Defining Initial Conditions

Defining Initial Conditions#

To specify a custom initial condition case, set the following parameters in para.py according to your requirements or preferences. The INPUT_SET_CASE = True flag is required for any case where input is defined through the code rather than provided by the user via a field file.

Predefined Field Configurations#

Use a built-in initialization method by setting the input case in para.py:

INPUT_SET_CASE = True
input_case = 'taylor-green'

User-Defined Fields#

Define custom initial conditions by specifying 'custom' as the input case:

INPUT_SET_CASE = True
input_case = 'custom'

The initial condition can be specified in three different ways: through Fourier modes, a real-space field, or directly from a field dataset.

Fourier Modes#

For each solver, initial conditions can be provided through Fourier modes. For example, with the Hydrodynamic solver, modes and their respective amplitudes can be defined in the init_modes/init_hydro.py file.

Modes can be assigned as follows:

# Assigning amplitudes to specific Fourier modes
Vkx[1,0] = 0+0j  # Mode (1,0) has zero amplitude in the x-direction
Vkz[1,0] = 1+0j  # Mode (1,0) has amplitude 1 in the z-direction

Vkx[0,1] = 1+0j
Vkz[0,1] = 0+0j

Vkx[1,1] = 0-1j
Vkz[1,1] = 0+1j

Vkx[-1,0] = 0+0j
Vkz[-1,0] = 1+0j

Here:

  • Vkx and Vkz correspond to components of the velocity field.

  • The indices specify the Fourier modes to which the amplitude is assigned.

  • The same approach can be applied to the magnetic field in the Magnetohydrodynamics solver and the scalar field in the Scalar solver.

  • The last index always denotes the mode activated in the Z-direction, which is always positive.

Real-Space Initialization#

Alternatively, initial conditions can be provided in real space and then transformed into Fourier modes for compatibility with the spectral solver.

A real-space field can be defined as follows:

X, Z = ncp.meshgrid(ncp.arange(Nx), ncp.arange(Nz))

Vx = ncp.cos(X) * ncp.sin(Z)
Vz = ncp.sin(X) * ncp.cos(Z)

Vkx = forward_transform(Vx, Vkx)
Vkz = forward_transform(Vz, Vkz)

  • ncp refers to either NumPy or CuPy, depending on the computation device (CPU or GPU).

  • The forward_transform function applies a Fourier transform to convert real-space data into spectral space.

HDF5 Dataset Input#

Initial conditions can also be provided via .h5 datasets by specifying the path in para.py:

INPUT_SET_CASE = False

INPUT_FROM_FILE = True
INPUT_REAL_FIELD = False  # Set to True if the field is in real space

input_file_name = 'init_cond.h5'
input_dir = 'path/to/directory/'

This method allows reusing a previously generated field as input for a new simulation run by simply providing the path and file name.

  • The datasets for each field can be named in the paraIO.py file.

  • Fourier fields have dimensions [Nx, Ny, Nz//2+1] for 3D and [Nx, Nz//2+1] for 2D.

  • Real fields have dimensions [Nx, Ny, Nz] for 3D and [Nx, Nz] for 2D.

  • When INPUT_REAL_FIELD = False, the .h5 dataset should contain Fourier-space data.

  • If INPUT_REAL_FIELD = True, the dataset should store real-space field values, which will be transformed internally.

Each method provides flexible initialization options for different solvers, depending on computational requirements and problem setup.

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