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https://github.com/gerlero/fronts.jl

Nonlinear diffusion problems in Julia
https://github.com/gerlero/fronts.jl

boltzmann-transformation capillarity differential-equations diffusion-equation groundwater-flow-equation julia microfluidics nonlinear-equations numerical-methods richards-equation

Last synced: 16 days ago
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Nonlinear diffusion problems in Julia

Host: GitHub
URL: https://github.com/gerlero/fronts.jl
Owner: gerlero
License: mit
Created: 2020-12-07T02:25:02.000Z (almost 4 years ago)
Default Branch: main
Last Pushed: 2024-10-20T22:03:08.000Z (24 days ago)
Last Synced: 2024-10-22T04:42:44.044Z (22 days ago)
Topics: boltzmann-transformation, capillarity, differential-equations, diffusion-equation, groundwater-flow-equation, julia, microfluidics, nonlinear-equations, numerical-methods, richards-equation
Language: Julia
Homepage: https://gerlero.github.io/Fronts.jl
Size: 2.32 MB
Stars: 6
Watchers: 3
Forks: 0
Open Issues: 1
Metadata Files:
- Readme: README.md
- License: LICENSE
- Citation: CITATION.cff

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README

        [](https://github.com/gerlero/Fronts.jl)

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**_Fronts_, at the speed of Julia ⚡️**

This is the (fully native) Julia version of our numerical package for nonlinear diffusion problems, [also available as a Python library](https://github.com/gerlero/fronts).

```julia

julia> using Fronts

julia> D(u) = u^4

D (generic function with 1 method)

julia> eq = DiffusionEquation(D)

∂u/∂t = ∂(D(u)*∂u/∂r)/∂r

julia> prob = DirichletProblem(eq, i=0.1, b=1)

⎧ ∂u/∂t = ∂(D(u)*∂u/∂r)/∂r, r>0,t>0

⎨ u(r,0) = 0.1, r>0

⎩ u(0,t) = 1.0, t>0

julia> u = solve(prob)

Solution u after 10 iterations

retcode: Success

ub = 1.0

du/do|b = -0.28388671875000004

ui = 0.10006060603081587

julia> u(0.25, 2) # Evaluate the solution anywhere and at any time

0.9440546607878473

julia> d_dr(u, 0.25, 2) # Obtain derivatives

-0.25038534184881966

julia> flux(u, 0.25, 2) # Obtain the flux

0.19888290889257723

```

[](https://cimec.conicet.gov.ar)   [](https://intec.conicet.gov.ar)   [](https://microfluidica.ar)