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TestAdvectionCG2D.jl
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TestAdvectionCG2D.jl
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using LinearAlgebra
using CairoMakie
include("GaussLobattoQuad.jl")
include("Lagrange.jl")
include("DLagrange.jl")
include("Jacobi2D.jl")
include("Initial2D.jl")
include("AdvectionCG2D.jl")
include("Visualization.jl")
include("DSS.jl")
include("Flux.jl")
function TestAdvectionCG2D()
n = 4
Nx = 30
Ny = 30
Lx = 10
Ly = 10
Pert = 0.0
wF,xF = GaussLobattoQuad(n)
xe = zeros(n+1)
xe[1] = -1
for i = 2 : n
xe[i] = xe[i-1] + 2 / n
end
xe[n+1] = 1
xec = zeros(n)
xec[1] = -1+1/n
for i = 2 : n-1
xec[i] = xec[i-1] + 2 / n
end
xec[n] = 1-1/n
DF = zeros(n+1,n+1)
for i = 1 : n + 1
for j = 1 : n + 1
DF[i,j] = DLagrange(xF[i],xF,j)
end
end
DW = -inv(diagm(wF)) * DF' * diagm(wF)
IntF2EC = zeros(n,n+1)
for j = 1 : n + 1
for i = 1 : n
IntF2EC[i,j] = Lagrange(xec[i],xF,j)
end
end
@show IntF2EC
Q = diagm(wF) * DF
S = Q - Q'
P = zeros(Nx+1,Ny+1,2)
dx = Lx / Nx
dy = Ly / Ny
@views @. P[1,:,1] = 0
@views @. P[:,1,2] = 0
for ix = 1 : Nx
@views @. P[ix+1,:,1] = P[ix,:,1] + dx
end
for iy = 1 : Ny
@views @. P[:,iy+1,2] = P[:,iy,2] + dy
end
for ix = 2 : Nx
for iy = 2 : Ny
P[ix,iy,1] = P[ix,iy,1] + Pert * (2.0 * rand() - 1.0) * dx
P[ix,iy,2] = P[ix,iy,2] + Pert * (2.0 * rand() - 1.0) * dy
end
end
X = zeros(n+1,n+1,2,Nx,Ny)
dXdxI = zeros(n+1,n+1,2,2,Nx,Ny)
J = zeros(n+1,n+1,Nx,Ny)
for ix = 1 : Nx
for iy = 1 : Ny
X[:,:,:,ix,iy],dXdxI[:,:,:,:,ix,iy],J[:,:,ix,iy] = Jacobi2D(P[ix,iy,:],P[ix+1,iy,:],
P[ix+1,iy+1,:],P[ix,iy+1,:],xF,DF)
end
end
cF0 = zeros(n+1,n+1,Nx,Ny)
uF = ones(n+1,n+1,Nx,Ny)
vF = zeros(n+1,n+1,Nx,Ny)
for ix = 1 : Nx
for iy = 1 : Ny
for j = 1 : n + 1
for i = 1 : n +1
cF0[i,j,ix,iy] = Initial2D(X[i,j,1,ix,iy],X[i,j,2,ix,iy])
end
end
end
end
Plot2DC(cF0,IntF2EC,"Scalar")
nIter = 2000
dtau = 0.005
cFn = zeros(n+1,n+1,Nx,Ny)
cFCG = zeros(n+1,n+1,Nx,Ny)
fF = zeros(n+1,n+1,Nx,Ny)
@. cFCG = cF0
for iTer = 1 : nIter
@. cFn = cFCG
AdvectionCG2D!(fF,cFCG,uF,vF,dXdxI,J,S,wF)
@. cFCG = cFn + 1/3 * dtau * fF
AdvectionCG2D!(fF,cFCG,uF,vF,dXdxI,J,S,wF)
@. cFCG = cFn + 1/2 * dtau * fF
AdvectionCG2D!(fF,cFCG,uF,vF,dXdxI,J,S,wF)
@. cFCG = cFn + dtau * fF
end
Plot2DC(cFCG,IntF2EC,"ScalarEnde")
stop
end