TwoPointFluxFVM

Solver for coupled nonlinear partial differential equations based on the two point flux finite volume method on admissible grids.

This Julia package merges the ideas behind pdelib/fvsys with the multiple dispatch paradigm of Julia. It allows to avoid the implementation of function derivatives. It instead uses the ForwardDiff and DiffResults to evaluate user fucntions along with their jacobians.

So far this is merely a design study to learn and evaluate Julia. It is however aimed to be feasible at least for small projects.

It requires Julia 1.0.

Documentation created with Documenter.jl resides here

Typical usage

"""
Structure containing  userdata information
"""
mutable struct Physics
    reaction::Function
    flux::Function
    storage::Function
    source::Function
    eps::Float64 
    Physics()=new()
end

"""
Reaction term
"""
physics.reaction=function(physics,node,f,u)
    f[1]=u[1]^2
end

"""
Storage term
"""
physics.storage=function(physics,node,f,u)
    f[1]=u[1]
end

"""
Flux term
"""
physics.flux=function(physics,edge,f,uk,ul)
    f[1]=this.eps*(uk[1]^2-ul[1]^2)
end 


"""
Source term
"""
physics.source=function(physics,node,f)
    f[1]=1.0e-4*node.coord[1]
end 

TwoPointFluxFVM.Grid

This is a simplex grid structure.

TwoPointFluxFVM.Node

This represents a node in TwoPointFluxFVM.Grid.

TwoPointFluxFVM.Edge

This represents an edge between two neigboring control volumes created from TwoPointFluxFVM.Grid.

Currently, constructors are TwoPointFluxFVM.Grid(X::Array{Real,1}) for one-dimensional domains and TwoPointFluxFVM.Grid(X::Array{Float64,1},Y::Array{Float64,1}) for two-dimensional domains.

TwoPointFluxFVM.System

From instances of TwoPointFluxFVM.Graph and TwoPointFluxFVM.Physics, a TwoPointFluxFVM.System which contains all the necessary data for the solution of the nonlinear system described by them.