veloren_world/sim/diffusion.rs
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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
*/
#[expect(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)
*/
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
*/
}