预测行为序列的事件控制。建模通常用在更广泛，更静态的状态：一个模型能代表其整体的发展，而不指定一个动态现象研究。一个模型可以是一个公式，定量关系，电路收集经验数据，模拟一组方程，甚至等同模拟电路。

建模目标并不一定是产生一个系统的精确复制，但一定是复制系统的若干特点。由于近似推导出了模型，该模型是理解系统的不完善的一个代表性。其结果是，一个模型是不精确的一些制度和一些几乎无处不在的无效的数量。一个模拟，是在特定的物理参数条件下，初步选择一个特定的模式或模型的集合，和边界条件。

在整个著作，尽管模拟和建模使用条件是重叠，但它们有时可以互换使用。建模和仿真词语的使用已经产生了进一步的混乱，因为最近几个共享已经适应的条款，是指用非常快的数据驱动的模式，以创造一个规划用途为交互式虚拟现实培训或目标。为了打击范围使用的混乱造成的退化，我们通常听到的修改说明的“详细模拟”、“详细的造型”、“高保真模拟”或“基本模式”是指在以严谨的科学和工程计算为主题的书。

数值计算的条款经常互换使用，尽管他们有所不同的含义。数值分析，一般的理论课题，其主要是为了解决电脑上的实际应用问题，而不是所有的计算。在模拟的计算工作中，不是所有的数值。例如，一个反应流计算可能涉及到编程交互系统，文字处理，数据管理，图形等。在这里我们考虑的计算模型和算法的描述时，他们的问题是如何分解、代

表、操纵和在计算机的存储。我们用数字数据这个词来描述技术，方法和算法的时候，他们所关注的方程的计算公式和数字的定量评价。

一个算法是一个解决方案实施过程中使用的模型。它不是一个模式，它也并不一定是数值。并不是每一个模型有一个与它相关联的算法；有可能根本不是一个算法来实现模型。通过数值模拟并不一定能解决的方程可以直接的构成数学模型。推进和整合的话可能会使这个词在更为恰当的范围内，而不是一个模拟。由于一般反应流问题发生在不同的时间，我们解决了模型设定的时间依赖性，反应的Navier-Stokes方程的数学以设置离散的代数方程被转化为一个计算模式而整体推进。代数这一套方程是来自数学模型微分方程原设置的部分。算法取代了各种数学计算，其相互作用，从而成为底层物理现象。

An Overview of Numerical Simulation

Reactive flows include a broad range of phenomena, such as flames, detonations, chemical lasers, the earth?s atmosphere, stars and supernovae, and perhaps even the elementary particle interactions in the very early stages of the universe. There are striking physical differences among these flows, even though the general forms of the underlying equations are all quite similar. Therefore, considerations and procedures for constructing numerical models of these systems are also similar. The obvious and major differences are in the scales of the phenomena, the input data, the mathematical approximations that arise in representing different contributing physical processes, and the strength of the coupling among these processes.

For example, in flames and detonations, there is a close coupling among the chemical reactions, subsequent heat release, and the fluid dynamics, so that all of the processes must be considered simultaneously. In the earth?s upper atmosphere, which is a weakly ionized plasma in a background neutral wind, the chemical reactions among ionized gases and the fluid dynamics are weakly coupled. These reactions take place in the background provided by the neutral gas motions. The sun?s atmosphere is highly ionized, with reactions among photons, elections, and ionized and neutral atomic species, all in the presence of strong electromagnetic fields. A Type la supernova creates the heavier elements in the periodic table through a series of strongly coupled thermonuclear reactions that occur in nuclear flames and detonations. The types of reactions, the major physical processes, and the degree and type of coupling among the processes vary substantially in these systems. Sometimes reactions are essentially decoupled from the fluid flow, sometimes radiation is important, and sometimes diffusive transport effects are important. These very different systems, however, are generally all dynamic and unsteady.

Some Comments on Terminology

The words model, simulation, algorithm, numerical, and computational are used repeatedly in this book. Even though these words seem easy enough to understand and use in ordinary conversation, their technical use is confused and imprecise. To different individuals and research communities, these words have different and sometimes overlapping meanings. To attack this technical “Tower of Babel” by proposing rigid definitions would only add more confusion. Here, instead, we discuss some of the nuances of key terms used in this book, and then try to use the

terms consistently.

What is generally meant by modeling is much broader than what is generally meant by simulation. A simulation attempts to imitate the dynamic behavior of a system and to predict the sequence of events that control that behavior. Modeling is generally used in a broader, more static sense: a model can represent a dynamic phenomenon in its entirety without specifying its evolution. A model can be a formula, a quantitative relation, a collection of empirical data, a set of equations, or even its equivalent analog circuit.

The objective of modeling is not necessarily to produce an exact copy of a system, but to reproduce certain salient features of the system. Because approximations are made to derive the model, it is understood that the model is an imperfect representation of the system. The result is that a model is invalid in some regimes and imprecise by some amount almost everywhere. A simulation, then, exercises a model or collection of models for a particular choice of physical parameters, initial conditions, and boundary conditions.

Throughout the literature, however, the use of the terms modeling and simulation overlap, and they are sometimes used interchangeably. The use of the words modeling and simulation has been further confused recently because several communities have adapted the terms to mean the use of very fast, data-driven models to create a virtual reality for interactive training or planning purposes. To combat the confusion caused by this degraded use of the terms, we usually hear the modified descriptions …detailed simulation,”“detailed modeling”“high-fidelity simulation,”or “fundamental model”to mean the careful scientific and engineering computations that are the subject of this book.

The terms numerical and computational are often used interchangeably, although they have somewhat different meanings. Numerical analysis, generally a theoretical subject whose main practical application is to solve problems on computers, is not all computational. Computational work in simulations is not all numerical. For example, a reactive-flow computation may involve interactive systems programming, text manipulation, data management, graphics, and so on. Here we consider models and algorithms as computational when they describe how the problem is broken down, represented, manipulated, and stored in the computer. We use the word numerical to describe techniques, methods, and algorithms when they concern the calculation of numbers of the quantitative evaluation of formulas and equations.

An algorithm is a solution procedure used to implement a model. It is not a model, and it is not necessarily numerical. Not every model has an algorithm associated with it; there simply might not be an algorithm to implement a model. A numerical simulation does not necessarily solve the equations that make up the mathematical model directly. The words advance and integrate might be more appropriate within the context of a simulation than the word solve. As the general reactive-flow problem varies in time, we solve a set of time-dependent, reactive Navier-Stokes equations that have been converted into a set of discrete algebraic equations in the computational model to advance the overall mathematical model. This algebraic set of equations is derived

from the original set of partial differential equations in the mathematical model. Algorithms are substituted for the various mathematical terms, for their interactions, and thus for the underlying physical phenomena.