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1.
随机扰动对拟小波方法求解对流扩散方程的影响   总被引:2,自引:0,他引:2       下载免费PDF全文
引进拟小波方法数值求解对流扩散方程,研究结果表明,计算带宽W有一个极值,当计算带宽W取该极值时,该方程的拟小波解的精度最高,且好于迎风格式。当边界发生随机不等幅扰动时,对于积分时间较长的情况,拟小波格式的效果要稍逊于迎风格式;当边界发生随机等幅扰动时,若计算带宽W取大于等于20的整数时,方程拟小波解的精度与迎风格式相同;当参数受到随机扰动时,W取10时的拟小波解的均方根误差要小于迎风格式;在初值发生随机扰动且计算带宽W取10时,方程的拟小波解的精度最高,好于迎风格式。  相似文献   

2.
构造定常对流扩散方程高精度紧致差分格式的新方法   总被引:5,自引:1,他引:4  
田振夫 《计算物理》1997,14(4):611-613
以一维定常对流扩散方程的高精度差分格式为基础,提出了一种构造二维定常对扩散方程高精度紧致差分格式的新方法,并给出数值例子。  相似文献   

3.
一维非线性对流占优扩散方程的变网格特征差分方法   总被引:1,自引:0,他引:1  
王同科 《计算物理》2003,20(6):493-497
针对一维非线性对流占优扩散方程,提出了一类变网格特征差分格式,该格式能够根据解的梯度变化及时对计算网格进行调整,与均匀网格格式相比,给出的变网格特征差分格式对于对流占优扩散问题有着更好的计算效果。  相似文献   

4.
基于中心差分的对流扩散方程四阶紧凑格式   总被引:6,自引:0,他引:6  
陈国谦  陈矛章 《计算物理》1994,11(4):413-424
在经典中心差分格式的基础上,提出对流扩散方程的四阶紧凑差分格式。具体方法是,先就一维情形,将中心差分格式改造为不受网格Reynolds数限制恒稳二阶格式,再在不增加相关网格点的前提下,通过格式中对流系数和源项的摄动处理,使稳格式的精度提高至四阶。本文并作一,二,三维流动模型方程及高Rayleigh数自然对流传热问题的数值求解,例示本文格式的优良性态。  相似文献   

5.
陆君安  吕金虎  夏军 《计算物理》2000,17(6):664-670
在自记忆动力学的基础上推导了对流扩散方程的单参数自忆回溯时间积分格式,并应用差分理论讨论了其稳定性。计算结果表明,这种单参数回溯时间积分格式不仅精度高,而且稳定性好。  相似文献   

6.
将已经建立的求解三维定常对流扩散方程的高阶紧致差分格式直接推广到三维非定常对流扩散方程的数值求解,时间导数项利用二阶向后欧拉差分公式,所得到的高阶隐式紧致差分格式时间为二阶精度,空间为四阶精度,并且是无条件稳定的.数值实验结果验证了本文方法的精确性和稳健性.  相似文献   

7.
非定常对流扩散方程的高精度多重网格方法   总被引:1,自引:0,他引:1  
由已有的求解定常对流扩散方程的高阶紧致差分格式出发,直接推导出了数值求解非定常对流扩散方程的一种高阶隐式紧致差分格式,其时间为二阶精度,空间为四阶精度,并且是无条件稳定的。为了加快传统迭代法在求解隐格式时在每一个时间步上的迭代收敛速度,采用了多重网格加速技术。数值实验结果验证了本文方法的高阶精度、高效性及高稳定性。  相似文献   

8.
统一的对流扩散型可压缩流体力学方程与解法   总被引:1,自引:1,他引:0  
流体力学的动量方程、能量方程、湍动能方程和耗散方程都具有对流扩散方程的形式,但连续方程却不是对流扩散型的。对于可压缩问题,本文通过合理的数学推导,不作任何近似、假定与简化,得到一个全新的连续方程形式.该连续方程以压力为未知变量,并具有对流扩散型形式,使得所有的流体动力学方程组都具有完全统一的方程形式,给出了这种三维对流扩散方程组的有限精确差分计算格式。对流体力学的进一步发展具有一定意义.  相似文献   

9.
热声波数值模拟的虚假振荡研究   总被引:10,自引:4,他引:6  
采用可压缩流动的SIMPLE算法对一维封闭空腔内由边界突然加热所引起的非稳态热声波进行了数值模拟,对流-扩散项采用了中心差分、一阶迎风差分、QUICK、及MIJSCL等不同格式。计算表明各种格式均存在不同程度的虚假振荡现象,其大小与热声波的强度及离散格式的形式等多种因素有关。这些结果对热声波的进一步研究及高效可靠的对流差分格式的开发具有重要意义。  相似文献   

10.
对流项离散格式的对比与讨论   总被引:2,自引:0,他引:2  
本文简单介绍了利用规正变量定义的各种对流项差分格式,给出了利用有限容积法离散粘性对流一扩散问题时的离散方程,其中的对流项采用高阶格式进行离散。以方腔顶盖驱动及圆管突扩区内层流流动考察了各种格式的计算精度与时效。通过对比分析得出:对于常规区域中的流动, QUICK、中心差分(CD)及SMART三种格式的精度与计算时效是比较合理的。  相似文献   

11.
楚艳丽*  王振会  冉令坤  郝寿昌 《物理学报》2013,62(9):99201-099201
在水平风场切变形变的基础上引入物理量——位势切变形变, 把水平风场的垂直分量和切变形变与广义位温的空间梯度结合起来. 该物理量的二阶扰动被定义为波作用密度, 在局地直角坐标系中推导了能够描述中尺度扰动系统发展演变的波作用方程. 对2009年登陆台风莫拉克引发的暴雨过程进行诊断分析, 结果表明, 台风中心区切变形变向涡度的转化显著, 该转化通过纬向风的经向梯度实现. 纬向风速的经向梯度与广义位温垂直梯度的耦合引起位涡和位势切变形变之间的转化, 以至于位势切变形变和位涡的异常值区分别位于台风环流的外侧和内侧. 波作用密度因能够描述水平扰动风场的垂直切变和切变形变以及凝 结潜热函数扰动梯度而与观测降水联系紧密. 相关统计分析表明, 2009年夏季波作用密度与6 h观测降水存在明显滞后相关性, 对未来6 h降水有一定的指示意义. 另外, 波作用密度通量散度和扰动非地转风位涡是影响波作用密度局地变化的主要物理因素. 基于波作用密度与观测降水的良好相关性, 建立了波作用密度暴雨预报方程. 2009年登陆台风"苏迪罗", "天鹅", "莫拉菲"和"巨爵"的暴雨预报个例分析和长时间序列的ETS评分计算表明, 波作用密度对台风暴雨具有较好的预报效果, 其预报降水能力略优于美国全球预报系统(GFS)的直接降水预报. 关键词: 位势切变形变 波作用密度 波作用通量散度 台风暴雨  相似文献   

12.
Based on the combination of stochastic mathematics and conventional finite difference method,a new numerical computing technique named stochastic finite difference for solving heat conduction problems with random physical parameters,initial and boundary conditions is discussed.Begin with the analysis of steady-state heat conduction problems,difference discrete equations with random parameters are established,and then the computing formulas for the mean value and variance of temperature field are derived by the second-order stochastic parameter perturbation method.Subsequently,the proposed random model and method are extended to the field of transient heat conduction and the new analysis theory of stability applicable to stochastic difference schemes is developed.The layer-by-layer recursive equations for the first two probabilistic moments of the transient temperature field at different time points are quickly obtained and easily solved by programming.Finally,by comparing the results with traditional Monte Carlo simulation,two numerical examples are given to demonstrate the feasibility and effectiveness of the presented method for solving both steady-state and transient heat conduction problems.  相似文献   

13.
We present experimental and theoretical studies of the dynamics of molecular motors in microtubule arrays and asters. By solving a convection-diffusion equation we find that the density profile of motors in a two-dimensional aster is characterized by continuously varying exponents. Simulations are used to verify the assumptions of the continuum model. We observe the concentration profiles of kinesin moving in quasi-two-dimensional artificial asters by fluorescent microscopy and compare with our theoretical results.  相似文献   

14.
We report on investigations on the consequences of the quasiclassical Langevin equation. This Langevin equation is an equation of motion of the classical type where, however, the stochastic Langevin force is correlated according to the quantum form of the dissipation-fluctuation theorem such that ultimately its power spectrum increases linearly with frequency. Most extensively, we have studied the decay of a metastable state driven by a stochastic force. For a particular type of potential well (piecewise parabolic), we have derived explicit expressions for the decay rate for an arbitrary power spectrum of the stochastic force. We have found that the quasiclassical Langevin equation leads to decay rates which are physically meaningful only within a very restricted range. We have also studied the influence of quantum fluctuations on a predominantly deterministic motion and we have found that there the predictions of the quasiclassical Langevin equations are correct.  相似文献   

15.
We have considered phase separation processes in binary stochastic systems with thermal diffusion and ballistic mixing representing irradiation influence. Introducing fluctuations of thermal flux and an external source of atom relocations due to ballistic diffusion into dynamics of a globally conserved field, we have shown that there are two competing mechanisms of phase transitions type of “order-disorder”: thermally assisted diffusion and irradiation induced atomic exchange. We have studied dynamics of the structure function at early stages of decomposition. In the framework of the mean field theory we have derived the effective Fokker-Planck equation to describe phase separation processes. It was shown that the ordering processes can be controlled by both regular and stochastic parts of external source influence. A reentrant behavior of a mean field order parameter versus the external noise intensity and fluctuations correlation radius is found.  相似文献   

16.
17.
The problem of optimal tracking control with zero steady-state error for linear time-delay systems with sinusoidal disturbances is considered. Based on the internal model principle, a disturbance compensator is constructed such that the system with external sinusoidal disturbances is transformed into an augmented system without disturbances. By introducing a sensitivity parameter and expanding power series around it, the optimal tracking control problem can be simplified into the problem of solving an infinite sum of linear optimal control series without time-delay and disturbance. The obtained optimal tracking control law with zero steady-state error consists of accurate linear state feedback terms and a time-delay compensating term, which is an infinite sum of an adjoint vector series. The accurate linear terms can be obtained by solving a Riccati matrix equation and a Sylvester equation, respectively. The compensation term can be approximately obtained through a recursive algorithm. A numerical simulation shows that the algorithm is effective and easily implemented, and the designed tracking controller is robust with respect to the sinusoidal disturbances.  相似文献   

18.
《中国物理 B》2021,30(6):60503-060503
Coupling-induced logical stochastic resonance(LSR) can be observed in a noise-driven coupled bistable system where the behaviors of system can be interpreted consistently as a specific logic gate in an appropriate noise level. Here constant coupling is extended to time-varying coupling, and then we investigate the effect of time-varying coupling on LSR in a periodically driven coupled bistable system. When coupling intensity oscillates periodically with the same frequency with periodic force or relatively high frequency, the system successfully yields the desired logic output. When coupling intensity oscillates irregularly with phase disturbance, large phase disturbance reduces the area of optimal parameter region of coupling intensity and response speed of logic devices. Although the system behaves as a desired logic gate when the frequency of time-periodic coupling intensity is precisely equal to that of periodic force, the desired logic gate is not robust against tiny frequency difference and phase disturbance. Therefore, periodic coupling intensity with high frequency ratio is an optimal option to obtain a reliable and robust logic operation.  相似文献   

19.
We study synchronization as a means of control of collective behavior of an ensemble of coupled stochastic units in which oscillations are induced merely by external noise. For a large number of one-dimensional continuous stochastic elements coupled non-homogeneously through the mean field with delay we developed an approach to find a boundary of synchronization domain and the frequency of the mean-field oscillations on it. Namely, the exact location of the synchronization threshold is shown to be a solution of the boundary value problem (BVP) which was derived from the linearized Fokker-Planck equation. Here the synchronization threshold is found by solving this BVP numerically. Approximate analytics is obtained by expanding the solution of the linearized Fokker-Planck equation into a series of eigenfunctions of the stationary Fokker-Planck operator. Bistable systems with a polynomial and piece-wise linear potential are considered as examples. Multistability and hysteresis in the mean-field behavior are observed in the stochastic network at finite noise intensities. In the limit of small noise intensities the critical coupling strength is shown to remain finite, provided that the delay in the coupling function is not infinitely small. Delay in the coupling term can be used as a control parameter that manipulates the location of the synchronization threshold.  相似文献   

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