Regularity of the solution at the boundaryIn this work we study the degenerate diffusion equation $\\partial_{t}=x^{\\alpha}a\\left(xight)\\partial_{x}^{2}+b\\left(xight)\\partial_{x}$ for $\\left(x,tight)\\in\\left(0,\\inftyight)^{2}$, equipped with a Cauchy initial ...
14.13.5 The Field Diffusion Equation and Its Solution Taking the space derivative of (14.102), and eliminating dEy/dx via (14.99), (14.103)d2Bzdx2=4πkmσdBzdt=μ0σdBzdt. This equation, when solved, leads to (14.95) for the skin depth. It is called a diffusion equation. (Fourier wa...
Its capabilities include the solution of the multigroup neutron diffusion equation of ID, 2D and 3D rectangular lattices. The BINDIF program has been checked against other methods used for global reactor calculations on benchmark problems, representative of realistic power reactor cores. The results ...
While this approach of conceptual dimensional analysis is valuable, it is useful to check both the analytical and numerical solutions of the diffusion equation in order to confirm these relations. We can consider a simple example. Let us imagine a 1D space of extent L, which initially contains ...
W1(x/L) can be expressed as 1 + F1(x/L), where F1(x/L) = A(L/ℓ)[4(x/L)(1−x/L)] is a solution of the diffusion equation with boundary conditions appropriate for perfect transmission40. A(L/ℓ) is the peak value of F1(x/L) at x/L = 1/2. We ...
摘要:针对1维非定常对流扩散方程,首先建立了1种2层有理型高阶紧致差分格式,其局部截断误差为 O(h 4 +τ 2 ).然后采用vonNeumann分析方法证明了该格式是无条件稳定的.由于在每个时间层上只涉及 到3个网格点,因此可直接采用追赶法求解此差分方程.最后通过3个数值算例验证了方法的精确性和 可靠性.数值结果表明...
We evaluated the difference between a discrete solution and an explicit solution that had been derived from the magnetization diffusion equation. The results revealed the existence of Deltax, which minimizes computational errors. The spatial step Deltax and computational errors increased as the time ...
4.2 Simulation of the 1D heat equation 非数学专业,理解不了公式的原理,直接给出公式吧: (x_{uu})_i = {2 \over \delta + \Delta}({x_{i-1} - x_i \over \delta} + {x_{i+1} - x_i \over \Delta} ) 公式中括号内的值有点像二阶导数求解。
In this study, a general 1D analytic solution of the CDRS equation is obtained by using a one-sided Laplace transform, by assuming constant diffusivity, velocity, and reactivity. This paper also provides a general formalism to derive 1D analytic solutions for Dirichlet/Dirichlet and Dirichlet/...
Subscriber Hello, I am solving some 1D transient diffusion problems for a sphere. I am doing this by just solving the energy equation within Fluent. I want to export my solution data (temperature at all spatial nodes at all time stamps) so I can analyze in Matlab. Currently I have it se...