圆柱绕流浸没边界法C++代码

以下是圆柱绕流浸没边界法的C++代码示例：

#include <iostream>
#include <cmath>

using namespace std;

const int N = 1010;
const double pi = acos(-1);

int n, m;
double u[N][N], v[N][N], p[N][N], b[N][N];
double dx, dy, dt, Re;
double x[N], y[N];

void init()
{
    dx = 1.0 / (n - 1);
    dy = 1.0 / (m - 1);
    dt = 0.001;
    Re = 100.0;

    for (int i = 0; i < n; i++) x[i] = i * dx;
    for (int i = 0; i < m; i++) y[i] = i * dy;
}

void calc_b()
{
    for (int i = 1; i < n - 1; i++)
        for (int j = 1; j < m - 1; j++)
            b[i][j] = (u[i + 1][j] - u[i - 1][j]) / (2 * dx) + (v[i][j + 1] - v[i][j - 1]) / (2 * dy) / dt;
}

void poisson()
{
    double alpha = dx / dy, beta = dy / dx, residual = 1e-10;
    int iter = 0;

    while (true)
    {
        double max_err = 0;

        for (int i = 1; i < n - 1; i++)
            for (int j = 1; j < m - 1; j++)
            {
                double t = p[i][j];
                p[i][j] = 0.5 * ((p[i + 1][j] + p[i - 1][j]) / (alpha * alpha) + (p[i][j + 1] + p[i][j - 1]) / (beta * beta) - b[i][j]) / ((1 / (alpha * alpha)) + (1 / (beta * beta)));

                max_err = max(max_err, abs(p[i][j] - t));
            }

        iter++;

        if (max_err < residual)
        {
            cout << "Poisson equation solved in " << iter << " iterations." << endl;
            break;
        }
    }
}

void calc_uv()
{
    for (int i = 1; i < n - 1; i++)
        for (int j = 1; j < m - 1; j++)
        {
            u[i][j] = u[i][j] - dt * (p[i + 1][j] - p[i - 1][j]) / (2 * dx) + (dt / Re) * ((u[i + 1][j] - 2 * u[i][j] + u[i - 1][j]) / (dx * dx) + (u[i][j + 1] - 2 * u[i][j] + u[i][j - 1]) / (dy * dy));
            v[i][j] = v[i][j] - dt * (p[i][j + 1] - p[i][j - 1]) / (2 * dy) + (dt / Re) * ((v[i + 1][j] - 2 * v[i][j] + v[i - 1][j]) / (dx * dx) + (v[i][j + 1] - 2 * v[i][j] + v[i][j - 1]) / (dy * dy));
        }
}

void apply_bc()
{
    for (int i = 0; i < n; i++)
    {
        u[i][0] = 0;
        u[i][m - 1] = 0;
        v[i][0] = 0;
        v[i][m - 1] = 0;
        p[i][0] = p[i][1];
        p[i][m - 1] = p[i][m - 2];
    }

    for (int j = 0; j < m; j++)
    {
        u[0][j] = -u[1][j];
        u[n - 1][j] = 2.0 - u[n - 2][j];
        v[0][j] = -v[1][j];
        v[n - 1][j] = -v[n - 2][j];
        p[0][j] = p[1][j];
        p[n - 1][j] = p[n - 2][j];
    }

    for (int i = 0; i < n; i++)
        for (int j = 0; j < m; j++)
        {
            if ((i - n / 2) * (i - n / 2) + (j - m / 2) * (j - m / 2) <= (n / 4) * (n / 4))
            {
                u[i][j] = 0;
                v[i][j] = 0;
            }
        }
}

int main()
{
    n = m = 51;
    init();

    for (int i = 0; i < n; i++)
        for (int j = 0; j < m; j++)
        {
            u[i][j] = 0;
            v[i][j] = 0;
            p[i][j] = 0;
            b[i][j] = 0;
        }

    for (int t = 1; t <= 1000; t++)
    {
        calc_b();
        poisson();
        calc_uv();
        apply_bc();
    }

    return 0;
}

该代码是一个简化版的圆柱绕流浸没边界法，仅用于演示目的。完整的代码可能包括更多的细节和优化，因此请注意。