most_kernel.h

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/*
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*/
 
#ifndef MOST_KERNEL_H
#define MOST_KERNEL_H
 
#include <cmath>
#include <algorithm>
 
/*
* Similarity laws and corrections for the STABLE regime:
* REFERENCE: Cheng, Y., and W. Brutsaert (2005), Flux-profile relationships
* for wind speed and temperature in the stable atmospheric boundary layer,
* Bound.-Layer Meteorol., 3, 519-538.
* NOTE: This formulation is chosen for its superior behavior in very stable
* conditions (large z/L), avoiding the numerical decoupling found in older linear (e.g., Webb or Holtslag) functions.
*/
 
template<typename T>
__device__ T corr_m_stable(T z, T L_ob)
{
    // Coefficients specific to Cheng & Brutsaert (2005)
    T a = 1.0;
    T b = 2.0/3.0;
    T c = 5.0;
    T d = 0.35;
    T zeta = z / L_ob;
 
    return -a*zeta - b*(zeta-c/d)*exp(-d*zeta) - b*c/d;
}
 
template<typename T>
__device__ T corr_h_stable(T z, T L_ob)
{
    // Coefficients specific to Cheng & Brutsaert (2005)
    T a = 1.0;
    T b = 2.0/3.0;
    T c = 5.0;
    T d = 0.35;
    T zeta = z / L_ob;
 
    return -b*(zeta-c/d)*exp(-d*zeta)
    -pow(1.0 + 2.0/3.0*a*zeta, 1.5)
    -b*c/d + 1.0;
}
 
template<typename T>
__device__ T slaw_m_stable(T z, T L_ob, T z0)
{
    return log(z/z0)
           - corr_m_stable<T>(z,L_ob)
           + corr_m_stable<T>(z0,L_ob);
}
 
template<typename T>
__device__ T slaw_h_stable(T z, T L_ob, T z0h)
{
    return log(z/z0h)
           - corr_h_stable<T>(z,L_ob)
           + corr_h_stable<T>(z0h,L_ob);
}
 
template<typename T>
__device__ T f_neumann_stable(T Ri_b, T z, T z0, T z0h, T L_ob, T Pr)
{
    return Ri_b - Pr*z/L_ob / (
            slaw_m_stable<T>(z,L_ob,z0)
            *slaw_m_stable<T>(z,L_ob,z0)
            *slaw_m_stable<T>(z,L_ob,z0)
            );
}
 
template<typename T>
__device__ T dfdl_neumann_stable(T l_upper,
                          T l_lower,
                          T z,
                          T z0,
                          T z0h,
                          T fd_h,
                          T Pr)
{
    T up = -z/l_upper /
           (
            slaw_m_stable<T>(z,l_upper,z0)
           *slaw_m_stable<T>(z,l_upper,z0)
           *slaw_m_stable<T>(z,l_upper,z0)
        );
 
    T low =  z/l_lower /
            (
              slaw_m_stable<T>(z,l_lower,z0)
            *slaw_m_stable<T>(z,l_lower,z0)
            *slaw_m_stable<T>(z,l_lower,z0)
        );
 
    return Pr*(up + low) / (2*fd_h);
}
 
template<typename T>
__device__ T f_dirichlet_stable(T Ri_b, T z, T z0, T z0h, T L_ob, T Pr)
{
    return Ri_b - Pr*z/L_ob * slaw_h_stable<T>(z,L_ob,z0h) / (
        slaw_m_stable<T>(z,L_ob,z0)*slaw_m_stable<T>(z,L_ob,z0)
    );
}
 
template<typename T>
__device__ T dfdl_dirichlet_stable(T l_upper,
                          T l_lower,
                          T z,
                          T z0,
                          T z0h,
                          T fd_h,
                          T Pr)
{
    T up = -z/l_upper *
            slaw_h_stable<T>(z,l_upper,z0h) / (
            slaw_m_stable<T>(z,l_upper,z0)*slaw_m_stable<T>(z,l_upper,z0)
        );
 
    T low =  z/l_lower *
            slaw_h_stable<T>(z,l_lower,z0h) / (
            slaw_m_stable<T>(z,l_lower,z0)*slaw_m_stable<T>(z,l_lower,z0)
        );
 
    return Pr*(up + low) / (2*fd_h);
}
 
/*
* Similarity laws and corrections for the UNSTABLE (convective) regime:
* REFERENCE: Dyer, A. J. (1974), A review of flux-profile relationships,
* Bound.-Layer Meteorol., 7, 363-372.
* INTEGRATION: Paulson, C. A. (1970), The mathematical representation
* of wind speed and temperature profiles in the unstable atmospheric
* surface layer, J. Appl. Meteorol., 9, 857-861.
*/
 
template<typename T>
__device__ T corr_m_convective(T z, T L_ob)
{
    T zeta = z / L_ob;
    T pi = 4*atan(1.0);
    // Standard Dyer-Businger coefficient gamma = 16.0
    T xi = sqrt(sqrt((1.0 - 16.0*zeta)));
 
    return 2*log(0.5*(1 + xi)) + log(0.5*(1 + xi*xi)) - 2*atan(xi) + pi/2;
}
 
template<typename T>
__device__ T corr_h_convective(T z, T L_ob)
{
    T zeta = z/L_ob;
    T pi = 4*atan(1.0);
    // Standard Dyer-Businger coefficient gamma = 16.0
    T xi = sqrt(sqrt((1.0 - 16.0*zeta)));
    return 2*log(0.5*(1 + xi*xi));
}
 
template<typename T>
__device__ T slaw_m_convective(T z, T L_ob, T z0)
{
    return log(z/z0)
           - corr_m_convective<T>(z,L_ob)
           + corr_m_convective<T>(z0,L_ob);
}
 
template<typename T>
__device__ T slaw_h_convective(T z, T L_ob, T z0h)
{
    return log(z/z0h)
           - corr_h_convective<T>(z,L_ob)
           + corr_h_convective<T>(z0h,L_ob);
}
 
template<typename T>
__device__ T f_neumann_convective(T Ri_b, T z, T z0, T z0h, T L_ob, T Pr)
{
    return Ri_b - Pr*z/L_ob / (
        slaw_m_convective<T>(z,L_ob,z0)
       *slaw_m_convective<T>(z,L_ob,z0)
       *slaw_m_convective<T>(z,L_ob,z0)
    );
}
 
template<typename T>
__device__ T dfdl_neumann_convective(T l_upper,
                          T l_lower,
                          T z,
                          T z0,
                          T z0h,
                          T fd_h,
                          T Pr)
{
    T up = -z/l_upper /
           (
            slaw_m_convective<T>(z,l_upper,z0)
           *slaw_m_convective<T>(z,l_upper,z0)
           *slaw_m_convective<T>(z,l_upper,z0)
        );
 
    T low =  z/l_lower /
             (
             slaw_m_convective<T>(z,l_lower,z0)
            *slaw_m_convective<T>(z,l_lower,z0)
            *slaw_m_convective<T>(z,l_lower,z0)
        );
 
    return Pr*(up + low) / (2*fd_h);
}
 
template<typename T>
__device__ T f_dirichlet_convective(T Ri_b, T z, T z0, T z0h, T L_ob, T Pr)
{
    return Ri_b - Pr*z/L_ob * slaw_h_convective<T>(z,L_ob,z0h) / (
        slaw_m_convective<T>(z,L_ob,z0)*slaw_m_convective<T>(z,L_ob,z0)
    );
}
 
template<typename T>
__device__ T dfdl_dirichlet_convective(T l_upper,
                          T l_lower,
                          T z,
                          T z0,
                          T z0h,
                          T fd_h,
                          T Pr)
{
    T up = -z/l_upper *
           slaw_h_convective<T>(z,l_upper,z0h) / (
            slaw_m_convective<T>(z,l_upper,z0)*slaw_m_convective<T>(z,l_upper,z0)
        );
 
    T low =  z/l_lower *
             slaw_h_convective<T>(z,l_lower,z0h) / (
              slaw_m_convective<T>(z,l_lower,z0)*slaw_m_convective<T>(z,l_lower,z0)
          );
 
    return Pr*(up + low) / (2*fd_h);
}
 
/*
* Similarity laws and corrections for the NEUTRAL regime:
*/
 
template<typename T>
__device__ T slaw_m_neutral(T z, T z0)
{
    return log(z/z0);
}
 
template<typename T>
__device__ T slaw_h_neutral(T z, T z0h)
{
    return log(z/z0h);
}
 
/*
 * HIP kernel for the MOST wall model.
 */
template<typename T, int BC_TYPE>
__global__ void most_compute(
    const T* __restrict__ u_d,
    const T* __restrict__ v_d,
    const T* __restrict__ w_d,
    const T* __restrict__ temp_d,
    const T* __restrict__ temp_w_d,
    const T* __restrict__ h_d,
    const T* __restrict__ n_x_d,
    const T* __restrict__ n_y_d,
    const T* __restrict__ n_z_d,
    T* __restrict__ tau_x_d,
    T* __restrict__ tau_y_d,
    T* __restrict__ tau_z_d,
    int n_nodes,
    T kappa,
    const T * __restrict__ mu_w_d,
    const T * __restrict__ rho_w_d,
    T g1,
    T g2,
    T g3,
    T Pr,
    T z0,
    T z0h_in,
    T bc_value,
    T* __restrict__ Ri_b_diagn,
    T* __restrict__ L_ob_diagn,
    T* __restrict__ utau_diagn,
    T* __restrict__ magu_diagn,
    T* __restrict__ ti_diagn,
    T* __restrict__ ts_diagn,
    T* __restrict__ q_diagn
) {
    const int idx = blockIdx.x * blockDim.x + threadIdx.x;
    const int str = blockDim.x * gridDim.x;
    if(idx >= n_nodes) return;
 
    const T Ri_threshold = 1e-4;
    const T tol = 1e-3;
    const T NR_step = 1e-3;
    const int max_iter = 50;
 
    for (int i = idx; i < n_nodes; i += str) {
        T ui = u_d[i];
        T vi = v_d[i];
        T wi = w_d[i];
        T ti = temp_d[i];
        T hi = h_d[i];
        T mu = mu_w_d[i];
        T rho = rho_w_d[i];
 
        // Extract the local normal vector
        T nx = n_x_d[i];
        T ny = n_y_d[i];
        T nz = n_z_d[i];
 
        // Get the tangential component
        T normu = ui * nx + vi * ny + wi * nz;
        ui -= normu * nx;
        vi -= normu * ny;
        wi -= normu * nz;
 
        // The magnitude used for MOST is the magnitude of the tangential vector
        T magu = sqrt(ui*ui + vi*vi + wi*wi);
        magu = fmax(magu, (T)1e-6); // Avoid division by zero in extreme cases
 
        // Initial utau estimate
        T utau = kappa * magu / log(hi/z0);
 
        // Zilitinkevich 1995 correlation for thermal roughness
        T z0h;
        if (z0h_in < 0.0) {
            z0h = z0 * exp(z0h_in * sqrt((utau*z0)/(mu/rho)));
        } else {
            z0h = z0h_in;
        }
 
        T ts = 0;
        T q  = 0;
 
        if constexpr (BC_TYPE == 0)      // Neumann
            q = bc_value;
        else                             // Dirichlet
        {
            ts = bc_value;
            q  = kappa/Pr*utau*(ts-ti)/log(hi/z0h);
        }
 
        T Ri_b;
        T g_dot_n = fabs(g1*nx + g2*ny + g3*nz);
        if constexpr (BC_TYPE == 0)
            Ri_b = -g_dot_n*hi/ti*q*Pr/(magu*magu*magu*kappa*kappa);
        else
            Ri_b =  g_dot_n*hi/ti*(ti-ts)/(magu*magu);
 
        T L_ob = 0.0;   // neutral default
 
        const T L_sign = (Ri_b > 0) ? 1.0 : -1.0;
 
        // Stability branching localy
        if (fabs(Ri_b) <= Ri_threshold) {
            // NEUTRAL CASe
            utau = kappa * magu / slaw_m_neutral<T>(hi, z0);
            if constexpr (BC_TYPE == 1) q = kappa/Pr * utau * (ts - ti) / slaw_h_neutral<T>(hi, z0h);
        }
        else {
            // STABLE or CONVECTIVE (NR)
            // Initial guess based on stability
            if (Ri_b > 0)
                L_ob = hi / fmax(Ri_b, Ri_threshold);
            else
                L_ob = hi / fmin(Ri_b, -Ri_threshold);
 
            T L_old;
            for (int it = 0; it < max_iter; ++it) {
                L_old = L_ob;
                T f_val, dfdl;
                T fd_h   = NR_step * L_ob;
                T L_upper = L_ob + fd_h;
                T L_lower = L_ob - fd_h;
 
                // Use the appropriate simlarity law based on stability and b.c. type
                if (Ri_b > 0) { // Stable
                    if constexpr (BC_TYPE == 0) {
                        f_val = f_neumann_stable<T>(Ri_b, hi, z0, z0h, L_ob, Pr);
                        dfdl = dfdl_neumann_stable<T>(L_upper, L_lower, hi, z0, z0h, fd_h, Pr);
                    } else {
                        f_val = f_dirichlet_stable<T>(Ri_b, hi, z0, z0h, L_ob, Pr);
                        dfdl = dfdl_dirichlet_stable<T>(L_upper, L_lower, hi, z0, z0h, fd_h, Pr);
                    }
                } else { // Convective
                    if constexpr (BC_TYPE == 0) {
                        f_val = f_neumann_convective<T>(Ri_b, hi, z0, z0h, L_ob, Pr);
                        dfdl = dfdl_neumann_convective<T>(L_upper, L_lower, hi, z0, z0h, fd_h, Pr);
                    } else {
                        f_val = f_dirichlet_convective<T>(Ri_b, hi, z0, z0h, L_ob, Pr);
                        dfdl = dfdl_dirichlet_convective<T>(L_upper, L_lower, hi, z0, z0h, fd_h, Pr);
                    }
                }
 
                if (fabs(dfdl) < (T)1e-12) break;
                L_ob -= f_val / dfdl;
                if (L_ob * L_sign <= 0) L_ob = 0.5 * L_old;
                L_ob = L_sign * fmax(fmin(fabs(L_ob), (T)1e8), (T)1e-8);
                if (fabs((L_ob - L_old) / L_ob) < tol) break;
            }
 
            // Final local variables update
            if (Ri_b > 0) {
                utau = kappa * magu / slaw_m_stable<T>(hi, L_ob, z0);
                if constexpr (BC_TYPE == 1) q = kappa/Pr * utau * (ts - ti) / slaw_h_stable<T>(hi, L_ob, z0h);
            } else {
                utau = kappa * magu / slaw_m_convective<T>(hi, L_ob, z0);
                if constexpr (BC_TYPE == 1) q = kappa/Pr * utau * (ts - ti) / slaw_h_convective<T>(hi, L_ob, z0h);
            }
        }
        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;
 
        Ri_b_diagn[i] = Ri_b;
        L_ob_diagn[i] = L_ob;
        utau_diagn[i] = utau;
        magu_diagn[i] = magu;
        ti_diagn[i] = ti;
        ts_diagn[i] = temp_w_d[i];
        q_diagn[i] = q;
    }
}
 
#endif // MOST_KERNEL_H