CN107273629B - Simulate the method for solving of complex fluid movement - Google Patents
Simulate the method for solving of complex fluid movement Download PDFInfo
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- CN107273629B CN107273629B CN201710499663.6A CN201710499663A CN107273629B CN 107273629 B CN107273629 B CN 107273629B CN 201710499663 A CN201710499663 A CN 201710499663A CN 107273629 B CN107273629 B CN 107273629B
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Abstract
Present disclose provides a kind of method for solving of simulation complex fluid movement, for fluid motion equation, high-precision space derivation is first calculated, and then calculates high-precision time-derivative, it reuses Taylor format and finds out calculating solution in next step, and integrate and obtain the numerical solution of specified object time.When the scheme of the disclosure is suitable for atmospheric science numerical model/higher order algorithm of sky Accuracy Matching, the overall error in numerical simulation is controlled, the uncertainty as caused by calculating error in weather and weather numerical model is reduced.
Description
Technical field
This disclosure relates to atmospheric science field more particularly to a kind of high-precision method for solving of simulation complex fluid movement.
Background technique
Numerical model and numerical simulation are the main tools of quantitative study complex fluid movement such as weather and climate change, but
It is to lead in analog result that there is uncertainties due to nonlinear interaction relationship complicated between variable each in mathematical model.
The influence for wherein calculating error logarithm analog result can be in terms of complicated general circulation model, coupled mode operation result
Out, it can also be verified from simple Chaos dynamic system, the numerical experimentation of quasi geostrophic model.Therefore, how to take effectively
Method control the growth for calculating error, the prolonged numerical value that synoptic process and complex fluid move is calculated and accurate
Numerical simulation is most important.
Many flow motions (from complicated N-S equation to simple advective equation) can be written as operational form:In order to use this class equation of computer solving, have at present some researchs introduced multiprecision arithmetic come to its into
Row numerical simulation.But these researchs use the more of high accurate scheme in the difference of space, and Time integral scheme is mostly lower
3 rank of order or algorithm below (are traditionally known as low precision or low order algorithm by the computational format of precision；High-precision is generally 4-
9 order algorithms, also referred to as higher order algorithm；10 ranks are referred above to Ultra-High Order or superhigh precision algorithm).Which results in space, times to count
It calculates precision to mismatch sometimes, will affect the accuracy of mode long-time numerical behavior.The only whole precision for improving algorithm (mentions simultaneously
High time and spatial accuracy), just the overall error in numerical simulation can be made to be controlled, that is, need to study suitable for atmospheric science number
Value mode when/sky Accuracy Matching higher order algorithm, with reduce in weather and weather numerical model as calculate error caused by
It is uncertain.
Disclosure
(1) technical problems to be solved
Present disclose provides a kind of high-precision Taylor-Li method for solving of simulation complex fluid movement, at least partly
Solve technical problem set forth above.
(2) technical solution
According to one aspect of the disclosure, a kind of high-precision method for solving of simulation complex fluid movement is provided, for
Fluid motion equationF is the variable about time and space, and L is comprising F and F about space variable derivative
Operator first calculates high-precision space derivation, and then calculates high-precision time-derivative, reuses Taylor format and finds out down
One step calculates solution；Include:
Step A gives primary condition, rotates suitable spatial mesh size h and time step τ, set the final value moment of integral,
Highest time integral precision is M rank；
Step B carries out space difference meter using n rank higher order accuracy spatial differencing scheme under selected M rank time precision
It calculates, the value of n and highest time integral precision M match；
Step C, setting time integral precision are k rank, and k=1,2 ... M using high-precision space derivation, and then are calculated
High-precision k rank time-derivative out；
Step D, increase time integral order k, repeat step C, until k=M circulation terminate, using Taylor Series Method into
Row time integral calculates a step time integral；
Step E, repeat the above steps B~D, and integral, which obtains specified object time, indicates the numerical solution in fluid velocity direction.
In some embodiments of the present disclosure, in the step A, highest time integral precision M is whole more than or equal to 3
Number；Space difference order n is the integer more than or equal to 6, such as highest time integral precision M is 5,10 or 20；Space parallax sublevel
Number n is 30,50,100 or 500.When highest time integral precision M is bigger, it is higher that matched space difference accuracy n rank is set.
In some embodiments of the present disclosure, the given primary condition is continuous and derivable, periodic initial strip
Part.
In some embodiments of the present disclosure, the high-precision method for solving has used Multiple precision (MP)
Library, using 1024 binary digit precision.
In some embodiments of the present disclosure, in the step B, space Difference Calculation meter by the way of recurrence differential
It calculates, space difference method uses following formula:
Wherein u is a related x, the function u=u (x, t) of t, “ux (1)(xi) " it is in xiThe first derivative of function u on lattice point to xOr space difference method uses compact space differential scheme.
In some embodiments of the present disclosure, in the step D, time integral, which calculates, uses following formula:
Wherein k=1,2 ... M,
In some embodiments of the present disclosure, in the step C, the complex fluid of linear equation description is movedTime-derivative is acquired using following formula
WhereinK=1,2 ... M,For space derivation.
In some embodiments of the present disclosure, the complex fluid of nonlinear equation description is movedWherein
A is nonlinear operator, acquires time-derivative using following formula:
WhereinK=1,2 ... M,For space derivation.
(3) beneficial effect
It can be seen from the above technical proposal that the high-precision method for solving that the simulation complex fluid of the disclosure moves at least has
There is one of following beneficial effect:
It (1), can be with compared to the fixation low order time integral that conventional method uses by neatly adjusting computational accuracy order
Realize 5 ranks, 10 ranks even the time integral algorithm of 20 ranks, thus corresponding space difference accuracy can be also extended to from 6 ranks 30 ranks,
50 ranks, 100 ranks even 500 ranks, thus this when/higher order algorithm of sky Accuracy Matching makes the precision of algorithm be overally improved,
The overall error of numerical simulation is controlled；
(2) by using continuous and derivable, periodically preferable initial value, it can obtain and calculate effect, precision order well
Higher, error is smaller.The precision of space difference can be shown for the calculating complex fluid analog result of linear and nonlinear problem
Far to surpass 6 ranks；
(3) recurrence differential has been used to improve calculating speed, so that the quick high accuracy difference scheme realized is than direct
The scheme speed for calculating high order spatial differential term is obviously improved.Not only EMS memory occupation is small for this calculation method, and calculating speed is fast,
And more than the space difference accuracy of 20 ranks, for the calculating that conventional scheme can not have been completed in Conventional Time, the disclosure
Method it is still effective, still be able to when precision is increased to 100 rank in routine by interior completion calculate；
(4) since method for solving has used the library Multiple precision (MP), using 1024 binary digit precision, phase
When in 200 or more decimal system effective digitals, therefore it is enough to distinguish absolute error small to 10-200Numerical solution.
Detailed description of the invention
Fig. 1 is the calculation flow chart of first embodiment of the present disclosure fluid motion equation.
Fig. 2 is calculation flow chart of the second embodiment of the present disclosure to linear equation.
Fig. 3 is that error is calculated under second embodiment of the present disclosure case linear with the variation of spatial accuracy order.
Fig. 4 is calculation flow chart of the third embodiment of the present disclosure to nonlinear equation.
Fig. 5 is that error is calculated under third embodiment of the present disclosure nonlinear case with the variation of spatial accuracy order.
Specific embodiment
For the purposes, technical schemes and advantages of the disclosure are more clearly understood, below in conjunction with specific embodiment, and reference
The disclosure is further described in attached drawing.
Disclosure some embodiments will be done referring to appended attached drawing in rear and more comprehensively describe to property, some of but not complete
The embodiment in portion will be shown.In fact, the various embodiments of the disclosure can be realized in many different forms, and should not be construed
To be limited to this several illustrated embodiment；Relatively, these embodiments are provided so that the disclosure meets applicable legal requirement.
In first exemplary embodiment of the disclosure, the high-precision for providing a kind of simulation complex fluid movement is solved
Method, Fig. 1 are first embodiment of the present disclosure flow equation calculation method flow chart.It is directed to fluid motion equation as shown in Figure 1:High-precision space derivation is first calculated, and then calculates high-precision time-derivative, reuses Taylor format
It finds out and calculates solution in next step.Specific step is as follows:
Step A. gives primary condition, rotates suitable spatial mesh size h and time step τ, sets the final value moment of integral,
Highest time integral precision is M rank；
Wherein:
Highest time integral precision M is the integer more than or equal to 3, for example, M=5,10 or 20；
Given primary condition is continuous and derivable, periodically good primary condition；
Step B. carries out space difference meter under selected M rank time precision, using n rank higher order accuracy spatial differencing scheme
It calculates, the value of n and highest time integral precision M match；
Wherein: n is integer more than or equal to 6, such as n=30,50,100 or 500, when highest time integral precision M is bigger
When, installation space difference accuracy n rank is higher；
Space Difference Calculation is calculated by the way of recurrence differential, and space difference method uses following formula:
Wherein(i=j), " ux (1)(xi) " be
In xiThe first derivative of function u on lattice point to x
The disclosure is calculating Spatial higher order derivative uy (m)(yi) Shi Jinliang avoids coefficient of utilizationDirectly calculate, but
It usesIt computes repeatedly m times, the mode of this i.e. recurrence differential.The benefit done so is as follows: only used two control ginsengs
Number m and i, therefore than using 4 parameter n, m, i, the circulation of j is efficient.As m and n larger, if being calculated in solverIt is relatively time consuming, is especially become apparent when m is greater than 10 ranks or more.And it is required in save as m × (n+1) ×
(n+1) × (n+1), it is also larger, it also will affect the cache utilization rate of CPU, to reduce calculating speed.In addition,In reality
Border calculate when formula it is simple, speed is fast, and store once can Reusability, EMS memory occupation ratioSmall 1-2 magnitude.
It is k rank that time integral precision, which is arranged, in step C., and k=1,2 ... M using high-precision space derivation, and then are calculated
High-precision k rank time-derivative out；
Step D. increase time integral order k, repeat step C, until k=M circulation terminate, using Taylor Series Method into
Row time integral calculates a step time integral；
Step E. repeats the above steps B~D, and integral obtains the numerical solution of specified object time.
To solve the problems, such as the high-precision method for solving rounding error that can also encounter when calculating, if only with double precision meter
It calculates, it is found that the absolute error that multiprecision arithmetic obtains can hover 10-15~10-16, this is precisely phase when double precision calculates
To the limit of error.So the calculating effect of superhigh precision scheme in order to obtain, is necessary using more accuracy computations.The disclosure
Method for solving has used the library Multipleprecision (MP) to be equivalent to 200 or more using 1024 binary digit precision
Decimal system effective digital, it is sufficient to it is small to 10 to distinguish absolute error-200Numerical solution.
So far, the high-precision method for solving of the simulation complex fluid movement in the case of first embodiment of the present disclosure linear equation
Introduction finishes.
In second exemplary embodiment of the disclosure, the high-precision for additionally providing a kind of simulation complex fluid movement is asked
Solution method.
In order to make it easy to understand, it is existing come using the canonical equation (Burgers equation) that a complex fluid moves as example into
Row explanation.In the present embodiment, it is illustrated for linear.
Fig. 2 is second embodiment of the present disclosure linear equation calculation method flow chart.It is as shown in Figure 2:
The first step carries out space Difference Calculation to linear equation (1),
U is a related x, the function u=u (x, t) of t in formula.
In the present solution, space difference method selection Arbitrary Order Accuracy finite-difference formula (2).Its advantage is that can be real
The spatial differencing scheme of existing higher order accuracy (or even Ultra-High Order precision), so that easy to find integrate matched precision with high order time
Higher difference accuracy.
Wherein
Second step is to calculate time integral, this method for solving is using Taylor Series Method.The core of Taylor Series Method
The heart is to calculate derivativeTherefore it can use linear equationI.e.To time-derivativeBecome
It changes, obtains formula (3):
WhereinK is the precision of time integral, if in our calculating being up to M rank time integral precision,
So k=1,2 ... M.The key of accounting equation (3) is to calculate derivative termFormula (2) can be used to calculate for this,
“ux (1)(xi) " it is in xiThe first derivative of function u on lattice point to x
K=1 when calculating, 2 ... M are recycled, and as k=M, circulation terminates.At this point it is possible to be acquired down using formula (4)
The numerical solution at one moment.
Wherein
This is just x in lattice siteiComplete a step time integral of the Taylor format for the M rank that time step is τ.Weight
The multiple above process, i.e. integrable obtain the numerical solution of specified object time.
Variation for the integral accuracy at any time of error in verification result can use following steps:
A. primary condition is given, suitable spatial mesh size and time step is rotated, sets the final value moment of integral；
By integral accuracy it is 3 ranks when b. selecting, is calculated.
C. under selected time precision, change different space difference accuracies and calculated by 3 ranks to 30 ranks.
D. the situation of change with spatial accuracy of error in result is analyzed.
E. change time integral order, repeat step b~d, obtain the variation of the integral accuracy at any time of error in result.
Fig. 3, which is shown under second embodiment case linear, calculates error with the variation of spatial accuracy order, and abscissa is sky
Between precision order, ordinate be error take logarithm (log10), in figure, " ","●", " * " line respectively represent the time
Precision is 3,4,5,6 ranks.
When solving advective equation (1) shown in Fig. 3, Gauss wave primary condition is used:It calculates
When the direction x spatial mesh size be h=1/200, time step be τ=1/400, zoning be [0,1], calculate 400 steps, from figure
5 if M=3 rank as it can be seen that when n reaches 6 rank, calculating calculating error when error is greater than 6 rank with n and being not much different, this is with Feng07's
As a result consistent；But when M=4 rank, n reaches 8 ranks or so and calculates error close to smooth variation；When M=5 rank, n reaches 10 ranks or so meter
Error is calculated close to smooth variation；When M=6 rank, n reaches 12 ranks or so and calculates error close to smooth variation；These results explanation, examination
Error is always calculated in testing to be affected by time orientation difference accuracy, when the time, directional precision was sufficiently high, direction in space
Format precision can be far more than 6 ranks.
So far, the high-precision method for solving of the simulation complex fluid movement in the case of second embodiment of the present disclosure linear equation
Introduction finishes.
In the third exemplary embodiment of the disclosure, the simulation complexity stream in the case of a kind of nonlinear equation is provided
The high-precision method for solving of body movement.
In order to make it easy to understand, it is existing come using the canonical equation (Burgers equation) that a complex fluid moves as example into
Row explanation.In the present embodiment, it is illustrated for non-linear.
Fig. 4 is third embodiment of the present disclosure linear equation calculation method flow chart.As shown in figure 4, in the present embodiment, for
The nonlinear equation (5) of one description complex fluid, space difference method are also selected as the finite-difference formula of Arbitrary Order Accuracy
(2)。
Wherein A is nonlinear operator, and when calculating time integral, nonlinear equation is different with linear equation, uses
It is the formula (6) being derived by.
WhereinTo nonlinear equation, the formula of space difference is still used
(2) come in accounting equation (6)Make k=1,2 ... M cycle calculations, when k=M, circulation terminates, can be complete
A step in pairs of nonlinear equation calculates.It repeats the above process, i.e., integrable obtains the numerical solution of specified object time.
Variation for the integral accuracy at any time of error in verification result can use following steps:
A. primary condition is given, suitable spatial mesh size and time step is rotated, sets the final value moment of integral；
By integral accuracy it is 3 ranks when b. selecting, is calculated.
C. under selected time precision, change different space difference accuracies and calculated by 3 ranks to 30 ranks.
D. the situation of change with spatial accuracy of error in result is analyzed.
E. change time integral order, repeat step b~d, obtain the variation of the integral accuracy at any time of error in result.
Fig. 5, which is shown under nonlinear case, calculates error with the variation of spatial accuracy order, and abscissa is spatial accuracy rank
Number, ordinate is that error takes logarithm (log10), in figure, " ","●", " * " line respectively represent time precision be 3,
4,5,6 rank.
When solving inviscid Burgers equation (7) shown in Fig. 5, primary condition are as follows: u (x, 0)=- sin (x).When test,
Zoning is selected as [- π, π], grid number N=800, and time step is τ=0.001, and lateral boundary conditions are cycle boundary item
Part.: the t=0.8 that tests when calculating and be selected as at the time of calculating error amounts to and calculates 800 steps.From fig. 5, it can be seen that when time essence
When degree is 3 rank, calculates error and be just held essentially constant after spatial accuracy reaches 6 ranks；When time precision is 4,5,6 rank, have
The space difference accuracy order number of effect is respectively up to 11,18,33.This test illustrates to non-linear Burgers equation, as long as when
Between integral accuracy order it is sufficiently high, the difference accuracy order of direction in space can be more than 6 ranks.
In order to achieve the purpose that brief description, any technical characteristic narration for making same application in above-mentioned first embodiment
All and in this, without repeating identical narration.
So far, the high-precision solution side of the simulation complex fluid movement in the case of third embodiment of the present disclosure nonlinear equation
Method introduction finishes.
In the 4th exemplary embodiment of the disclosure, the high-precision for providing a kind of simulation complex fluid movement is solved
Method first calculates high-precision space derivation, and then calculates high-precision time-derivative, reuses Taylor format and finds out down
One step calculates solution.Specific step is as follows:
Step A. gives primary condition, rotates suitable spatial mesh size and time step, sets the final value moment of integral, most
High time integral precision is M rank；
Step B. is micro- by recurrence using n rank higher order accuracy uniform space difference scheme under selected M rank time precision
Divide and carry out space Difference Calculation, the value of n and highest time integral precision M match；
It is k rank that time integral precision, which is arranged, in step C., k=1,2 ... M, using the high-precision space derivation of calculating, into
And calculate high-precision time-derivative；
Step D. increase time integral order k, repeat step C, until k=M circulation terminate, using Taylor Series Method into
Row time integral calculates a step time integral；
Step E. repeats the above steps B~D, and integral, which obtains specified object time, indicates the numerical solution in fluid velocity direction.
In order to achieve the purpose that brief description, any technical characteristic narration for making same application in above-mentioned first embodiment
All and in this, without repeating identical narration.
So far, the high-precision method for solving introduction of the simulation complex fluid movement of the fourth embodiment of the present disclosure finishes.
The solver (case linear) that table 1. is realized using algorithms of different, when calculating required wall clock time, wherein
DP meaning is double precision, and MP is Multiple precision, and test platform is to use Intel E5-2640
The linux system of 2.6GHz CPU, chronomere are as follows: second.
It unless there are known entitled phase otherwise anticipates, the numerical parameter in this specification and appended claims is approximation, energy
Enough bases pass through the resulting required characteristic changing of content of this disclosure.Specifically, all be used in specification and claim
The middle content for indicating composition, the number of reaction condition etc., it is thus understood that repaired by the term of " about " in all situations
Decorations.Under normal circumstances, the meaning expressed refers to include by specific quantity ± 10% variation in some embodiments, some
± 5% variation in embodiment, ± 1% variation in some embodiments, in some embodiments ± 0.5% variation.
Furthermore word "comprising" does not exclude the presence of element or step not listed in the claims.It is located in front of the element
Word "a" or "an" does not exclude the presence of multiple such elements.
In addition, unless specifically described or the step of must sequentially occur, there is no restriction in the above institute for the sequence of above-mentioned steps
Column, and can change or rearrange according to required design.And above-described embodiment can be based on the considerations of design and reliability, that
This mix and match is used using or with other embodiments mix and match, i.e., the technical characteristic in different embodiments can be freely combined
Form more embodiments.
Algorithm and display are not inherently related to any particular computer, virtual system, or other device provided herein.
Various general-purpose systems can also be used together with enlightenment based on this.As described above, it constructs required by this kind of system
Structure be obvious.In addition, the disclosure is also not for any particular programming language.It should be understood that can use various
Programming language realizes content of this disclosure described herein, and the description done above to language-specific is to disclose this public affairs
The preferred forms opened.
The disclosure can by means of include several different elements hardware and by means of properly programmed computer come
It realizes.The various component embodiments of the disclosure can be implemented in hardware, or to run on one or more processors
Software module is realized, or is implemented in a combination thereof.It will be understood by those of skill in the art that can be used in practice micro-
Processor or digital signal processor (DSP) are some or all in the relevant device according to the embodiment of the present disclosure to realize
The some or all functions of component.The disclosure be also implemented as a part for executing method as described herein or
Whole device or device programs (for example, computer program and computer program product).Such journey for realizing the disclosure
Sequence can store on a computer-readable medium, or may be in the form of one or more signals.Such signal can
To download from internet website, perhaps it is provided on the carrier signal or is provided in any other form.
Those skilled in the art will understand that can be carried out adaptively to the module in the equipment in embodiment
Change and they are arranged in one or more devices different from this embodiment.It can be the module or list in embodiment
Member or component are combined into a module or unit or component, and furthermore they can be divided into multiple submodule or subelement or
Sub-component.Other than such feature and/or at least some of process or unit exclude each other, it can use any
Combination is to all features disclosed in this specification (including adjoint claim, abstract and attached drawing) and so disclosed
All process or units of what method or apparatus are combined.Unless expressly stated otherwise, this specification is (including adjoint power
Benefit require, abstract and attached drawing) disclosed in each feature can carry out generation with an alternative feature that provides the same, equivalent, or similar purpose
It replaces.Also, in the unit claims listing several devices, several in these devices can be by same hard
Part item embodies.
Similarly, it should be understood that in order to simplify the disclosure and help to understand one or more of each open aspect,
Above in the description of the exemplary embodiment of the disclosure, each feature of the disclosure is grouped together into single implementation sometimes
In example, figure or descriptions thereof.However, the disclosed method should not be interpreted as reflecting the following intention: i.e. required to protect
The disclosure of shield requires features more more than feature expressly recited in each claim.More precisely, as following
Claims reflect as, open aspect is all features less than single embodiment disclosed above.Therefore,
Thus the claims for following specific embodiment are expressly incorporated in the specific embodiment, wherein each claim itself
All as the separate embodiments of the disclosure.
Particular embodiments described above has carried out further in detail the purpose of the disclosure, technical scheme and beneficial effects
Describe in detail it is bright, it is all it should be understood that be not limited to the disclosure the foregoing is merely the specific embodiment of the disclosure
Within the spirit and principle of the disclosure, any modification, equivalent substitution, improvement and etc. done should be included in the guarantor of the disclosure
Within the scope of shield.
Claims (7)
1. a kind of method for solving of simulation complex fluid movement, for fluid motion equationF is about time and sky
Between variable, L is operator comprising F and F about space variable derivative, first calculates high-precision space derivation, and then calculate
High-precision time-derivative out reuses Taylor format and finds out calculating solution in next step；Include:
Step A gives primary condition, rotates suitable spatial mesh size h and time step τ, set the final value moment of integral, highest
Time integral precision is M rank；
Step B carries out space Difference Calculation, n using n rank higher order accuracy spatial differencing scheme under selected M rank time precision
Match with the value of highest time integral precision M；
Step C, setting time integral precision are k rank, and k=1,2 ... M using high-precision space derivation, and then calculate height
The k rank time-derivative of precision；
Step D increases time integral order k, repeats step C, until k=M circulation terminates, when being carried out using Taylor Series Method
Between one step time integral of integral calculation；And
Step E, repeat the above steps B~D, and integral, which obtains specified object time, indicates the numerical solution in fluid velocity direction；
In the step B, space Difference Calculation is calculated by the way of recurrence differential, and space difference method uses following formula:
Wherein u is a related x, the function u=u (x, t) of t, “ux (1)(xi) " it is in xiThe first derivative of function u on lattice point to x
In the step D, time integral, which calculates, uses following formula:
Wherein k=1,2 ... M,
For the complex fluid movement of linear equation descriptionTime-derivative is acquired using following formula
WhereinK=1,2 ... M,For space derivation；
For the complex fluid movement of nonlinear equation descriptionWherein A is nonlinear operator, is asked using following formula
Obtain time-derivative:
WhereinK=1,2 ... M,For space derivation.
2. method for solving according to claim 1, in the step A, highest time integral precision M is more than or equal to 3
Integer；Space difference order n is the integer more than or equal to 6.
3. method for solving according to claim 2, in the step A, highest time integral precision M is 5,10 or 20；It is empty
Between difference order n be 30,50,100 or 500.
4. method for solving according to claim 2, in the step A, the given primary condition is continuous and derivable,
Periodic primary condition.
5. method for solving according to claim 2, the step B, when highest time integral precision M is bigger, setting
The space difference accuracy n rank matched is higher.
6. method for solving according to claim 2 has used the library Multiple precision, using 1024 binary digits
Precision.
7. the method for solving according to any one of claim 2 to 6, in the step B, caused using n rank higher order accuracy empty
Between difference scheme, pass through recurrence differentiated manner carry out space Difference Calculation.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104239625A (en) * | 2014-09-05 | 2014-12-24 | 中国矿业大学 | Corrective fluid motion equation linear iteration-based steady state solution method |
| CN104636566A (en) * | 2015-03-13 | 2015-05-20 | 中国矿业大学 | Dynamic mesh numerical solution method based on modified fluid motion equation |
| CN106570285A (en) * | 2016-11-09 | 2017-04-19 | 中国人民解放军装备学院 | J2 perturbation Lambert problem solving method based on state transition matrix analytic solution |
| CN106599331A (en) * | 2015-10-16 | 2017-04-26 | 南京理工大学 | Antenna optimization method capable of combining moment method with confidence region space mapping algorithm |
-
2017
- 2017-06-27 CN CN201710499663.6A patent/CN107273629B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104239625A (en) * | 2014-09-05 | 2014-12-24 | 中国矿业大学 | Corrective fluid motion equation linear iteration-based steady state solution method |
| CN104636566A (en) * | 2015-03-13 | 2015-05-20 | 中国矿业大学 | Dynamic mesh numerical solution method based on modified fluid motion equation |
| CN106599331A (en) * | 2015-10-16 | 2017-04-26 | 南京理工大学 | Antenna optimization method capable of combining moment method with confidence region space mapping algorithm |
| CN106570285A (en) * | 2016-11-09 | 2017-04-19 | 中国人民解放军装备学院 | J2 perturbation Lambert problem solving method based on state transition matrix analytic solution |
Non-Patent Citations (1)
| Title |
|---|
| 旋转气幕式排风罩数值模拟及实验研究;王鹏飞;《中国优秀硕士学位论文全文数据库 工程科技Ⅱ辑》;20100630(第6期);第C038-87页 * |
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