共查询到19条相似文献,搜索用时 109 毫秒
1.
研究了由扩散张量导出的各向异性扩散的图像处理模型,并构造了隐式差分格式,形成了有13条对角线的大型稀疏矩阵.利用代数多重网格法求解了这个线性代数方程组.并进行了数值试验. 相似文献
2.
3.
用渐近展开方法,给出和讨论辐射传输问题的P2近似扩散方程,并进行了数值模拟计算。结果表明,P2扩散方法优于普通扩散和限流扩散方法,其数值结果与输运方程结果十分接近。 相似文献
4.
反应扩散方程模型常被用于描述生物学中斑图的形成.从反应扩散模型出发,理论推导得到GiererMeinhardt模型的斑图形成机理,解释了非线性常微分方程系统的稳定常数平衡态在加入扩散项后会发生失稳并产生图灵斑图的过程.通过计算该模型,得到图灵斑图产生的参数条件.数值方法中采用一类有效的高精度数值格式,即在空间离散条件下采用Chebyshev谱配置方法,在时间离散条件下采用紧致隐积分因子方法.该方法结合了谱方法和紧致隐积分因子方法的优点,具有精度高、稳定性好、存储量小等优点.数值模拟表明,在其他条件一定的情况下,系统控制参数κ取不同值对于斑图的产生具有重要的影响,数值结果验证了理论结果. 相似文献
5.
针对窜流型油藏的特点,抽象出物理原型,同时考虑纵向和横向扩散,建立层内突进传质扩散数学模型.应用拉普拉斯变换,求得层内突进传质扩散数学模型的解析解,并得到小段塞情况下的解析解.应用通用有限元分析软件,建立层内突进传质扩散的几何模型,并求得层内突进传质扩散数学模型的数值解.绘制层内突进传质扩散数学模型的浓度分布二维剖面及不同时间步的浓度变化剖面;通过无因次距离和无因次浓度关系及孔隙体积与无因次浓度关系可以看出,贝克莱特(Pe)数越大,峰值浓度越高,见剂时间越晚.通过解析解及数值解结合的方法,可加深对传质扩散本质的理解. 相似文献
6.
7.
8.
9.
基于商用软件的等离子体数值模拟方案大多是基于标准Galerkin格式的有限元方法,在计算大气压流注放电时,存在数值振荡和伪扩散的问题,计算结果可靠性不高.针对针-板体流注放电结构,构建了修正的COMSOL Multiphysics等离子体模型.修正模型与COMSOL Multiphysics内置等离子体模块的区别主要在于增加了基于弱形式的人工稳定项.利用修正模型复现了经典的雪崩-流注转捩算例,并与经典纳秒秒冲过电压针板放电实验结果进行了对比验证.结果表明,引入修正后的商用软件模型能够克服数值振荡和伪扩散缺陷,确保等离子体数值计算的准确性和可复现性. 相似文献
10.
11.
An analytical scheme on the initial transient process in a simple helical flux
compression generator, which includes the distributions of both the magnetic field
in the hollow of an armature and the conducting current density in the stator, is
developed by means of a diffusion equation. A relationship between frequency of the
conducting current, root of the characteristic function of Bessel equation and decay
time in the armature is given. The skin depth in the helical stator is calculated
and is compared with the approximate one which is widely used in the calculation of
magnetic diffusion. Our analytical results are helpful to understanding the
mechanism of the loss of magnetic flux in both the armature and stator and to
suggesting an optimal design for improving performance of the helical flux
compression generator. 相似文献
12.
We present a generalized delta-Eddington phase function to simplify the radiative transfer equation to an integral equation with respect to the photon flux vector. The solution of the integral equation is highly accurate to model the photon propagation in the biological tissue over a broad range of optical parameters, especially in the visible light spectrum where the diffusion approximation breaks down. The methodology is validated in the Monte Carlo simulation and can be applied in various optical imaging applications. 相似文献
13.
The non-linear flux equation, the non-linear Fokker-Planck equation (or Smoluchowski equation), and the non-linear Langiven equation are the basicequations for describing particle diffusion in non-ideal system subjected totime-dependent external fields. Nevertheless, the exact solution of thoseequations is still a challenge because of their inherent complexity of thenon-linear mathematics. Li et al. found that, based on the defined apparentvariables, the non-linear Fokker-Planck equation and the non-linear flux equation could be transformed to linear forms under the condition of strong friction limit or local equilibrium assumption. In this paper, some new features of the theory were found: (i) The linear flux equation for describing non-linear diffusion can be obtained from the irreversible thermodynamic theory; (ii) The linear non-steady state diffusion equation for describing non-linear diffusion of the non-steady state, which was described by the non-linear Fokker-Planck equation, can be derived more consistently from the microscopic molecular statistical theory; (iii) In the theory, thenon-linear Langiven equation also bears a linear form; (iv) For some special cases, e.g. diffusion in a periodic total potential system, the local equilibrium assumption or the strong friction limit is not required in establishing the linear theory for describing non-linear diffusion, so the linear theory may be important in the study of Brown motor. 相似文献
14.
文中基于超导磁通动力学理论,考虑电磁力与热激活对磁通运动的影响,基本物理模型由等效电阻率随超导体温度和磁场变化的磁通扩散方程,以及比热随超导体温度变化的热传导方程组成。在此基础上,用差分法数值求解了这一复杂非线性系统的磁热耦合控制方程,得到了与实验观测结果基本一致的数值模拟结果。结果还表明:外加磁场变化速度、超导体初始温度以及超导尺寸对于磁通跳跃均产生明显的影响。 相似文献
15.
16.
《Solid State Ionics》2006,177(3-4):205-209
The influence of the concentration dependence of the diffusion coefficient is introduced in the theoretical analysis of lithium insertion by transient electrochemical techniques. The model is based on the numerical integration of the diffusion equation. The procedure proves to be useful to study the behaviour of systems involving phase transition processes in which a large change of the chemical potential induces an important contribution to the diffusion flux. In this case, the use of the complementary error function provides an efficient mean to describe the thermodynamic and kinetic properties of the system. 相似文献
17.
对几种典型的限流扩散理论的局限性与含时间吸收项的渐近扩散理论的长处作了分析和数字计算比较。结论是,理论上所导出的限流扩散方程,虽然形式上解决了中子迁移的限流问题,但由于理论推导中所作的假定带有一定的局限性,往往使限流过度;而带有时间吸收项的渐近扩散理论避免了上述的局限性,因而它对中子迁移问题的描述优于限流扩散理论。 相似文献
18.
19.
A model for diffusion and phase separation which takes into account exponential relaxation of the solute diffusion flux and its fluctuations is developed. The model describes a system undergoing phase separation governed by a partial differential equation of hyperbolic type. The analysis is done for the evolution of patterns in spinodal decomposition for the system supercooled below critical temperature. Analytical results show that relaxation processes of the solute diffusion flux lead to the selection of patterns with different wavenumbers. Considering spatial-temporal correlations of the flux fluctuations, we have found that the temporal correlations promote selecting large-period patterns, whereas the corresponding spatial correlations accelerate such processes. 相似文献