/
PDEDefs.jl
159 lines (139 loc) · 7.16 KB
/
PDEDefs.jl
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################################################################################################
function GS_Periodic!(du, u ,p::Array{Float64, 1},t::Float64) # Works with square and rect grids
f, k, D₁, D₂, dx, dy, M = p
let N = Int(M)
@tturbo for j in 2:N-1, i in 2:N-1
du[i,j,1] = D₁*(1/dx^2*(u[i-1,j,1] + u[i+1,j,1] - 2u[i,j,1]) + 1/dy^2*(u[i,j+1,1] + u[i,j-1,1] - 2u[i,j,1])) +
-u[i,j,1]*u[i,j,2]^2 + f*(1-u[i,j,1])
du[i,j,2] = D₂*(1/dx^2*(u[i-1,j,2] + u[i+1,j,2] - 2u[i,j,2]) + 1/dy^2*(u[i,j+1,2] + u[i,j-1,2] - 2u[i,j,2])) +
u[i,j,1]*u[i,j,2]^2 - (f+k)*u[i,j,2]
end
let i = 1
@tturbo for j in 2:N-1
du[i,j,1] = D₁*(1/dx^2*(u[N,j,1] + u[i+1,j,1] - 2u[i,j,1]) + 1/dy^2*(u[i,j+1,1] + u[i,j-1,1] - 2u[i,j,1])) +
-u[i,j,1]*u[i,j,2]^2 + f*(1-u[i,j,1])
du[i,j,2] = D₂*(1/dx^2*(u[N,j,2] + u[i+1,j,2] - 2u[i,j,2]) + 1/dy^2*(u[i,j+1,2] + u[i,j-1,2] - 2u[i,j,2])) +
u[i,j,1]*u[i,j,2]^2 - (f+k)*u[i,j,2]
end
end
let i = N
@tturbo for j in 2:N-1
du[i,j,1] = D₁*(1/dx^2*(u[i-1,j,1] + u[1,j,1] - 2u[i,j,1]) + 1/dy^2*(u[i,j+1,1] + u[i,j-1,1] - 2u[i,j,1])) +
-u[i,j,1]*u[i,j,2]^2 + f*(1-u[i,j,1])
du[i,j,2] = D₂*(1/dx^2*(u[i-1,j,2] + u[1,j,2] - 2u[i,j,2]) + 1/dy^2*(u[i,j+1,2] + u[i,j-1,2] - 2u[i,j,2])) +
u[i,j,1]*u[i,j,2]^2 - (f+k)*u[i,j,2]
end
end
let j = 1
@tturbo for i in 2:N-1
du[i,j,1] = D₁*(1/dx^2*(u[i-1,j,1] + u[i+1,j,1] - 2u[i,j,1]) + 1/dy^2*(u[i,j+1,1] + u[i,N,1] - 2u[i,j,1])) +
-u[i,j,1]*u[i,j,2]^2 + f*(1-u[i,j,1])
du[i,j,2] = D₂*(1/dx^2*(u[i-1,j,2] + u[i+1,j,2] - 2u[i,j,2]) + 1/dy^2*(u[i,j+1,2] + u[i,N,2] - 2u[i,j,2])) +
u[i,j,1]*u[i,j,2]^2 - (f+k)*u[i,j,2]
end
end
let j = N
@tturbo for i in 2:N-1
du[i,j,1] = D₁*(1/dx^2*(u[i-1,j,1] + u[i+1,j,1] - 2u[i,j,1]) + 1/dy^2*(u[i,1,1] + u[i,j-1,1] - 2u[i,j,1])) +
-u[i,j,1]*u[i,j,2]^2 + f*(1-u[i,j,1])
du[i,j,2] = D₂*(1/dx^2*(u[i-1,j,2] + u[i+1,j,2] - 2u[i,j,2]) + 1/dy^2*(u[i,1,2] + u[i,j-1,2] - 2u[i,j,2])) +
u[i,j,1]*u[i,j,2]^2 - (f+k)*u[i,j,2]
end
end
begin
let i = 1, j = 1
du[i,j,1] = D₁*(1/dx^2*(u[N,j,1] + u[i+1,j,1] - 2u[i,j,1]) + 1/dy^2*(u[i,j+1,1] + u[i,N,1] - 2u[i,j,1])) +
-u[i,j,1]*u[i,j,2]^2 + f*(1-u[i,j,1])
du[i,j,2] = D₂*(1/dx^2*(u[N,j,2] + u[i+1,j,2] - 2u[i,j,2]) + 1/dy^2*(u[i,j+1,2] + u[i,N,2] - 2u[i,j,2])) +
u[i,j,1]*u[i,j,2]^2 - (f+k)*u[i,j,2]
end
let i = 1, j = N
du[i,j,1] = D₁*(1/dx^2*(u[N,j,1] + u[i+1,j,1] - 2u[i,j,1]) + 1/dy^2*(u[i,1,1] + u[i,j-1,1] - 2u[i,j,1])) +
-u[i,j,1]*u[i,j,2]^2 + f*(1-u[i,j,1])
du[i,j,2] = D₂*(1/dx^2*(u[N,j,2] + u[i+1,j,2] - 2u[i,j,2]) + 1/dy^2*(u[i,1,2] + u[i,j-1,2] - 2u[i,j,2])) +
u[i,j,1]*u[i,j,2]^2 - (f+k)*u[i,j,2]
end
let i = N, j = 1
du[i,j,1] = D₁*(1/dx^2*(u[i-1,j,1] + u[1,j,1] - 2u[i,j,1]) + 1/dy^2*(u[i,j+1,1] + u[i,N,1] - 2u[i,j,1])) +
-u[i,j,1]*u[i,j,2]^2 + f*(1-u[i,j,1])
du[i,j,2] = D₂*(1/dx^2*(u[i-1,j,2] + u[1,j,2] - 2u[i,j,2]) + 1/dy^2*(u[i,j+1,2] + u[i,N,2] - 2u[i,j,2])) +
u[i,j,1]*u[i,j,2]^2 - (f+k)*u[i,j,2]
end
let i = N, j = N
du[i,j,1] = D₁*(1/dx^2*(u[i-1,j,1] + u[1,j,1] - 2u[i,j,1]) + 1/dy^2*(u[i,1,1] + u[i,j-1,1] - 2u[i,j,1])) +
-u[i,j,1]*u[i,j,2]^2 + f*(1-u[i,j,1])
du[i,j,2] = D₂*(1/dx^2*(u[i-1,j,2] + u[1,j,2] - 2u[i,j,2]) + 1/dy^2*(u[i,1,2] + u[i,j-1,2] - 2u[i,j,2])) +
u[i,j,1]*u[i,j,2]^2 - (f+k)*u[i,j,2]
end
end
end
nothing
end
function GS_Neumann0!(du, u, p::Array{Float64, 1},t::Float64) # Works with square and rect grids
f, k, D₁, D₂, dx, dy, M = p
let N = Int(M)
@tturbo for j in 2:N-1, i in 2:N-1
du[i,j,1] = D₁*(1/dx^2*(u[i-1,j,1] + u[i+1,j,1] - 2u[i,j,1])+ 1/dy^2*(u[i,j+1,1] + u[i,j-1,1] - 2u[i,j,1])) +
-u[i,j,1]*u[i,j,2]^2 + f*(1-u[i,j,1])
du[i,j,2] = D₂*(1/dx^2*(u[i-1,j,2] + u[i+1,j,2] - 2u[i,j,2])+ 1/dy^2*(u[i,j+1,2] + u[i,j-1,2] - 2u[i,j,2])) +
u[i,j,1]*u[i,j,2]^2 - (f+k)*u[i,j,2]
end
let i = 1
@tturbo for j in 2:N-1
du[i,j,1] = D₁*(1/dx^2*(2u[i+1,j,1] - 2u[i,j,1])+ 1/dy^2*(u[i,j+1,1] + u[i,j-1,1] - 2u[i,j,1])) +
-u[i,j,1]*u[i,j,2]^2 + f*(1-u[i,j,1])
du[i,j,2] = D₂*(1/dx^2*(2u[i+1,j,2] - 2u[i,j,2])+ 1/dy^2*(u[i,j+1,2] + u[i,j-1,2] - 2u[i,j,2])) +
u[i,j,1]*u[i,j,2]^2 - (f+k)*u[i,j,2]
end
end
let i = N
@tturbo for j in 2:N-1
du[i,j,1] = D₁*(1/dx^2*(2u[i-1,j,1] - 2u[i,j,1])+ 1/dy^2*(u[i,j+1,1] + u[i,j-1,1] - 2u[i,j,1])) +
-u[i,j,1]*u[i,j,2]^2 + f*(1-u[i,j,1])
du[i,j,2] = D₂*(1/dx^2*(2u[i-1,j,2] - 2u[i,j,2])+ 1/dy^2*(u[i,j+1,2] + u[i,j-1,2] - 2u[i,j,2])) +
u[i,j,1]*u[i,j,2]^2 - (f+k)*u[i,j,2]
end
end
let j = 1
@tturbo for i in 2:N-1
du[i,j,1] = D₁*(1/dx^2*(u[i-1,j,1] + u[i+1,j,1] - 2u[i,j,1])+ 1/dy^2*(2u[i,j+1,1] - 2u[i,j,1])) +
-u[i,j,1]*u[i,j,2]^2 + f*(1-u[i,j,1])
du[i,j,2] = D₂*(1/dx^2*(u[i-1,j,2] + u[i+1,j,2] - 2u[i,j,2])+ 1/dy^2*(2u[i,j+1,2] - 2u[i,j,2])) +
u[i,j,1]*u[i,j,2]^2 - (f+k)*u[i,j,2]
end
end
let j = N
@tturbo for i in 2:N-1
du[i,j,1] = D₁*(1/dx^2*(u[i-1,j,1] + u[i+1,j,1] - 2u[i,j,1])+ 1/dy^2*(2u[i,j-1,1] - 2u[i,j,1])) +
-u[i,j,1]*u[i,j,2]^2 + f*(1-u[i,j,1])
du[i,j,2] = D₂*(1/dx^2*(u[i-1,j,2] + u[i+1,j,2] - 2u[i,j,2])+ 1/dy^2*(2u[i,j-1,2] - 2u[i,j,2])) +
u[i,j,1]*u[i,j,2]^2 - (f+k)*u[i,j,2]
end
end
let i = 1, j = 1
du[i,j,1] = D₁*(1/dx^2*(2u[i+1,j,1] - 2u[i,j,1])+ 1/dy^2*(2u[i,j+1,1] - 2u[i,j,1])) +
-u[i,j,1]*u[i,j,2]^2 + f*(1-u[i,j,1])
du[i,j,2] = D₂*(1/dx^2*(2u[i+1,j,2] - 2u[i,j,2])+ 1/dy^2*(2u[i,j+1,2] - 2u[i,j,2])) +
u[i,j,1]*u[i,j,2]^2 - (f+k)*u[i,j,2]
end
let i = 1, j = N
du[i,j,1] = D₁*(1/dx^2*(2u[i+1,j,1] - 2u[i,j,1])+ 1/dy^2*(2u[i,j-1,1] - 2u[i,j,1])) +
-u[i,j,1]*u[i,j,2]^2 + f*(1-u[i,j,1])
du[i,j,2] = D₂*(1/dx^2*(2u[i+1,j,2] - 2u[i,j,2])+ 1/dy^2*(2u[i,j-1,2] - 2u[i,j,2])) +
u[i,j,1]*u[i,j,2]^2 - (f+k)*u[i,j,2]
end
let i = N, j = 1
du[i,j,1] = D₁*(1/dx^2*(2u[i-1,j,1] - 2u[i,j,1])+ 1/dy^2*(2u[i,j+1,1] - 2u[i,j,1])) +
-u[i,j,1]*u[i,j,2]^2 + f*(1-u[i,j,1])
du[i,j,2] = D₂*(1/dx^2*(2u[i-1,j,2] - 2u[i,j,2])+ 1/dy^2*(2u[i,j+1,2] - 2u[i,j,2])) +
u[i,j,1]*u[i,j,2]^2 - (f+k)*u[i,j,2]
end
let i = N, j = N
du[i,j,1] = D₁*(1/dx^2*(2u[i-1,j,1] - 2u[i,j,1])+ 1/dy^2*(2u[i,j-1,1] - 2u[i,j,1])) +
-u[i,j,1]*u[i,j,2]^2 + f*(1-u[i,j,1])
du[i,j,2] = D₂*(1/dx^2*(2u[i-1,j,2] - 2u[i,j,2])+ 1/dy^2*(2u[i,j-1,2] - 2u[i,j,2])) +
u[i,j,1]*u[i,j,2]^2 - (f+k)*u[i,j,2]
end
end
nothing
end