场和边界 我们把上述方程转化为一个场(field)。试想存在一维(因为ϕϕ仅与一个变量有关)直线,线上有若干等距分布的结点(node),每个结点都有唯一的ϕϕ,那么ϕϕ和xx的关系满足上述方程。 内部结点满足方程,那么边界上的ϕ(xL)ϕ(xL)和ϕ(xR)ϕ(xR)呢?事实上,边界应是内部结点的延申,即边...
This section describes the formulation and methodology of finite difference method to solve the governing equations on a computational domain.The finite difference method is the oldest method for the numerical solution of partial differential equations. It is also the easiest to formulate and program ...
In this contribution, we presented the capabilities of the generalized finite difference method (GFDM) implemented in the simulation software MESHFREE regarding solution mining processes on a macroscopic and a microscopic scale. Both Lagrangian and Eulerian approaches were considered. On the macroscopic sca...
Using a forward difference at time and a second-order central difference for the space derivative at position we get the recurrence equation: This is an explicit method for solving the one-dimensional heat equation. We can obtain from the other values this way: where So, knowing the val...
Hi all, I am developing a LES code firstly to compute a back-facing step problem using finite difference method. But I simply cannot keep the flux the same value at cross sections before and after the step. Though not very large, there always exists this difference. I guess it is the ...
Kwok S.K.: An improved curvilinear Finite Difference (CFD) method for arbitrary mesh systems, Computers and Structures, 18, 719-731, 1984.Kwok SK (1984) An improved curvilinear finite difference (CFD) method for arbitrary mesh systems. Compos Struct 18:719–731 MATH...
3.1 The finite difference method In order to solve the boundary value problem associated to find periodical responses, the finite difference method is introduced. Firstly, the fundamental time period of the periodical response under study is discretized in a finite set of n points. Secondly, derivat...
For compressible two-phase displacement problem, a kind of upwind operator splitting finite difference schemes is put forward and make use of operator spli... Y Yuan - 《Acta Mathematica Scientia》 被引量: 0发表: 2002年 The Modified Upwind Finite Difference Fractional Steps Method for Compressible...
method to his students. Zienkiewicz was considered one of the world’s experts on the application of the finite difference method to the solution of continuum mechanics problems in Civil Engineering; therefore, Clough was prepared to debate the relative merits of the two methods. However, after a...
Two numerical methods used to study this model are the weighted average finite difference method and the nonstandard compact finite difference method. The proportional Caputo hybrid operator has been used to fractionalize the proposed model. Stability analysis has been construed by a kind of John ...