Newer
Older
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
#include <cmath>
#include <iostream>
#include "../includeCXX/FluxComputeFunc.h"
template<typename T>
void get_charnock_roughness(const T h, const T U,
const T kappa,
const T h_charnock, const T c1_charnock, const T c2_charnock,
T &z0_m, T &u_dyn0,
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 = std::max(c - a, c_min);
b = c;
}
z0_m = h_charnock * exp(-c * kappa);
z0_m = std::max(z0_m, T(0.000015e0));
Uc = U * log(h_charnock / z0_m) / log(h / z0_m);
}
u_dyn0 = Uc / c;
}
template void get_charnock_roughness(const float h, const float U,
const float kappa,
const float h_charnock, const float c1_charnock, const float c2_charnock,
float &z0_m, float &u_dyn0,
const int maxiters);
template void get_charnock_roughness(const double h, const double U,
const double kappa,
const double h_charnock, const double c1_charnock, const double c2_charnock,
double &z0_m, double &u_dyn0,
const int maxiters);
template<typename T>
void get_convection_lim(const T h0_m, const T h0_t, const T B,
const T Pr_t_inf_inv, const T Pr_t_0_inv,
const T alpha_h, const T alpha_m, const T alpha_h_fix,
T &zeta_lim, T &Rib_lim, T &f_m_lim, T &f_h_lim)
{
T psi_m, psi_h, f_m, f_h, c;
c = pow(Pr_t_inf_inv / Pr_t_0_inv, 4);
zeta_lim = (2.0 * alpha_h - c * alpha_m - sqrt( (c * alpha_m)*(c * alpha_m) + 4.0 * c * alpha_h * (alpha_h - alpha_m))) / (2.0 * alpha_h*alpha_h);
f_m_lim = pow(1.0 - alpha_m * zeta_lim, 0.25);
f_h_lim = sqrt(1.0 - alpha_h * zeta_lim);
f_m = zeta_lim / h0_m;
f_h = zeta_lim / h0_t;
if (fabs(B) < 1.0e-10) f_h = f_m;
f_m = pow(1.0 - alpha_m * f_m, 0.25);
f_h = sqrt(1.0 - alpha_h_fix * f_h);
psi_m = 2.0 * (atan(f_m_lim) - atan(f_m)) + log((f_m_lim - 1.0) * (f_m + 1.0)/((f_m_lim + 1.0) * (f_m - 1.0)));
psi_h = log((f_h_lim - 1.0) * (f_h + 1.0)/((f_h_lim + 1.0) * (f_h - 1.0))) / Pr_t_0_inv;
Rib_lim = zeta_lim * psi_h / (psi_m * psi_m);
}
template void get_convection_lim(const float h0_m, const float h0_t, const float B,
const float Pr_t_inf_inv, const float Pr_t_0_inv,
const float alpha_h, const float alpha_m, const float alpha_h_fix,
float &zeta_lim, float &Rib_lim, float &f_m_lim, float &f_h_lim);
template void get_convection_lim(const double h0_m, const double h0_t, const double B,
const double Pr_t_inf_inv, const double Pr_t_0_inv,
const double alpha_h, const double alpha_m, const double alpha_h_fix,
double &zeta_lim, double &Rib_lim, double &f_m_lim, double &f_h_lim);
template<typename T>
void get_psi_stable(const T Rib, const T h0_m, const T h0_t, const T B,
const T Pr_t_0_inv, const T beta_m,
T &psi_m, T &psi_h, T &zeta)
{
T Rib_coeff, psi0_m, psi0_h, phi, c;
psi0_m = log(h0_m);
psi0_h = B / psi0_m;
Rib_coeff = beta_m * Rib;
c = (psi0_h + 1.0) / Pr_t_0_inv - 2.0 * Rib_coeff;
zeta = psi0_m * (sqrt(c*c + 4.0 * Rib_coeff * (1.0 - Rib_coeff)) - c) / (2.0 * beta_m * (1.0 - Rib_coeff));
phi = beta_m * zeta;
psi_m = psi0_m + phi;
psi_h = (psi0_m + B) / Pr_t_0_inv + phi;
}
template void get_psi_stable(const float Rib, const float h0_m, const float h0_t, const float B,
const float Pr_t_0_inv, const float beta_m,
float &psi_m, float &psi_h, float &zeta);
template void get_psi_stable(const double Rib, const double h0_m, const double h0_t, const double B,
const double Pr_t_0_inv, const double beta_m,
double &psi_m, double &psi_h, double &zeta);
template<typename T>
void get_psi_convection(const T Rib, const T h0_m, const T h0_t, const T B,
const T zeta_conv_lim, const T f_m_conv_lim, const T f_h_conv_lim,
const T Pr_t_0_inv,
const T alpha_h, const T alpha_m, const T alpha_h_fix,
T &psi_m, T &psi_h, T &zeta,
const int maxiters)
{
T zeta0_m, zeta0_h, f0_m, f0_h, p_m, p_h, a_m, a_h, c_lim, f;
p_m = 2.0 * atan(f_m_conv_lim) + log((f_m_conv_lim - 1.0) / (f_m_conv_lim + 1.0));
p_h = log((f_h_conv_lim - 1.0) / (f_h_conv_lim + 1.0));
zeta = zeta_conv_lim;
for (int i = 1; i <= maxiters + 1; i++)
{
zeta0_m = zeta / h0_m;
zeta0_h = zeta / h0_t;
if (fabs(B) < 1.0e-10)
zeta0_h = zeta0_m;
f0_m = pow(1.0 - alpha_m * zeta0_m, 0.25);
f0_h = sqrt(1.0 - alpha_h_fix * zeta0_h);
a_m = -2.0*atan(f0_m) + log((f0_m + 1.0)/(f0_m - 1.0));
a_h = log((f0_h + 1.0)/(f0_h - 1.0));
c_lim = pow(zeta_conv_lim / zeta, 1.0 / 3.0);
f = 3.0 * (1.0 - c_lim);
psi_m = f / f_m_conv_lim + p_m + a_m;
psi_h = (f / f_h_conv_lim + p_h + a_h) / Pr_t_0_inv;
if (i == maxiters + 1)
break;
zeta = Rib * psi_m * psi_m / psi_h;
}
}
template void get_psi_convection(const float Rib, const float h0_m, const float h0_t, const float B,
const float zeta_conv_lim, const float f_m_conv_lim, const float f_h_conv_lim,
const float Pr_t_0_inv,
const float alpha_h, const float alpha_m, const float alpha_h_fix,
float &psi_m, float &psi_h, float &zeta,
const int maxiters);
template void get_psi_convection(const double Rib, const double h0_m, const double h0_t, const double B,
const double zeta_conv_lim, const double f_m_conv_lim, const double f_h_conv_lim,
const double Pr_t_0_inv,
const double alpha_h, const double alpha_m, const double alpha_h_fix,
double &psi_m, double &psi_h, double &zeta,
const int maxiters);
template<typename T>
void get_psi_neutral(const T h0_m, const T h0_t, const T B,
const T Pr_t_0_inv,
T &psi_m, T &psi_h, T &zeta)
{
zeta = 0.0;
psi_m = log(h0_m);
psi_h = log(h0_t) / Pr_t_0_inv;
if (fabs(B) < 1.0e-10)
psi_h = psi_m / Pr_t_0_inv;
}
template void get_psi_neutral(const float h0_m, const float h0_t, const float B,
const float Pr_t_0_inv,
float &psi_m, float &psi_h, float &zeta);
template void get_psi_neutral(const double h0_m, const double h0_t, const double B,
const double Pr_t_0_inv,
double &psi_m, double &psi_h, double &zeta);
template<typename T>
void get_psi_semi_convection(const T Rib, const T h0_m, const T h0_t, const T B,
const T Pr_t_0_inv,
const T alpha_m, const T alpha_h_fix,
T &psi_m, T &psi_h, T &zeta,
const int maxiters)
{
T zeta0_m, zeta0_h, f0_m, f0_h, f_m, f_h;
psi_m = log(h0_m);
psi_h = log(h0_t);
if (fabs(B) < 1.0e-10)
psi_h = psi_m;
zeta = Rib * Pr_t_0_inv * psi_m * psi_m / psi_h;
for (int i = 1; i <= maxiters + 1; i++)
{
zeta0_m = zeta / h0_m;
zeta0_h = zeta / h0_t;
if (fabs(B) < 1.0e-10)
zeta0_h = zeta0_m;
f_m = pow(1.0 - alpha_m * zeta, 0.25e0);
f_h = sqrt(1.0 - alpha_h_fix * zeta);
f0_m = pow(1.0 - alpha_m * zeta0_m, 0.25e0);
f0_h = sqrt(1.0 - alpha_h_fix * zeta0_h);
f0_m = std::max(f0_m, T(1.000001e0));
f0_h = std::max(f0_h, T(1.000001e0));
psi_m = log((f_m - 1.0e0)*(f0_m + 1.0e0)/((f_m + 1.0e0)*(f0_m - 1.0e0))) + 2.0e0*(atan(f_m) - atan(f0_m));
psi_h = log((f_h - 1.0e0)*(f0_h + 1.0e0)/((f_h + 1.0e0)*(f0_h - 1.0e0))) / Pr_t_0_inv;
if (i == maxiters + 1)
break;
zeta = Rib * psi_m * psi_m / psi_h;
}
}
template void get_psi_semi_convection(const float Rib, const float h0_m, const float h0_t, const float B,
const float Pr_t_0_inv,
const float alpha_m, const float alpha_h_fix,
float &psi_m, float &psi_h, float &zeta,
const int maxiters);
template void get_psi_semi_convection(const double Rib, const double h0_m, const double h0_t, const double B,
const double Pr_t_0_inv,
const double alpha_m, const double alpha_h_fix,
double &psi_m, double &psi_h, double &zeta,
const int maxiters);
template<typename T>
void compute_flux_cpu(const T *U_, const T *dT_, const T *Tsemi_, const T *dQ_, const T *h_, const T *in_z0_m_,
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 kappa, const T Pr_t_0_inv, const T Pr_t_inf_inv,
const T alpha_m, const T alpha_h, const T alpha_h_fix,
const T beta_m, const T beta_h, const T Rib_max, 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 maxiters_convection,
const int grid_size)
{
T h, U, dT, Tsemi, dQ, z0_m;
T Re, z0_t, B, h0_m, h0_t, u_dyn0, zeta, Rib, zeta_conv_lim, Rib_conv_lim, f_m_conv_lim, f_h_conv_lim, psi_m, psi_h, phi_m, phi_h, Km, Pr_t_inv, Cm, Ct;
int surface_type;
T fval;
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;
for (int step = 0; step < grid_size; step++)
{
U = U_[step];
Tsemi = Tsemi_[step];
dT = dT_[step];
dQ = dQ_[step];
h = h_[step];
z0_m = in_z0_m_[step];
if (z0_m < 0.0) surface_type = 0;
else surface_type = 1;
if (surface_type == 0)
{
get_charnock_roughness(h, U, kappa, h_charnock, c1_charnock, c2_charnock, z0_m, u_dyn0, 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;
if(Re <= Re_rough_min) B = B1_rough * log(B3_rough * Re) + B2_rough;
else B = B4_rough * (pow(Re, B2_rough));
if (surface_type == 0) B = std::min(B, B_max_ocean);
if (surface_type == 1) B = std::min(B, B_max_land);
if (surface_type == 2) B = std::min(B, B_max_lake);
z0_t = z0_m / exp(B);
h0_t = h / z0_t;
Rib = (g / Tsemi) * h * (dT + 0.61e0 * Tsemi * dQ) / (U*U);
get_convection_lim(h0_m, h0_t, B, Pr_t_inf_inv, Pr_t_0_inv, alpha_h, alpha_m, alpha_h_fix, zeta_conv_lim, Rib_conv_lim, f_m_conv_lim, f_h_conv_lim);
if (Rib > 0.0)
{
Rib = std::min(Rib, Rib_max);
get_psi_stable(Rib, h0_m, h0_t, B, Pr_t_0_inv, beta_m, psi_m, psi_h, zeta);
fval = beta_m * zeta;
phi_m = 1.0 + fval;
phi_h = 1.0/Pr_t_0_inv + fval;
}
else if (Rib < Rib_conv_lim)
{
get_psi_convection(Rib, h0_m, h0_t, B, zeta_conv_lim, f_m_conv_lim, f_h_conv_lim, Pr_t_0_inv, alpha_h, alpha_m, alpha_h_fix, psi_m, psi_h, zeta, maxiters_convection);
fval = pow(zeta_conv_lim / zeta, 1.0/3.0);
phi_m = fval / f_m_conv_lim;
phi_h = fval / (Pr_t_0_inv * f_h_conv_lim);
}
else if (Rib > -0.001)
{
get_psi_neutral(h0_m, h0_t, B, Pr_t_0_inv, psi_m, psi_h, zeta);
phi_m = 1.0;
phi_h = 1.0 / Pr_t_0_inv;
}
else
{
get_psi_semi_convection(Rib, h0_m, h0_t, B, Pr_t_0_inv, alpha_m, alpha_h_fix, psi_m, psi_h, zeta, maxiters_convection);
phi_m = pow(1.0 - alpha_m * zeta, -0.25);
phi_h = 1.0 / (Pr_t_0_inv * sqrt(1.0 - alpha_h_fix * zeta));
}
Cm = kappa / psi_m;
Ct = kappa / psi_h;
Km = kappa * Cm * U * h / phi_m;
Pr_t_inv = phi_m / phi_h;
zeta_[step] = zeta;
Rib_[step] = Rib;
Re_[step] = Re;
B_[step] = B;
z0_m_[step] = z0_m;
z0_t_[step] = z0_t;
Rib_conv_lim_[step] = Rib_conv_lim;
Cm_[step] = Cm;
Ct_[step] = Ct;
Km_[step] = Km;
Pr_t_inv_[step] = Pr_t_inv;
}
}
template void compute_flux_cpu(const float *U, const float *dt, const float *T_semi, const float *dq, const float *H, const float *in_z0_m,
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 kappa, const float Pr_t_0_inv, const float Pr_t_inf_inv,
const float alpha_m, const float alpha_h, const float alpha_h_fix,
const float beta_m, const float beta_h, const float Rib_max, 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 maxiters_convection,
const int grid_size);
template void compute_flux_cpu(const double *U, const double *dt, const double *T_semi, const double *dq, const double *H, const double *in_z0_m,
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 kappa, const double Pr_t_0_inv, const double Pr_t_inf_inv,
const double alpha_m, const double alpha_h, const double alpha_h_fix,
const double beta_m, const double beta_h, const double Rib_max, 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 maxiters_convection,
const int grid_size);