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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473
use super::Alt;
use rayon::prelude::*;
/// From https://github.com/fastscape-lem/fastscapelib-fortran/blob/master/src/Diffusion.f90
///
/// See https://fastscape-lem.github.io/fastscapelib-fortran
///
/// nx = grid size x
///
/// ny = grid size y
///
/// xl = x-dimension of the model topography in meters (double precision)
///
/// yl = y-dimension of the model topography in meters (double precision)
///
/// dt = length of the time step in years (double precision)
///
/// ibc = boundary conditions for grid. For now, we assume all four boundaries
/// are fixed height, so this parameter is ignored.
///
/// h = heights of cells at each cell in the grid.
///
/// b = basement height at each cell in the grid (see https://en.wikipedia.org/wiki/Basement_(geology)).
///
/// kd = bedrock transport coefficient (or diffusivity) for hillslope processes
/// in meter squared per year (double precision) at each cell in the grid.
///
/// kdsed = sediment transport coefficient (or diffusivity) for hillslope
/// processes in meter squared per year; (double precision;) note that when
/// kdsed < 0, its value is not used, i.e., kd for sediment and bedrock have the
/// same value, regardless of sediment thickness
/* subroutine Diffusion ()
! subroutine to solve the diffusion equation by ADI
use FastScapeContext
implicit none
*/
#[allow(clippy::needless_late_init)]
pub fn diffusion(
nx: usize,
ny: usize,
xl: f64,
yl: f64,
dt: f64,
_ibc: (),
h: &mut [Alt],
b: &mut [Alt],
kd: impl Fn(usize) -> f64,
kdsed: f64,
) {
let aij = |i: usize, j: usize| j * nx + i;
/*
double precision, dimension(:), allocatable :: f,diag,sup,inf,res
double precision, dimension(:,:), allocatable :: zint,kdint,zintp
integer i,j,ij
double precision factxp,factxm,factyp,factym,dx,dy
*/
let mut f: Vec<f64>;
let mut diag: Vec<f64>;
let mut sup: Vec<f64>;
let mut inf: Vec<f64>;
let mut res: Vec<f64>;
let mut zint: Vec<f64>;
let mut kdint: Vec<f64>;
let mut zintp: Vec<f64>;
let mut ij: usize;
let mut factxp: f64;
let mut factxm: f64;
let mut factyp: f64;
let mut factym: f64;
let dx: f64;
let dy: f64;
/*
character cbc*4
!print*,'Diffusion'
write (cbc,'(i4)') ibc
dx=xl/(nx-1)
dy=yl/(ny-1)
*/
// 2048*32/2048/2048
// 1 / 64 m
dx = xl / /*(nx - 1)*/nx as f64;
dy = yl / /*(ny - 1)*/ny as f64;
/*
! creates 2D internal arrays to store topo and kd
allocate (zint(nx,ny),kdint(nx,ny),zintp(nx,ny))
*/
zint = vec![Default::default(); nx * ny];
kdint = vec![Default::default(); nx * ny];
/*
do j=1,ny
do i=1,nx
ij=(j-1)*nx+i
zint(i,j)=h(ij)
kdint(i,j)=kd(ij)
if (kdsed.gt.0.d0 .and. (h(ij)-b(ij)).gt.1.d-6) kdint(i,j)=kdsed
enddo
enddo
zintp = zint
*/
for j in 0..ny {
for i in 0..nx {
// ij = vec2_as_uniform_idx(i, j);
ij = aij(i, j);
zint[ij] = h[ij];
kdint[ij] = kd(ij);
if kdsed > 0.0 && (h[ij] - b[ij]) > 1.0e-6 {
kdint[ij] = kdsed;
}
}
}
zintp = zint.clone();
/*
! first pass along the x-axis
allocate (f(nx),diag(nx),sup(nx),inf(nx),res(nx))
f=0.d0
diag=0.d0
sup=0.d0
inf=0.d0
res=0.d0
do j=2,ny-1
*/
f = vec![0.0; nx];
diag = vec![0.0; nx];
sup = vec![0.0; nx];
inf = vec![0.0; nx];
res = vec![0.0; nx];
for j in 1..ny - 1 {
/*
do i=2,nx-1
factxp=(kdint(i+1,j)+kdint(i,j))/2.d0*(dt/2.)/dx**2
factxm=(kdint(i-1,j)+kdint(i,j))/2.d0*(dt/2.)/dx**2
factyp=(kdint(i,j+1)+kdint(i,j))/2.d0*(dt/2.)/dy**2
factym=(kdint(i,j-1)+kdint(i,j))/2.d0*(dt/2.)/dy**2
diag(i)=1.d0+factxp+factxm
sup(i)=-factxp
inf(i)=-factxm
f(i)=zintp(i,j)+factyp*zintp(i,j+1)-(factyp+factym)*zintp(i,j)+factym*zintp(i,j-1)
enddo
*/
for i in 1..nx - 1 {
factxp = (kdint[aij(i + 1, j)] + kdint[aij(i, j)]) / 2.0 * (dt / 2.0) / (dx * dx);
factxm = (kdint[aij(i - 1, j)] + kdint[aij(i, j)]) / 2.0 * (dt / 2.0) / (dx * dx);
factyp = (kdint[aij(i, j + 1)] + kdint[aij(i, j)]) / 2.0 * (dt / 2.0) / (dy * dy);
factym = (kdint[aij(i, j - 1)] + kdint[aij(i, j)]) / 2.0 * (dt / 2.0) / (dy * dy);
diag[i] = 1.0 + factxp + factxm;
sup[i] = -factxp;
inf[i] = -factxm;
f[i] = zintp[aij(i, j)] + factyp * zintp[aij(i, j + 1)]
- (factyp + factym) * zintp[aij(i, j)]
+ factym * zintp[aij(i, j - 1)];
}
/*
! left bc
if (cbc(4:4).eq.'1') then
diag(1)=1.
sup(1)=0.
f(1)=zintp(1,j)
else
factxp=(kdint(2,j)+kdint(1,j))/2.d0*(dt/2.)/dx**2
factyp=(kdint(1,j+1)+kdint(1,j))/2.d0*(dt/2.)/dy**2
factym=(kdint(1,j-1)+kdint(1,j))/2.d0*(dt/2.)/dy**2
diag(1)=1.d0+factxp
sup(1)=-factxp
f(1)=zintp(1,j)+factyp*zintp(1,j+1)-(factyp+factym)*zintp(1,j)+factym*zintp(1,j-1)
endif
*/
if true {
diag[0] = 1.0;
sup[0] = 0.0;
f[0] = zintp[aij(0, j)];
} else {
// reflective boundary
factxp = (kdint[aij(1, j)] + kdint[aij(0, j)]) / 2.0 * (dt / 2.0) / (dx * dx);
factyp = (kdint[aij(0, j + 1)] + kdint[aij(0, j)]) / 2.0 * (dt / 2.0) / (dy * dy);
factym = (kdint[aij(0, j - 1)] + kdint[aij(0, j)]) / 2.0 * (dt / 2.0) / (dy * dy);
diag[0] = 1.0 + factxp;
sup[0] = -factxp;
f[0] = zintp[aij(0, j)] + factyp * zintp[aij(0, j + 1)]
- (factyp + factym) * zintp[aij(0, j)]
+ factym * zintp[aij(0, j - 1)];
}
/*
! right bc
if (cbc(2:2).eq.'1') then
diag(nx)=1.
inf(nx)=0.
f(nx)=zintp(nx,j)
else
factxm=(kdint(nx-1,j)+kdint(nx,j))/2.d0*(dt/2.)/dx**2
factyp=(kdint(nx,j+1)+kdint(nx,j))/2.d0*(dt/2.)/dy**2
factym=(kdint(nx,j-1)+kdint(nx,j))/2.d0*(dt/2.)/dy**2
diag(nx)=1.d0+factxm
inf(nx)=-factxm
f(nx)=zintp(nx,j)+factyp*zintp(nx,j+1)-(factyp+factym)*zintp(nx,j)+factym*zintp(nx,j-1)
endif
*/
if true {
diag[nx - 1] = 1.0;
inf[nx - 1] = 0.0;
f[nx - 1] = zintp[aij(nx - 1, j)];
} else {
// reflective boundary
factxm = (kdint[aij(nx - 2, j)] + kdint[aij(nx - 1, j)]) / 2.0 * (dt / 2.0) / (dx * dx);
factyp =
(kdint[aij(nx - 1, j + 1)] + kdint[aij(nx - 1, j)]) / 2.0 * (dt / 2.0) / (dy * dy);
factym =
(kdint[aij(nx - 1, j - 1)] + kdint[aij(nx - 1, j)]) / 2.0 * (dt / 2.0) / (dy * dy);
diag[nx - 1] = 1.0 + factxm;
inf[nx - 1] = -factxm;
f[nx - 1] = zintp[aij(nx - 1, j)] + factyp * zintp[aij(nx - 1, j + 1)]
- (factyp + factym) * zintp[aij(nx - 1, j)]
+ factym * zintp[aij(nx - 1, j - 1)];
}
/*
call tridag (inf,diag,sup,f,res,nx)
do i=1,nx
zint(i,j)=res(i)
enddo
*/
tridag(&inf, &diag, &sup, &f, &mut res, nx);
for i in 0..nx {
zint[aij(i, j)] = res[i];
}
/*
enddo
deallocate (f,diag,sup,inf,res)
*/
}
/*
! second pass along y-axis
allocate (f(ny),diag(ny),sup(ny),inf(ny),res(ny))
f=0.d0
diag=0.d0
sup=0.d0
inf=0.d0
res=0.d0
do i=2,nx-1
*/
f = vec![0.0; ny];
diag = vec![0.0; ny];
sup = vec![0.0; ny];
inf = vec![0.0; ny];
res = vec![0.0; ny];
for i in 1..nx - 1 {
/*
do j=2,ny-1
factxp=(kdint(i+1,j)+kdint(i,j))/2.d0*(dt/2.)/dx**2
factxm=(kdint(i-1,j)+kdint(i,j))/2.d0*(dt/2.)/dx**2
factyp=(kdint(i,j+1)+kdint(i,j))/2.d0*(dt/2.)/dy**2
factym=(kdint(i,j-1)+kdint(i,j))/2.d0*(dt/2.)/dy**2
diag(j)=1.d0+factyp+factym
sup(j)=-factyp
inf(j)=-factym
f(j)=zint(i,j)+factxp*zint(i+1,j)-(factxp+factxm)*zint(i,j)+factxm*zint(i-1,j)
enddo
*/
for j in 1..ny - 1 {
factxp = (kdint[aij(i + 1, j)] + kdint[aij(i, j)]) / 2.0 * (dt / 2.0) / (dx * dx);
factxm = (kdint[aij(i - 1, j)] + kdint[aij(i, j)]) / 2.0 * (dt / 2.0) / (dx * dx);
factyp = (kdint[aij(i, j + 1)] + kdint[aij(i, j)]) / 2.0 * (dt / 2.0) / (dy * dy);
factym = (kdint[aij(i, j - 1)] + kdint[aij(i, j)]) / 2.0 * (dt / 2.0) / (dy * dy);
diag[j] = 1.0 + factyp + factym;
sup[j] = -factyp;
inf[j] = -factym;
f[j] = zint[aij(i, j)] + factxp * zint[aij(i + 1, j)]
- (factxp + factxm) * zint[aij(i, j)]
+ factxm * zint[aij(i - 1, j)];
}
/*
! bottom bc
if (cbc(1:1).eq.'1') then
diag(1)=1.
sup(1)=0.
f(1)=zint(i,1)
else
factxp=(kdint(i+1,1)+kdint(i,j))/2.d0*(dt/2.)/dx**2
factxm=(kdint(i-1,1)+kdint(i,1))/2.d0*(dt/2.)/dx**2
factyp=(kdint(i,2)+kdint(i,1))/2.d0*(dt/2.)/dy**2
diag(1)=1.d0+factyp
sup(1)=-factyp
f(1)=zint(i,1)+factxp*zint(i+1,1)-(factxp+factxm)*zint(i,1)+factxm*zint(i-1,1)
endif
*/
if true {
diag[0] = 1.0;
sup[0] = 0.0;
f[0] = zint[aij(i, 0)];
} else {
// reflective boundary
// TODO: Check whether this j was actually supposed to be a 0 in the original
// (probably).
// factxp = (kdint[aij(i+1, 0)] + kdint[aij(i, j)]) / 2.0 * (dt / 2.0) / (dx *
// dx);
factxp = (kdint[aij(i + 1, 0)] + kdint[aij(i, 0)]) / 2.0 * (dt / 2.0) / (dx * dx);
factxm = (kdint[aij(i - 1, 0)] + kdint[aij(i, 0)]) / 2.0 * (dt / 2.0) / (dx * dx);
factyp = (kdint[aij(i, 1)] + kdint[aij(i, 0)]) / 2.0 * (dt / 2.0) / (dy * dy);
diag[0] = 1.0 + factyp;
sup[0] = -factyp;
f[0] = zint[aij(i, 0)] + factxp * zint[aij(i + 1, 0)]
- (factxp + factxm) * zint[aij(i, 0)]
+ factxm * zint[aij(i - 1, 0)];
}
/*
! top bc
if (cbc(3:3).eq.'1') then
diag(ny)=1.
inf(ny)=0.
f(ny)=zint(i,ny)
else
factxp=(kdint(i+1,ny)+kdint(i,ny))/2.d0*(dt/2.)/dx**2
factxm=(kdint(i-1,ny)+kdint(i,ny))/2.d0*(dt/2.)/dx**2
factym=(kdint(i,ny-1)+kdint(i,ny))/2.d0*(dt/2.)/dy**2
diag(ny)=1.d0+factym
inf(ny)=-factym
f(ny)=zint(i,ny)+factxp*zint(i+1,ny)-(factxp+factxm)*zint(i,ny)+factxm*zint(i-1,ny)
endif
*/
if true {
diag[ny - 1] = 1.0;
inf[ny - 1] = 0.0;
f[ny - 1] = zint[aij(i, ny - 1)];
} else {
// reflective boundary
factxp =
(kdint[aij(i + 1, ny - 1)] + kdint[aij(i, ny - 1)]) / 2.0 * (dt / 2.0) / (dx * dx);
factxm =
(kdint[aij(i - 1, ny - 1)] + kdint[aij(i, ny - 1)]) / 2.0 * (dt / 2.0) / (dx * dx);
factym = (kdint[aij(i, ny - 2)] + kdint[aij(i, ny - 1)]) / 2.0 * (dt / 2.0) / (dy * dy);
diag[ny - 1] = 1.0 + factym;
inf[ny - 1] = -factym;
f[ny - 1] = zint[aij(i, ny - 1)] + factxp * zint[aij(i + 1, ny - 1)]
- (factxp + factxm) * zint[aij(i, ny - 1)]
+ factxm * zint[aij(i - 1, ny - 1)];
}
/*
call tridag (inf,diag,sup,f,res,ny)
do j=1,ny
zintp(i,j)=res(j)
enddo
*/
tridag(&inf, &diag, &sup, &f, &mut res, ny);
for j in 0..ny {
zintp[aij(i, j)] = res[j];
}
/*
enddo
deallocate (f,diag,sup,inf,res)
*/
}
/*
! stores result in 1D array
do j=1,ny
do i=1,nx
ij=(j-1)*nx+i
etot(ij)=etot(ij)+h(ij)-zintp(i,j)
erate(ij)=erate(ij)+(h(ij)-zintp(i,j))/dt
h(ij)=zintp(i,j)
enddo
enddo
b=min(h,b)
*/
for j in 0..ny {
for i in 0..nx {
ij = aij(i, j);
// FIXME: Track total erosion and erosion rate.
h[ij] = zintp[ij] as Alt;
}
}
b.par_iter_mut().zip(h).for_each(|(b, h)| {
*b = h.min(*b);
});
/*
deallocate (zint,kdint,zintp)
return
end subroutine Diffusion
*/
}
/*
!----------
! subroutine to solve a tri-diagonal system of equations (from Numerical Recipes)
SUBROUTINE tridag(a,b,c,r,u,n)
implicit none
INTEGER n
double precision a(n),b(n),c(n),r(n),u(n)
*/
#[allow(clippy::needless_late_init)]
pub fn tridag(a: &[f64], b: &[f64], c: &[f64], r: &[f64], u: &mut [f64], n: usize) {
/*
INTEGER j
double precision bet
double precision,dimension(:),allocatable::gam
allocate (gam(n))
if(b(1).eq.0.d0) stop 'in tridag'
*/
let mut bet: f64;
let mut gam: Vec<f64>;
gam = vec![Default::default(); n];
assert_ne!(b[0], 0.0);
/*
! first pass
bet=b(1)
u(1)=r(1)/bet
do 11 j=2,n
gam(j)=c(j-1)/bet
bet=b(j)-a(j)*gam(j)
if(bet.eq.0.) then
print*,'tridag failed'
stop
endif
u(j)=(r(j)-a(j)*u(j-1))/bet
11 continue
*/
bet = b[0];
u[0] = r[0] / bet;
for j in 1..n {
gam[j] = c[j - 1] / bet;
bet = b[j] - a[j] * gam[j];
assert_ne!(bet, 0.0);
// Round 0: u[0] = r[0] / b[0]
// = r'[0] / b'[0]
// Round j: u[j] = (r[j] - a[j] * u'[j - 1]) / b'[j]
// = (r[j] - a[j] * r'[j - 1] / b'[j - 1]) / b'[j]
// = (r[j] - (a[j] / b'[j - 1]) * r'[j - 1]) / b'[j]
// = (r[j] - w[j] * r'[j - 1]) / b'[j]
// = r'[j] / b'[j]
u[j] = (r[j] - a[j] * u[j - 1]) / bet;
}
/*
! second pass
do 12 j=n-1,1,-1
u(j)=u(j)-gam(j+1)*u(j+1)
12 continue
*/
for j in (0..n - 1).rev() {
u[j] -= gam[j + 1] * u[j + 1];
}
/*
deallocate (gam)
return
END
*/
}