ns方程matlab代码

Navier-Stokes方程组是描述不可压缩流体运动的基本方程组，在流体力学中得到了广泛应用。在MATLAB中，可以借助有限元或有限差分算法来求解NS方程，其代码如下：

% 定义参数

L = 10;
W = 10;
rho = 1;
mu = 1;
u_top = 1;
delta_t = 0.001;
delta_x = 0.1;
delta_y = 0.1;
nt = 100;

% 初始化变量

u = zeros(Nx,Ny);
v = zeros(Nx,Ny);
p = zeros(Nx,Ny);
b = zeros(Nx,Ny);

% 在每个时间步骤中迭代

for n = 1:nt

% 执行步骤1：计算b的值
for i = 2:nx-1
for j = 2:ny-1
b(i,j) = rho*(1/delta_t * ((u(i,j+1)-u(i,j-1))/(2*delta_y) + (v(i+1,j)-v(i-1,j))/(2*delta_x)) - ((u(i,j+1)-u(i,j-1))/(2*delta_y))^2 - 2*((u(i+1,j)-u(i-1,j))/(2*delta_x)*(v(i,j+1)-v(i,j-1))/(2*delta_y)) - ((v(i+1)-v(i-1))/(2*delta_x))^2);
end
end

% 执行步骤2：计算p的值
for i = 2:Nx-1
for j = 2:ny-1
p(i,j) = ((p(i,j+1)+p(i,j-1))*delta_x^2 + (p(i+1,j)+p(i-1,j))*delta_y^2 - b(i,j)*delta_x^2*delta_y^2)/(2*(delta_x^2+delta_y^2));
end
end

% 执行步骤3：计算u和v的值
u(2:end-1,2:end-1) = u(2:end-1,2:end-1) - delta_t/rho * (p(2:end-1,3:end) - p(2:end-1,1:end-2))/(2*delta_y) - u(2:end-1,2:end-1) * (delta_t/delta_x) .* (u(2:end-1,2:end-1) - u(2:end-1,1:end-2)) - v(2:end-1,2:end-1) * (delta_t/delta_y) .* (u(2:end-1,2:end-1) - u(1:end-2,2:end-1));
v(2:end-1,2:end-1) = v(2:end-1,2:end-1) - delta_t/rho * (p(3:end,2:end-1) - p(1:end-2,2:end-1))/(2*delta_x) - u(2:end-1,2:end-1) * (delta_t/delta_x) .* (v(2:end-1,2:end-1) - v(2:end-1,1:end-2)) - v(2:end-1,2:end-1) * (delta_t/delta_y) .* (v(2:end-1,2:end-1) - v(1:end-2,2:end-1));

% 处理上边界条件
u(1,:) = u_top;
v(1,:) = 0;
v(:,1) = 0;
u(end,:) = 0;
v(:,end) = 0;

end

通过以上代码，可以得到NS方程的数值解，在计算流体运动等问题时，具有一定的适用性。