spalding_kernel.h

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#ifndef __COMMON_SPALDING_KERNEL_H__
#define __COMMON_SPALDING_KERNEL_H__
/*
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     contributors may be used to endorse or promote products derived
     from this software without specific prior written permission.
 
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 "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
 FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
 COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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 BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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*/
 
#include <cmath>
#include <algorithm>
template<typename T>
__device__ T solve(const T u, const T y, const T guess, const T nu,
                   const T kappa, const T B);
 
template<typename T>
__global__ void spalding_compute(const T * __restrict__ u_d,
                                 const T * __restrict__ v_d,
                                 const T * __restrict__ w_d,
                                 const int * __restrict__ ind_r_d,
                                 const int * __restrict__ ind_s_d,
                                 const int * __restrict__ ind_t_d,
                                 const int * __restrict__ ind_e_d,
                                 const T * __restrict__ n_x_d,
                                 const T * __restrict__ n_y_d,
                                 const T * __restrict__ n_z_d,
                                 const T * __restrict__ nu_d,
                                 const T * __restrict__ rho_w_d,
                                 const T * __restrict__ h_d,
                                 T * __restrict__ tau_x_d,
                                 T * __restrict__ tau_y_d,
                                 T * __restrict__ tau_z_d,
                                 const int n_nodes,
                                 const int lx,
                                 const T kappa,
                                 const T B,
                                 const int tstep) {
                                    
    const int idx = blockIdx.x * blockDim.x + threadIdx.x;
    const int str = blockDim.x * gridDim.x;
    for (int i = idx; i < n_nodes; i += str) {
        // Sample the velocity
        const int index = (ind_e_d[i] - 1) * lx * lx * lx +
                          (ind_t_d[i] - 1) * lx * lx +
                          (ind_s_d[i] - 1) * lx +
                          (ind_r_d[i] - 1);
 
        T ui = u_d[index];
        T vi = v_d[index];
        T wi = w_d[index];
        T rho = rho_w_d[i];
 
        // Load normal vectors and wall shear stress values once
        T nx = n_x_d[i];
        T ny = n_y_d[i];
        T nz = n_z_d[i];
        T h = h_d[i];
 
        // Project on tangential direction
        T normu = ui * nx + vi * ny + wi * nz;
 
        ui -= normu * nx;
        vi -= normu * ny;
        wi -= normu * nz;
 
        T magu = sqrt(ui * ui + vi * vi + wi * wi);
 
        // Get initial guess for Newton solver
        T guess;
        if (tstep == 1) {
            guess = sqrt(magu * nu_d[i] / h);
        } else {
            guess = tau_x_d[i] * tau_x_d[i] +
                    tau_y_d[i] * tau_y_d[i] +
                    tau_z_d[i] * tau_z_d[i];
            guess = sqrt(sqrt(guess));
        }
 
        // Solve for utau using Newton's method
        T utau = solve(magu, h, guess, nu_d[i], kappa, B);
 
        // Distribute according to the velocity vector
        tau_x_d[i] = -rho * utau * utau * ui / magu;
        tau_y_d[i] = -rho * utau * utau * vi / magu;
        tau_z_d[i] = -rho * utau * utau * wi / magu;
    }
}
 
template<typename T>
__device__ T solve(const T u, const T y, const T guess, const T nu,
                   const T kappa, const T B) {
    T utau = guess;
    T yp, up, f, df, old, error;
    const int maxiter = 100;
 
    for (int k = 0; k < maxiter; ++k) {
        up = u / utau;
        yp = y * utau / nu;
        old = utau;
 
        // Evaluate function and its derivative
        f = (up + exp(-kappa * B) *
                  (exp(kappa * up) - 1.0 - kappa * up -
                   0.5 * (kappa * up) * (kappa * up) -
                   (1.0 / 6.0) * (kappa * up) * (kappa * up) * (kappa * up)) -
             yp);
 
        df = (-y / nu - u / (utau * utau) -
              kappa * up / utau * exp(-kappa * B) *
                  (exp(kappa * up) - 1.0 - kappa * up -
                   0.5 * (kappa * up) * (kappa * up)));
 
        // Update solution
        utau -= f / df;
 
        error = fabs((old - utau) / old);
 
        if (error < 1e-3) {
            break;
        }
    }
 
    return utau;
}
 
#endif // __COMMON_SPALDING_KERNEL_H__