Hi Experts ,I’m just start studing Julia. But I’m in truble.

Berrow 2D turblence simulation code is that I translated from Matlab. But It is not working well, very slow and use a lot of memory so I couldn’t run 3D version.

I would like to borrow your help.

using FFTW

using Printf

using LinearAlgebra

using Plots

using MAT

# set parameters

N = 128 ; # N*N grid,

dt = 0.02 ; # timestep

simutimeSeconds = 10 ;

HowOftenSave = 10 ; # save velocity field per ‘HowOftenSave’ timesteps

HowOftenVisu = 10 ; # show illustration per ‘HowOftenVisu’ timesteps

simutimeSteps = round(simutimeSeconds/dt);

nu = 1/1000 ; # kinematic viscosity [nu] = m^2/s

L = 2*pi ; # domain side length

dx = L/N ; # grid spacing assumed dx=dy

Umax = 1 ;

F_0 = 0.03 ; ;

# create fields

x = (L-dx)*(0:(N-1))/(N-1) ; # to be precise, dx is subtracted here
y = (L-dx)*(0:(N-1))/(N-1) ; # otherwise the derivative of e.g. sin(x) wouldnt be differentiable on this periodic grid

X=zeros(N,N);

Y=zeros(N,N);

for jx=1:N

for ix=1:N

X[ix,jx]=x[jx]

Y[ix,jx]=y[ix]

end

end

# wavenumbers

kx1 = mod.(1/2 .+ (0:(N-1))/N, 1) .- 1/2;

ky1 = mod.(1/2 .+ (0:(N-1))/N, 1) .- 1/2;

kx = kx1*(2*pi/dx); # wavenumbers
ky = ky1*(2*pi/dx); # wavenumbers

KX=zeros(N,N);

KY=zeros(N,N);

for jkx=1:N

for ikx=1:N

KX[ikx,jkx]=kx[jkx]

KY[ikx,jkx]=ky[ikx]

end

end

# Anti-aliasing filter based on the 2/3*kNyq rule

AA = (abs.(KX) .< (2/3) * maximum(kx)) .* (abs.(KY) .< (2/3) * maximum(ky))

# Runge-Kutta 4 coefficients

a=[1/6 1/3 1/3 1/6]; b=[1/2 1/2 1 1];

#-- Taylor-Green --#

kmax = 4;

U = -Umax .* cos.(kmax .* X) .* sin.(kmax .* Y)

V = Umax .* sin.(kmax .* X) .* cos.(kmax .* Y)

U = U + randn(N,N)*F_0;

V = V + randn(N,N)*F_0;

Uhat = fft(U)

Vhat = fft(V)

Uhat = Uhat - (KX .* Uhat + KY .* Vhat) .* KX ./ (KX .^ 2 + KY .^ 2)

Uhat[isnan.(Uhat)] .= 0

Vhat = Vhat - (KX .* Uhat + KY .* Vhat) .* KY ./ (KX .^ 2 + KY .^ 2)

Vhat[isnan.(Vhat)] .= 0

matwrite(“uv0000.mat”, Dict(“U” => U, “V” => V));

# Navier-Stokes simulation begins

@elapsed begin

for t=1:simutimeSteps

@printf(“| Time step # %0.4d |\n”,t)

```
#SolveNavierStokes2D;
Uold = Uhat;
Vold = Vhat;
Uc = Uhat;
Vc = Vhat;
for rk in 1:4
U = real.(ifft(AA .* Uc))
V = real.(ifft(AA .* Vc))
dUdx = real.(ifft(1im * KX .* AA .* Uc));
dUdy = real.(ifft(1im * KY .* AA .* Uc));
dVdx = real.(ifft(1im *KX .* AA .* Vc));
dVdy = real.(ifft(1im * KY .* AA .* Vc));
dUconv = fft(dt*(-U .* dUdx -V .* dUdy));
dVconv = fft(dt*(-U .* dVdx -V .* dVdy));
dUdiff = nu * dt * (-KX .* KX .* Uc - KY .* KY .* Uc);
dVdiff = nu * dt * (-KX .* KX .* Vc - KY .* KY .* Vc);
dU = dUconv + dUdiff;
dV = dVconv + dVdiff;
Uhat = Uhat-(KX.*Uhat + KY.*Vhat).*KX./(KX.^2 + KY.^2); Uhat[isnan.(Uhat)] .= 0;
Vhat = Vhat-(KX.*Uhat + KY.*Vhat).*KY./(KX.^2 + KY.^2); Vhat[isnan.(Vhat)] .= 0;
if rk < 4
Uhat = Uold + b[rk] * dU
Vhat = Vold + b[rk] * dV
end
Uc = Uc + a[rk] * dU
Vc = Vc + a[rk] * dV
end
Uhat = Uc
Vhat = Vc
Uhat = Uhat - (KX .* Uhat + KY .* Vhat) .* KX ./ (KX .^ 2 + KY .^ 2)
Uhat[isnan.(Uhat)] .= 0
Vhat = Vhat - (KX .* Uhat + KY .* Vhat) .* KY ./ (KX .^ 2 + KY .^ 2)
Vhat[isnan.(Vhat)] .= 0
U = real(ifft(Uhat));
V = real(ifft(Vhat));
# SaveInstantField2D
if mod(t, HowOftenSave) == 0
filename = "uv$(@sprintf("%04d", t)).mat"
matwrite(filename, Dict("U" => U, "V" => V))
end
```

end

end