feat: added julia FTCS implementation
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@ -77,6 +77,28 @@ struct Boundary{T}
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end
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end
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function getBoundaryElementType(boundary::Boundary{T}, side::SIDE, index::Int)::TYPE where {T}
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if boundary.dim == 1 && (side == BOTTOM || side == TOP)
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throw(ArgumentError("For the one-dimensional case, only the left and right borders exist."))
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end
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if index < 1 || index > (side in (LEFT, RIGHT) ? boundary.rows : boundary.cols)
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throw(ArgumentError("Index out of bounds!"))
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end
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getType(boundary.boundaries[Int(side)][index])
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end
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function getBoundaryElementValue(boundary::Boundary{T}, side::SIDE, index::Int)::T where {T}
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if boundary.dim == 1 && (side == BOTTOM || side == TOP)
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throw(ArgumentError("For the one-dimensional case, only the left and right borders exist."))
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end
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if index < 1 || index > (side in (LEFT, RIGHT) ? boundary.rows : boundary.cols)
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throw(ArgumentError("Index out of bounds!"))
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end
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getValue(boundary.boundaries[Int(side)][index])
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end
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function getBoundarySide(boundary::Boundary{T}, side::SIDE)::Vector{BoundaryElement{T}} where {T}
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if boundary.dim == 1 && (side == BOTTOM || side == TOP)
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throw(ArgumentError("For the one-dimensional case, only the left and right borders exist."))
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@ -10,19 +10,7 @@ using Base.Threads
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include("../Boundary.jl")
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include("../Grid.jl")
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function calcAlphaIntercell(alpha1::T, alpha2::T) where {T}
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2 / ((1 / alpha1) + (1 / alpha2))
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end
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function calcAlphaIntercell(alpha1::Vector{T}, alpha2::Vector{T}) where {T}
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2 ./ ((1 ./ alpha1) .+ (1 ./ alpha2))
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end
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function calcAlphaIntercell(alpha1::Matrix{T}, alpha2::Matrix{T}) where {T}
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2 ./ ((1 ./ alpha1) .+ (1 ./ alpha2))
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end
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include("Utils.jl")
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function calcBoundaryCoeffClosed(alpha_center::T, alpha_side::T, sx::T) where {T}
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alpha = calcAlphaIntercell(alpha_center, alpha_side)
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258
julia/tug/Core/FTCS.jl
Normal file
258
julia/tug/Core/FTCS.jl
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@ -0,0 +1,258 @@
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# FTCS.jl
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# Implementation of heterogenous FTCS (forward time-centered space)
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# solution of diffusion equation in 1D and 2D space.
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# Translated from C++'s FTCS.hpp.
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include("../Boundary.jl")
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include("../Grid.jl")
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include("Utils.jl")
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function calcHorizontalChange(grid::Grid{T}, row::Int, col::Int) where {T}
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return calcAlphaIntercell(getAlphaX(grid)[row, col+1],
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getAlphaX(grid)[row, col]) *
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getConcentrations(grid)[row, col+1] -
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(calcAlphaIntercell(getAlphaX(grid)[row, col+1],
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getAlphaX(grid)[row, col]) +
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calcAlphaIntercell(getAlphaX(grid)[row, col-1],
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getAlphaX(grid)[row, col])) *
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getConcentrations(grid)[row, col] +
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calcAlphaIntercell(getAlphaX(grid)[row, col-1],
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getAlphaX(grid)[row, col]) *
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getConcentrations(grid)[row, col-1]
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end
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function calcHorizontalChangeLeftBoundary(grid::Grid{T}, bc::Boundary{T}, row::Int, col::Int) where {T}
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if getBoundaryElementType(bc, LEFT, row) == CONSTANT
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return calcHorizontalChangeLeftBoundaryConstant(grid, bc, row, col)
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elseif getBoundaryElementType(bc, LEFT, row) == CLOSED
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return calcHorizontalChangeLeftBoundaryClosed(grid, row, col)
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else
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error("Undefined Boundary Condition Type!")
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end
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end
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function calcHorizontalChangeLeftBoundaryConstant(grid::Grid{T}, bc::Boundary{T}, row::Int, col::Int) where {T}
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return calcAlphaIntercell(getAlphaX(grid)[row, col+1],
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getAlphaX(grid)[row, col]) *
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getConcentrations(grid)[row, col+1] -
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(calcAlphaIntercell(getAlphaX(grid)[row, col+1],
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getAlphaX(grid)[row, col]) +
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2 * getAlphaX(grid)[row, col]) *
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getConcentrations(grid)[row, col] +
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2 * getAlphaX(grid)[row, col] *
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getBoundaryElementValue(bc, LEFT, row)
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end
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function calcHorizontalChangeLeftBoundaryClosed(grid::Grid{T}, row::Int, col::Int) where {T}
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return calcAlphaIntercell(getAlphaX(grid)[row, col+1],
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getAlphaX(grid)[row, col]) *
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(getConcentrations(grid)[row, col+1] -
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getConcentrations(grid)[row, col])
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end
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function calcHorizontalChangeRightBoundary(grid::Grid{T}, bc::Boundary{T}, row::Int, col::Int) where {T}
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if getBoundaryElementType(bc, RIGHT, row) == CONSTANT
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return calcHorizontalChangeRightBoundaryConstant(grid, bc, row, col)
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elseif getBoundaryElementType(bc, RIGHT, row) == CLOSED
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return calcHorizontalChangeRightBoundaryClosed(grid, row, col)
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else
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error("Undefined Boundary Condition Type!")
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end
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end
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function calcHorizontalChangeRightBoundaryConstant(grid::Grid{T}, bc::Boundary{T}, row::Int, col::Int) where {T}
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return 2 * getAlphaX(grid)[row, col] *
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getBoundaryElementValue(bc, RIGHT, row) -
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(calcAlphaIntercell(getAlphaX(grid)[row, col-1],
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getAlphaX(grid)[row, col]) +
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2 * getAlphaX(grid)[row, col]) *
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getConcentrations(grid)[row, col] +
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calcAlphaIntercell(getAlphaX(grid)[row, col-1],
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getAlphaX(grid)[row, col]) *
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getConcentrations(grid)[row, col-1]
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end
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function calcHorizontalChangeRightBoundaryClosed(grid::Grid{T}, row::Int, col::Int) where {T}
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return -(calcAlphaIntercell(getAlphaX(grid)[row, col-1],
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getAlphaX(grid)[row, col]) *
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(getConcentrations(grid)[row, col] -
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getConcentrations(grid)[row, col-1]))
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end
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function calcVerticalChange(grid::Grid{T}, row::Int, col::Int) where {T}
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return calcAlphaIntercell(getAlphaY(grid)[row+1, col],
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getAlphaY(grid)[row, col]) *
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getConcentrations(grid)[row+1, col] -
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(calcAlphaIntercell(getAlphaY(grid)[row+1, col],
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getAlphaY(grid)[row, col]) +
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calcAlphaIntercell(getAlphaY(grid)[row-1, col],
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getAlphaY(grid)[row, col])) *
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getConcentrations(grid)[row, col] +
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calcAlphaIntercell(getAlphaY(grid)[row-1, col],
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getAlphaY(grid)[row, col]) *
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getConcentrations(grid)[row-1, col]
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end
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function calcVerticalChangeTopBoundary(grid::Grid{T}, bc::Boundary{T}, row::Int, col::Int) where {T}
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if getBoundaryElementType(bc, TOP, col) == CONSTANT
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return calcVerticalChangeTopBoundaryConstant(grid, bc, row, col)
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elseif getBoundaryElementType(bc, TOP, col) == CLOSED
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return calcVerticalChangeTopBoundaryClosed(grid, row, col)
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else
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error("Undefined Boundary Condition Type!")
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end
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end
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function calcVerticalChangeTopBoundaryConstant(grid::Grid{T}, bc::Boundary{T}, row::Int, col::Int) where {T}
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return calcAlphaIntercell(getAlphaY(grid)[row+1, col],
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getAlphaY(grid)[row, col]) *
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getConcentrations(grid)[row+1, col] -
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(calcAlphaIntercell(getAlphaY(grid)[row+1, col],
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getAlphaY(grid)[row, col]) +
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2 * getAlphaY(grid)[row, col]) *
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getConcentrations(grid)[row, col] +
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2 * getAlphaY(grid)[row, col] *
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getBoundaryElementValue(bc, TOP, col)
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end
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function calcVerticalChangeTopBoundaryClosed(grid::Grid{T}, row::Int, col::Int) where {T}
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return calcAlphaIntercell(getAlphaY(grid)[row+1, col],
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getAlphaY(grid)[row, col]) *
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(getConcentrations(grid)[row+1, col] -
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getConcentrations(grid)[row, col])
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end
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function calcVerticalChangeBottomBoundary(grid::Grid{T}, bc::Boundary{T}, row::Int, col::Int) where {T}
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if getBoundaryElementType(bc, BOTTOM, col) == CONSTANT
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return calcVerticalChangeBottomBoundaryConstant(grid, bc, row, col)
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elseif getBoundaryElementType(bc, BOTTOM, col) == CLOSED
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return calcVerticalChangeBottomBoundaryClosed(grid, row, col)
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else
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error("Undefined Boundary Condition Type!")
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end
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end
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function calcVerticalChangeBottomBoundaryConstant(grid::Grid{T}, bc::Boundary{T}, row::Int, col::Int) where {T}
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return 2 * getAlphaY(grid)[row, col] *
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getBoundaryElementValue(bc, BOTTOM, col) -
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(calcAlphaIntercell(getAlphaY(grid)[row, col],
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getAlphaY(grid)[row-1, col]) +
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2 * getAlphaY(grid)[row, col]) *
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getConcentrations(grid)[row, col] +
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calcAlphaIntercell(getAlphaY(grid)[row, col],
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getAlphaY(grid)[row-1, col]) *
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getConcentrations(grid)[row-1, col]
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end
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function calcVerticalChangeBottomBoundaryClosed(grid::Grid{T}, row::Int, col::Int) where {T}
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return -(calcAlphaIntercell(getAlphaY(grid)[row, col],
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getAlphaY(grid)[row-1, col]) *
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(getConcentrations(grid)[row, col] -
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getConcentrations(grid)[row-1, col]))
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end
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function FTCS_1D(grid::Grid{T}, bc::Boundary{T}, timestep::T) where {T}
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colMax = getCols(grid)
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sx = timestep / getDeltaCol(grid) * getDeltaCol(grid)
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# matrix for concentrations at time t+1
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concentrations_t1 = zeros(1, colMax)
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# only one row in 1D case -> row constant at index 1
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row = 1
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# inner cells
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# independent of boundary condition type
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for col = 2:colMax-1
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concentrations_t1[row, col] = getConcentrations(grid)[row, col] +
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sx * calcHorizontalChange(grid, row, col)
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end
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# left boundary; hold column constant at index 1
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concentrations_t1[row, 1] = getConcentrations(grid)[row, 1] +
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sx * calcHorizontalChangeLeftBoundary(grid, bc, row, 1)
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# right boundary; hold column constant at max index
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concentrations_t1[row, colMax] = getConcentrations(grid)[row, colMax] +
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sx * calcHorizontalChangeRightBoundary(grid, bc, row, colMax)
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# overwrite obsolete concentrations
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setConcentrations!(grid, concentrations_t1)
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end
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function FTCS_2D(grid::Grid{T}, bc::Boundary{T}, timestep::T) where {T}
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rowMax = getRows(grid)
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colMax = getCols(grid)
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sx = timestep / (getDeltaCol(grid)^2)
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sy = timestep / (getDeltaRow(grid)^2)
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concentrations = getConcentrations(grid)
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concentrations_t1 = copy(concentrations)
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# inner cells
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# these are independent of the boundary condition type
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for row = 2:rowMax-1
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# inner cells
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for col = 2:colMax-1
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concentrations_t1[row, col] += sy * calcVerticalChange(grid, row, col) +
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sx * calcHorizontalChange(grid, row, col)
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end
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# left boundary without corners
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concentrations_t1[row, 1] += sx * calcHorizontalChangeLeftBoundary(grid, bc, row, 1) +
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sy * calcVerticalChange(grid, row, 1)
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# right boundary without corners
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concentrations_t1[row, colMax] += sx * calcHorizontalChangeRightBoundary(grid, bc, row, colMax) +
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sy * calcVerticalChange(grid, row, colMax)
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end
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# top / bottom without corners / looping over columns
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for col = 2:colMax-1
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# top
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concentrations_t1[1, col] += sy * calcVerticalChangeTopBoundary(grid, bc, 1, col) +
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sx * calcHorizontalChange(grid, 1, col)
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# bottom
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concentrations_t1[rowMax, col] += sy * calcVerticalChangeBottomBoundary(grid, bc, rowMax, col) +
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sx * calcHorizontalChange(grid, rowMax, col)
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end
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# corner top left
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concentrations_t1[1, 1] += sx * calcHorizontalChangeLeftBoundary(grid, bc, 1, 1) +
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sy * calcVerticalChangeTopBoundary(grid, bc, 1, 1)
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# corner top right
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concentrations_t1[1, colMax] += sx * calcHorizontalChangeRightBoundary(grid, bc, 1, colMax) +
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sy * calcVerticalChangeTopBoundary(grid, bc, 1, colMax)
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# corner bottom left
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concentrations_t1[rowMax, 1] += sx * calcHorizontalChangeLeftBoundary(grid, bc, rowMax, 1) +
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sy * calcVerticalChangeBottomBoundary(grid, bc, rowMax, 1)
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# corner bottom right
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concentrations_t1[rowMax, colMax] += sx * calcHorizontalChangeRightBoundary(grid, bc, rowMax, colMax) +
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sy * calcVerticalChangeBottomBoundary(grid, bc, rowMax, colMax)
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setConcentrations!(grid, concentrations_t1)
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end
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function runFTCS(grid::Grid{T}, bc::Boundary{T}, timestep::T, iterations::Int, stepCallback::Function) where {T}
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if getDim(grid) == 1
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for _ = 1:iterations
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FTCS_1D(grid, bc, timestep)
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stepCallback()
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end
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elseif getDim(grid) == 2
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for _ = 1:iterations
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FTCS_2D(grid, bc, timestep)
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stepCallback()
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end
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else
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error("FTCS only implemented for 1D and 2D grids")
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end
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end
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12
julia/tug/Core/Utils.jl
Normal file
12
julia/tug/Core/Utils.jl
Normal file
@ -0,0 +1,12 @@
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function calcAlphaIntercell(alpha1::T, alpha2::T) where {T}
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2 / ((1 / alpha1) + (1 / alpha2))
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end
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function calcAlphaIntercell(alpha1::Vector{T}, alpha2::Vector{T}) where {T}
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2 ./ ((1 ./ alpha1) .+ (1 ./ alpha2))
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end
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function calcAlphaIntercell(alpha1::Matrix{T}, alpha2::Matrix{T}) where {T}
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2 ./ ((1 ./ alpha1) .+ (1 ./ alpha2))
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end
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@ -9,8 +9,9 @@ using Printf
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include("Grid.jl")
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include("Boundary.jl")
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include("Core/BTCS.jl")
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include("Core/FTCS.jl")
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@enum APPROACH BTCS
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@enum APPROACH BTCS FTCS
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@enum CONSOLE_OUTPUT CONSOLE_OUTPUT_OFF CONSOLE_OUTPUT_ON CONSOLE_OUTPUT_VERBOSE
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@enum CSV_OUTPUT CSV_OUTPUT_OFF CSV_OUTPUT_ON CSV_OUTPUT_VERBOSE CSV_OUTPUT_XTREME
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@ -105,6 +106,8 @@ function run(simulation::Simulation{T}) where {T}
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if simulation.approach == BTCS
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runBTCS(simulation.grid, simulation.bc, simulation.timestep, simulation.iterations, simulationStepCallback)
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elseif simulation.approach == FTCS
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runFTCS(simulation.grid, simulation.bc, simulation.timestep, simulation.iterations, simulationStepCallback)
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else
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error("Undefined approach!")
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end
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