数值模拟概述-英文翻译

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

Navier-Stoke s

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