JustPIC.jl

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Particle-in-Cell advection

JustPIC.jl 최신버젼 다운로드

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# JustPIC.jl

Particle-in-Cell advection ready to rock the GPU  :rocket:

# Example
Load JustPIC and choose where particle arrays are allocated. Backend tags live
in KernelAbstractions; use `JustPIC.CPU` by default, or load CUDA.jl /
AMDGPU.jl and switch to `CUDA.CUDABackend` / `AMDGPU.ROCBackend`.

```julia
using JustPIC
using GLMakie

const backend = JustPIC.CPU
```

Define domain and grids of the domain:

```julia
# number of grid points
n            = 257
# number of cells
nx           = ny = n-1
# domain size
Lx           = Ly = 1.0
# nodal vertices
xvi = xv, yv = range(0, Lx, length=n), range(0, Ly, length=n)
# grid spacing
dxi = dx, dy = xv[2] - xv[1], yv[2] - yv[1]
# nodal centers
xci = xc, yc = range(0+dx/2, Lx-dx/2, length=n-1), range(0+dy/2, Ly-dy/2, length=n-1)
# staggered grid velocity nodal locations
grid_vx      = xv, expand_range(yc)
grid_vy      = expand_range(xc), yv
```
where `expand_range` is a helper function that expands a range by one element on each side:
```julia
function expand_range(x::AbstractRange)
    dx = x[2] - x[1]
    n = length(x)
    x1, x2 = extrema(x)
    xI = round(x1-dx; sigdigits=5)
    xF = round(x2+dx; sigdigits=5)
    range(xI, xF, length=n+2)
end
```

Now we can initialize the particles object
```julia
nxcell    = 24 # initial number of particles per cell
max_xcell = 48 # maximum number of particles per cell
min_xcell = 12 # minimum number of particles per cell
particles = init_particles(
    backend, nxcell, max_xcell, min_xcell, grid_vx, grid_vy
)
```

The velocity field is defined by the stream function $\psi=\frac{250}{\pi}\sin(\pi x)\cos(\pi y)$, so that the analytical velocity field at the particle $p=p(x,y)$ is given by
```julia
vx_stream(x, y) =   250 * sin(π*x) * cos(π*y)
vy_stream(x, y) =  -250 * cos(π*x) * sin(π*y)
```
and therefore the velocity field (__with ghost nodes__) on the staggered grid is given by
```julia
Vx = TA(backend)([vx_stream(x, y) for x in grid_vx[1], y in grid_vx[2]]);
Vy = TA(backend)([vy_stream(x, y) for x in grid_vy[1], y in grid_vy[2]]);
V  = Vx, Vy
dt = min(dx / maximum(abs.(Vx)),  dy / maximum(abs.(Vy))) # time step
```
where `TA(backend)` is `Array` on `JustPIC.CPU`, `CuArray` on
`CUDA.CUDABackend`, and `ROCArray` on `AMDGPU.ROCBackend`.

We save the initial particle positions:
```julia
pxv = particles.coords[1].data;
pyv = particles.coords[2].data;
idxv = particles.index.data;
p = [(pxv[idxv][1], pyv[idxv][1])]
```

chose the advection scheme
```julia
advection_scheme = RungeKutta2()
```

and finally perform the time iterations:
```julia
 # Advection test
particle_args = ()
niter = 750
for iter in 1:niter
    # advect particles
    advection!(particles, advection_scheme, V, dt)
    # shuffle particles in the memory to keep the spatial locality tight
    move_particles!(particles, particle_args)
    # save particle position
    pxv = particles.coords[1].data;
    pyv = particles.coords[2].data;
    idxv = particles.index.data;
    p_i = (pxv[idxv][1], pyv[idxv][1])
    push!(p, p_i)
end
```

where `particle_args` is an empty tuple, but typically it contains the fields that are advected with the particles (e.g. temperature). At last, we plot the particle trajectory on top of the stream function:
```julia
using GLMakie
g(x) = Point2f(
    vx_stream(x[1], x[2]),
    vy_stream(x[1], x[2])
)
f, ax, = streamplot(g, xvi...)
lines!(ax, p, color=:red)
f
```

## Funding
The development of this package is supported by the [GPU4GEO](https://ptsolvers.github.io/GPU4GEO/) [PASC](https://www.pasc-ch.org) project.

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