给我一段MATLAB代码,它的功能是用有限元法解决一维定常不可压粘性流动问题,并给出有限元分析过程、数值计算结果
时间: 2024-02-15 12:04:48 浏览: 20
好的,以下是一段MATLAB代码,它的功能是用有限元法解决一维定常不可压粘性流动问题,并给出有限元分析过程、数值计算结果:
```matlab
clc
clear all
close all
% Parameters
L = 1; % Length of the domain
h = 1/16; % Element size
nu = 0.1; % Viscosity
q = 1; % Source term
tol = 1e-6; % Tolerance for the iterative solver
maxit = 1000; % Maximum number of iterations for the iterative solver
% Mesh generation
x = 0:h:L; % Node coordinates
n = length(x)-1; % Number of elements
I = eye(n); % Identity matrix
e = ones(n,1); % Vector of ones
% Assembly of the stiffness matrix and the load vector
A = nu/h*(diag(-e,1) + diag(e,-1) - 2*diag(e)); % Stiffness matrix
f = q*h/2*(e - [0; e(1:end-1)]); % Load vector
% Boundary conditions
A(1,:) = 0; A(1,1) = 1; f(1) = 0; % Dirichlet boundary condition at x=0
A(end,:) = 0; A(end,end) = 1; f(end) = 0; % Dirichlet boundary condition at x=L
% Solution of the linear system
u = zeros(n+1,1); % Initial guess
res = norm(f-A*u); % Initial residual
iter = 0; % Initial iteration counter
while res > tol && iter < maxit
u = u + A\(f-A*u); % Iterative solver
res = norm(f-A*u); % Residual
iter = iter + 1; % Iteration counter
end
% Plot of the solution
plot(x,u)
xlabel('x')
ylabel('u')
title('One-dimensional steady-state incompressible viscous flow')
```
在这段代码中,我们首先定义了一些问题的参数,例如域的长度、元素大小、粘度等。然后,我们生成了网格,并使用有限元方法组装了刚度矩阵和载荷向量。最后,我们使用迭代求解器来求解线性系统,并绘制了解的图形。
此代码的输出是一张图像,显示了解在域内的分布。