请给出一个matlab用有限元求解三维N-S方程的代码
时间: 2023-12-14 21:38:45 浏览: 201
以下是一个使用有限元方法求解三维Navier-Stokes方程的MATLAB代码示例:
```matlab
%% 3D Navier-Stokes Solver using FEM
% Domain and boundary conditions
Lx = 1; Ly = 1; Lz = 1;
nu = 0.01;
u_bdr = @(x,y,z) [0,0,0]; % No-slip boundary condition
p_bdr = @(x,y,z) 0; % Zero-pressure boundary condition
% Mesh generation
nx = 10; ny = 10; nz = 10;
[x,y,z] = meshgrid(linspace(0,Lx,nx),linspace(0,Ly,ny),linspace(0,Lz,nz));
nodes = [x(:),y(:),z(:)];
elements = delaunay(x(:),y(:),z(:));
% Assemble matrices and vectors
[K,M,f] = assemble_matrices(nodes,elements,nu,u_bdr,p_bdr);
% Solve system of equations
u_p = K\f;
u = u_p(1:end/4); v = u_p(end/4+1:end/2); w = u_p(end/2+1:end*3/4); p = u_p(end*3/4+1:end);
% Postprocessing
trisurf(elements,nodes(:,1)+u,nodes(:,2)+v,nodes(:,3)+w);
```
其中,`assemble_matrices` 函数用于组装刚度矩阵 `K`、质量矩阵 `M` 和载荷向量 `f`。可以通过修改该函数来实现不同的有限元方法,如稳定化有限元法(SUPG)等。
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