Export velocity field as vector such that one can use the Paraview streamtracer function

[DanielDoehring]

Currently, the velocity field is exported as three scalars. If you want to use Paraview to compute e.g. the streamlines a vector-valued velocity field is required.

Exporting the velocities (and maybe also the magnetic field) as a vector-field would be a nice feature/change.

[DanielDoehring]

The goal would be putting the funcitonality provided by this code

pd = PlotData2D(sol)

using Printf

mkpath("out")  # Create output directory automatically

Velocities_String = "out/Velocities.vtk"
Velocities = open(Velocities_String, "w")

write(Velocities, "# vtk DataFile Version 3.0\n")
write(Velocities, "vtk output\n")
write(Velocities, "ASCII\n")
write(Velocities, "DATASET STRUCTURED_GRID\n")

Nx = length(pd.x)
Ny = length(pd.y)
NumPoints = Int(Nx * Ny)
NumPointsString = string(Int(Nx * Ny))

write(Velocities, "DIMENSIONS ", string(Nx), " ", string(Ny), " 1\n")
write(Velocities, "POINTS ", NumPointsString, " float\n")
for i in 1:Nx
  for j in 1:Ny
    write(Velocities, "$(pd.x[i]) $(pd.y[j]) 0\n")
  end
end

write(Velocities, "\n")
write(Velocities, "POINT_DATA ", NumPointsString, "\n")

write(Velocities, "\n")
write(Velocities, "VECTORS U float\n")
v1 = pd.data[2]
v2 = pd.data[3]
for i in 1:Nx
  for j in 1:Ny
    # Need to transpose back (note interchanged `j, i`), see l. 528 of src/visualization/utilities.jl
    write(Velocities, string(v1[j,i]), " ", string(v2[j,i]), " 0\n")
  end
end

close(Velocities)

in Trixi.jl/Trixi2Vtk.jl.