sfx_compute_sheba.cu

#include <cmath>
#include <iostream>
#include "../includeCU/sfx_compute_sheba.cuh"
#include "../includeCU/sfx_surface.cuh"

template<typename T>
__device__ void get_charnock_roughness(T &z0_m, T &u_dyn0,
    const T h, const T U,
    const T kappa, 
    const T h_charnock, const T c1_charnock, const T c2_charnock, 
    const int maxiters)
{
    T Uc, a, b, c, c_min, f;

    Uc = U;
    a = 0.0;
    b = 25.0;
    c_min = log(h_charnock) / kappa;

    for (int i = 0; i < maxiters; i++)
    {
        f = c1_charnock - 2.0 * log(Uc);
        for (int j = 0; j < maxiters; j++)
        {
            c = (f + 2.0 * log(b)) / kappa;
            if (U <= 8.0e0) 
                a = log(1.0 + c2_charnock * ( pow(b / Uc, 3) ) ) / kappa;
            c = max(c - a, c_min);
            b = c;
        }
        z0_m = h_charnock * exp(-c * kappa);
        z0_m = max(z0_m, T(0.000015e0));
        Uc = U * log(h_charnock / z0_m) / log(h / z0_m);
    }
    
    u_dyn0 = Uc / c;
}

template __device__ void get_charnock_roughness(float &z0_m, float &u_dyn0,
    const float h, const float U,
    const float kappa, 
    const float h_charnock, const float c1_charnock, const float c2_charnock, 
    const int maxiters);
template __device__ void get_charnock_roughness(double &z0_m, double &u_dyn0, 
    const double h, const double U,
    const double kappa, 
    const double h_charnock, const double c1_charnock, const double c2_charnock,
    const int maxiters);

template<typename T>
__device__ void get_thermal_roughness(T &z0_t, T &B,
    const T z0_m, const T Re, 
    const T Re_rough_min, 
    const T B1_rough, const T B2_rough, const T B3_rough, const T B4_rough, 
    const T B_max_ocean, const T B_max_lake, const T B_max_land,
    const int surface_type)
{
    // --- define B = log(z0_m / z0_t)
    if (Re <= Re_rough_min) 
        B = B1_rough * log(B3_rough * Re) + B2_rough;
    else
        // *: B4 takes into account Re value at z' ~ O(10) z0
        B = B4_rough * (pow(Re, B2_rough));

    //   --- apply max restriction based on surface type
    if (surface_type == 0) 
        B = min(B, B_max_ocean);
    else if (surface_type == 2) 
        B = min(B, B_max_lake);
    else if (surface_type == 1)
        B = min(B, B_max_land);

    // --- define roughness [thermal]
    z0_t = z0_m / exp(B);
}

template __device__ void get_thermal_roughness(float &z0_t, float &B,
    const float z0_m, const float Re, 
    const float Re_rough_min, 
    const float B1_rough, const float B2_rough, const float B3_rough, const float B4_rough, 
    const float B_max_ocean, const float B_max_lake, const float B_max_land,
    const int surface_type);
template __device__ void get_thermal_roughness(double &z0_t, double &B,
    const double z0_m, const double Re, 
    const double Re_rough_min, 
    const double B1_rough, const double B2_rough, const double B3_rough, const double B4_rough, 
    const double B_max_ocean, const double B_max_lake, const double B_max_land,
    const int surface_type);

template<typename T>
__device__ void get_psi_mh(T &psi_m, T &psi_h,
    const T zeta_m, const T zeta_h,
    const T alpha_m, const T alpha_h,
    const T a_m, const T a_h, 
    const T b_m, const T b_h,
    const T c_h)
{
    T x_m, x_h;
    T q_m, q_h;

    if (zeta_m >= 0.0) 
    {
        q_m = pow((1.0 - b_m) / b_m, 1.0 / 3.0);
        x_m = pow(1.0 + zeta_m, 1.0 / 3.0);

        psi_m = -3.0 * (a_m / b_m) * (x_m - 1.0) + 0.5 * (a_m / b_m) * q_m * (2.0 * log((x_m + q_m) / (1.0 + q_m)) - log((x_m * x_m - x_m * q_m + q_m * q_m) / (1.0 - q_m + q_m * q_m)) + 2.0 * sqrt(3.0) * (atan((2.0 * x_m - q_m) / (sqrt(3.0) * q_m)) - atan((2.0 - q_m) / (sqrt(3.0) * q_m))));
    }                                
    else
    {    x_m = pow(1.0 - alpha_m * zeta_m, 0.25);
        psi_m = (4.0 * atan(1.0) / 2.0) + 2.0 * log(0.5 * (1.0 + x_m)) + log(0.5 * (1.0 + x_m * x_m)) - 2.0 * atan(x_m);
    }

    if (zeta_h >= 0.0)
    {    
        q_h = sqrt(c_h * c_h - 4.0);
        x_h = zeta_h;

        psi_h = -0.5 * b_h * log(1.0 + c_h * x_h + x_h * x_h) + ((-a_h / q_h) + ((b_h * c_h) / (2.0 * q_h))) * (log((2.0 * x_h + c_h - q_h) / (2.0 * x_h + c_h + q_h)) - log((c_h - q_h) / (c_h + q_h)));
    }
    else
    {
        x_h = pow(1.0 - alpha_h * zeta_h, 0.25);
        psi_h = 2.0 * log(0.5 * (1.0 + x_h * x_h));
    }
}

template __device__ void get_psi_mh(float &psi_m, float &psi_h,
    const float zeta_m, const float zeta_h,
    const float alpha_m, const float alpha_h,
    const float a_m, const float a_h, 
    const float b_m, const float b_h,
    const float c_h);
template __device__ void get_psi_mh(double &psi_m, double &psi_h,
    const double zeta_m, const double zeta_h,
    const double alpha_m, const double alpha_h,
    const double a_m, const double a_h, 
    const double b_m, const double b_h,
    const double c_h);

template<typename T>
__device__ void get_psi(T &psi_m, T &psi_h,
    const T zeta,
    const T alpha_m, const T alpha_h,
    const T a_m, const T a_h, 
    const T b_m, const T b_h,
    const T c_h)
{
    T x_m, x_h;
    T q_m, q_h;

    if (zeta >= 0.0) 
    {
        q_m = pow((1.0 - b_m) / b_m, 1.0 / 3.0);
        q_h = sqrt(c_h * c_h - 4.0);

        x_m = pow(1.0 + zeta, 1.0 / 3.0);
        x_h = zeta;

        psi_m = -3.0 * (a_m / b_m) * (x_m - 1.0) + 0.5 * (a_m / b_m) * q_m * (2.0 * log((x_m + q_m) / (1.0 + q_m)) - log((x_m * x_m - x_m * q_m + q_m * q_m) / (1.0 - q_m + q_m * q_m)) + 2.0 * sqrt(3.0) * (atan((2.0 * x_m - q_m) / (sqrt(3.0) * q_m)) - atan((2.0 - q_m) / (sqrt(3.0) * q_m))));

        psi_h = -0.5 * b_h * log(1.0 + c_h * x_h + x_h * x_h) + ((-a_h / q_h) + ((b_h * c_h) / (2.0 * q_h))) * (log((2.0 * x_h + c_h - q_h) / (2.0 * x_h + c_h + q_h)) - log((c_h - q_h) / (c_h + q_h)));
    }
    else
    {
        x_m = pow(1.0 - alpha_m * zeta, 0.25);
        x_h = pow(1.0 - alpha_h * zeta, 0.25); 

        psi_m = (4.0 * atan(1.0) / 2.0) + 2.0 * log(0.5 * (1.0 + x_m)) + log(0.5 * (1.0 + x_m * x_m)) - 2.0 * atan(x_m);
        psi_h = 2.0 * log(0.5 * (1.0 + x_h * x_h));
    }
}

template __device__ void get_psi(float &psi_m, float &psi_h,
    const float zeta,
    const float alpha_m, const float alpha_h,
    const float a_m, const float a_h, 
    const float b_m, const float b_h,
    const float c_h);
template __device__ void get_psi(double &psi_m, double &psi_h,
    const double zeta,
    const double alpha_m, const double alpha_h,
    const double a_m, const double a_h, 
    const double b_m, const double b_h,
    const double c_h);

template<typename T>
__device__ void get_dynamic_scales(T &Udyn, T &Tdyn, T &Qdyn, T &zeta,
    const T U, const T Tsemi, const T dT, const T dQ, const T z, const T z0_m, const T z0_t, const T beta,
    const T kappa, const T Pr_t_0_inv,
    const T alpha_m, const T alpha_h,
    const T a_m, const T a_h, 
    const T b_m, const T b_h,
    const T c_h,
    const int maxiters)
{
    T psi_m, psi_h, psi0_m, psi0_h, Linv;
    const T gamma = 0.61;

    Udyn = kappa * U / log(z / z0_m);
    Tdyn = kappa * dT * Pr_t_0_inv / log(z / z0_t);
    Qdyn = kappa * dQ * Pr_t_0_inv / log(z / z0_t);
    zeta = 0.0;

    // --- no wind
    if (Udyn < 1e-5) 
        return;

    Linv = kappa * beta * (Tdyn + gamma * Qdyn * Tsemi) / (Udyn * Udyn);
    zeta = z * Linv;

    // --- near neutral case
    if (Linv < 1e-5) 
        return;

    for (int i = 0; i < maxiters; i++)
    {
        get_psi(psi_m, psi_h, zeta, alpha_m, alpha_h,
        a_m, a_h, 
        b_m, b_h,
        c_h);
        
        get_psi_mh(psi0_m, psi0_h, z0_m * Linv, z0_t * Linv, 
        alpha_m, alpha_h,
        a_m, a_h, 
        b_m, b_h,
        c_h);

        Udyn = kappa * U / (log(z / z0_m) - (psi_m - psi0_m));
        Tdyn = kappa * dT * Pr_t_0_inv / (log(z / z0_t) - (psi_h - psi0_h));
        Qdyn = kappa * dQ * Pr_t_0_inv / (log(z / z0_t) - (psi_h - psi0_h));

        if (Udyn < 1e-5) 
            break;

        Linv = kappa * beta * (Tdyn + gamma * Qdyn * Tsemi) / (Udyn * Udyn);
        zeta = z * Linv;
    }
}

template __device__ void get_dynamic_scales(float &Udyn, float &Tdyn, float &Qdyn, float & zeta,
    const float U, const float Tsemi, const float dT, const float dQ, const float z, const float z0_m, const float z0_t, const float beta,
    const float kappa, const float Pr_t_0_inv,
    const float alpha_m, const float alpha_h,
    const float a_m, const float a_h, 
    const float b_m, const float b_h,
    const float c_h,
    const int maxiters);
template __device__ void get_dynamic_scales(double &Udyn, double &Tdyn, double &Qdyn, double & zeta,
    const double U, const double Tsemi, const double dT, const double dQ, const double z, const double z0_m, const double z0_t, const double beta,
    const double kappa, const double Pr_t_0_inv,
    const double alpha_m, const double alpha_h,
    const double a_m, const double a_h, 
    const double b_m, const double b_h,
    const double c_h,
    const int maxiters);

template<typename T>
__device__ void get_phi(T &phi_m, T &phi_h,
    const T zeta, 
    const T alpha_m, const T alpha_h,
    const T a_m, const T a_h, 
    const T b_m, const T b_h,
    const T c_h)
{
    if (zeta >= 0.0) 
    {
        phi_m = 1.0 + (a_m * zeta * pow(1.0 + zeta, 1.0 / 3.0) ) / (1.0 + b_m * zeta);
        phi_h = 1.0 + (a_h * zeta + b_h * zeta * zeta) / (1.0 + c_h * zeta + zeta * zeta);
    }
    else
    {
        phi_m = pow(1.0 - alpha_m * zeta, -0.25);
        phi_h = pow(1.0 - alpha_h * zeta, -0.5);
    }
}

template __device__ void get_phi(float &phi_m, float &phi_h,
    const float zeta, 
    const float alpha_m, const float alpha_h,
    const float a_m, const float a_h, 
    const float b_m, const float b_h,
    const float c_h);
template __device__ void get_phi(double &phi_m, double &phi_h,
    const double zeta, 
    const double alpha_m, const double alpha_h,
    const double a_m, const double a_h, 
    const double b_m, const double b_h,
    const double c_h);

template<typename T>
__global__ void kernel_compute_flux_sheba(T *zeta_, T *Rib_, T *Re_, T *B_, T *z0_m_, T *z0_t_, T *Rib_conv_lim_, T *Cm_, T *Ct_, T *Km_, T *Pr_t_inv_,
    const T *U_, const T *dT_, const T *Tsemi_, const T *dQ_, const T *h_, const T *in_z0_m_,
    const T kappa, const T Pr_t_0_inv,
    const T alpha_m, const T alpha_h, 
    const T a_m, const T a_h, 
    const T b_m, const T b_h,
    const T c_h,
    const T Re_rough_min, 
    const T B1_rough, const T B2_rough,
    const T B_max_land, const T B_max_ocean, const T B_max_lake,
    const T gamma_c, const T Re_visc_min,
    const T Pr_m, const T nu_air, const T g, 
    const int maxiters_charnock,
    const int grid_size)
{
    const int index = blockIdx.x * blockDim.x + threadIdx.x;

    T h, U, dT, Tsemi, dQ, z0_m;
    T z0_t, B, h0_m, h0_t, u_dyn0, Re, 
    zeta, Rib, Udyn, Tdyn, Qdyn, phi_m, phi_h,
    Km, Pr_t_inv, Cm, Ct;

    const T B3_rough = kappa * Pr_m, B4_rough =(0.14 * (pow(30.0, B2_rough))) * (pow(Pr_m, 0.8));
    const T h_charnock = 10.0, c1_charnock = log(h_charnock * (g / gamma_c)), c2_charnock = Re_visc_min * nu_air * c1_charnock;

    int surface_type;

    if(index < grid_size)
    {
        U = U_[index];
        Tsemi = Tsemi_[index];
        dT = dT_[index];
        dQ = dQ_[index];
        h = h_[index];
        z0_m = in_z0_m_[index];

        if (z0_m < 0.0) surface_type = 0;
        else            surface_type = 1;

        if (surface_type == 0) 
        {
            get_charnock_roughness(z0_m, u_dyn0, h, U, kappa, h_charnock, c1_charnock, c2_charnock, maxiters_charnock);
            h0_m = h / z0_m;
        }
        if (surface_type == 1) 
        {
            h0_m = h / z0_m;
            u_dyn0 = U * kappa / log(h0_m);
        }

        Re = u_dyn0 * z0_m / nu_air;
        get_thermal_roughness(z0_t, B, z0_m, Re, Re_rough_min, B1_rough, B2_rough, B3_rough, B4_rough, B_max_ocean, B_max_lake, B_max_land, surface_type);

        // --- define relative height [thermal]
        h0_t = h / z0_t;

        // --- define Ri-bulk
        Rib = (g / Tsemi) * h * (dT + 0.61e0 * Tsemi * dQ) / (U*U);

        // --- get the fluxes
        // ----------------------------------------------------------------------------
        get_dynamic_scales(Udyn, Tdyn, Qdyn, zeta, U, Tsemi, dT, dQ, h, z0_m, z0_t, (g / Tsemi), kappa, Pr_t_0_inv, alpha_m, alpha_h, a_m, a_h, b_m, b_h, c_h, 10);
        // ----------------------------------------------------------------------------

        get_phi(phi_m, phi_h, zeta, alpha_m, alpha_h, a_m, a_h, b_m, b_h, c_h);
        // ----------------------------------------------------------------------------

        // --- define transfer coeff. (momentum) & (heat)
        Cm = 0.0;
        if (U > 0.0)
            Cm = Udyn / U;
        Ct = 0.0;
        if (fabs(dT) > 0.0) 
            Ct = Tdyn / dT;

        // --- define eddy viscosity & inverse Prandtl number
        Km = kappa * Cm * U * h / phi_m;
        Pr_t_inv = phi_m / phi_h;

        zeta_[index]         = 0.0;
        Rib_[index]          = 0.0;
        Re_[index]           = 0.0;
        B_[index]            = 0.0;
        z0_m_[index]         = 0.0;
        z0_t_[index]         = 0.0;
        Rib_conv_lim_[index] = 0.0;
        Cm_[index]           = 0.0;
        Ct_[index]           = 0.0;
        Km_[index]           = 0.0;
        Pr_t_inv_[index]     = 0.0;
    }
}

template __global__ void kernel_compute_flux_sheba(float *zeta_, float *Rib_, float *Re_, float *B_, float *z0_m_, float *z0_t_, float *Rib_conv_lim_, float *Cm_, float *Ct_, float *Km_, float *Pr_t_inv_,
    const float *U_, const float *dT_, const float *Tsemi_, const float *dQ_, const float *h_, const float *in_z0_m_,
    const float kappa, const float Pr_t_0_inv,
    const float alpha_m, const float alpha_h, 
    const float a_m, const float a_h, 
    const float b_m, const float b_h,
    const float c_h,
    const float Re_rough_min, 
    const float B1_rough, const float B2_rough,
    const float B_max_land, const float B_max_ocean, const float B_max_lake,
    const float gamma_c, const float Re_visc_min,
    const float Pr_m, const float nu_air, const float g, 
    const int maxiters_charnock,
    const int grid_size);
template __global__ void kernel_compute_flux_sheba(double *zeta_, double *Rib_, double *Re_, double *B_, double *z0_m_, double *z0_t_, double *Rib_conv_lim_, double *Cm_, double *Ct_, double *Km_, double *Pr_t_inv_,
    const double *U_, const double *dT_, const double *Tsemi_, const double *dQ_, const double *h_, const double *in_z0_m_,
    const double kappa, const double Pr_t_0_inv,
    const double alpha_m, const double alpha_h, 
    const double a_m, const double a_h, 
    const double b_m, const double b_h,
    const double c_h,
    const double Re_rough_min, 
    const double B1_rough, const double B2_rough,
    const double B_max_land, const double B_max_ocean, const double B_max_lake,
    const double gamma_c, const double Re_visc_min,
    const double Pr_m, const double nu_air, const double g, 
    const int maxiters_charnock,
    const int grid_size);

template<typename T>
void compute_flux_sheba_gpu(T *zeta_, T *Rib_, T *Re_, T *B_, T *z0_m_, T *z0_t_, T *Rib_conv_lim_, T *Cm_, T *Ct_, T *Km_, T *Pr_t_inv_,
    const T *U_, const T *dT_, const T *Tsemi_, const T *dQ_, const T *h_, const T *in_z0_m_,
    const T kappa, const T Pr_t_0_inv,
    const T alpha_m, const T alpha_h, 
    const T a_m, const T a_h, 
    const T b_m, const T b_h,
    const T c_h,
    const T Re_rough_min, 
    const T B1_rough, const T B2_rough,
    const T B_max_land, const T B_max_ocean, const T B_max_lake,
    const T gamma_c, const T Re_visc_min,
    const T Pr_m, const T nu_air, const T g, 
    const int maxiters_charnock,
    const int grid_size)
{
    const int BlockCount = int(ceil(float(grid_size) / 1024.0));
    dim3 cuBlock = dim3(1024, 1, 1);
	dim3 cuGrid = dim3(BlockCount, 1, 1);

    kernel_compute_flux_sheba<<<cuGrid, cuBlock>>>(zeta_, Rib_, Re_, B_, z0_m_, z0_t_, Rib_conv_lim_, Cm_, Ct_, Km_, Pr_t_inv_,
    U_, dT_, Tsemi_, dQ_, h_, in_z0_m_,
    kappa, Pr_t_0_inv, 
    alpha_m, alpha_h, 
    a_m, a_h, 
    b_m, b_h,
    c_h,
    Re_rough_min, 
    B1_rough, B2_rough,
    B_max_land, B_max_ocean, B_max_lake,
    gamma_c, Re_visc_min,
    Pr_m, nu_air, g, 
    maxiters_charnock, 
    grid_size);
}

template void compute_flux_sheba_gpu(float *zeta_, float *Rib_, float *Re_, float *B_, float *z0_m_, float *z0_t_, float *Rib_conv_lim_, float *Cm_, float *Ct_, float *Km_, float *Pr_t_inv_,
    const float *U_, const float *dT_, const float *Tsemi_, const float *dQ_, const float *h_, const float *in_z0_m_,
    const float kappa, const float Pr_t_0_inv,
    const float alpha_m, const float alpha_h, 
    const float a_m, const float a_h, 
    const float b_m, const float b_h,
    const float c_h,
    const float Re_rough_min, 
    const float B1_rough, const float B2_rough,
    const float B_max_land, const float B_max_ocean, const float B_max_lake,
    const float gamma_c, const float Re_visc_min,
    const float Pr_m, const float nu_air, const float g, 
    const int maxiters_charnock,
    const int grid_size);
template void compute_flux_sheba_gpu(double *zeta_, double *Rib_, double *Re_, double *B_, double *z0_m_, double *z0_t_, double *Rib_conv_lim_, double *Cm_, double *Ct_, double *Km_, double *Pr_t_inv_,
    const double *U_, const double *dT_, const double *Tsemi_, const double *dQ_, const double *h_, const double *in_z0_m_,
    const double kappa, const double Pr_t_0_inv,
    const double alpha_m, const double alpha_h, 
    const double a_m, const double a_h, 
    const double b_m, const double b_h,
    const double c_h,
    const double Re_rough_min, 
    const double B1_rough, const double B2_rough,
    const double B_max_land, const double B_max_ocean, const double B_max_lake,
    const double gamma_c, const double Re_visc_min,
    const double Pr_m, const double nu_air, const double g, 
    const int maxiters_charnock,
    const int grid_size);