construct-roms 1.0

A Python package to build reduced-order models for Rayleigh-Benard convection

Construct ROMs

Construct ROMs is a Python package that builds distinguished reduced-order models (ROMs) that approximate the dynamics of 2D Rayleigh–Bénard convection. The model domain is a horizontally periodic domain with stress-free, isothermal walls at top and bottom. ROMs are built using Galerkin expansion with Fourier basis functions.

Model equations:

Features:

• ROMs can be printed to the consoles in LaTeX format or printed to a MATLAB or Python ODE file for further analysis
• Models can be selected from the HK hierarchy or the user can input them manually
• Include scale factors for easier SDP scaling
• Can check certain conservation properties (energy and vorticity balance)

Package Requirements

• numpy (Version 1.5 or later)
• sympy (Version 1.6 or later)

Installation

To install the package, download or clone this repository and use from constructROM import construct_roms from the directory containing the package.

Instructions

To construct a system of ROMs, use the command construct_roms(*args). Options can be passed as function arguments as detailed below.

Options:

• mode_sel : Method of mode selection. Current options:
  • "hk" : select model from hk hierarchy
  • "input" : input list of modes manually (as p_modes, t_modes arguments)
• p_modes : List of psi modes, represented as a list of tuples. Only necessary if mode_type="input"
• t_modes : List of theta modes, formatted as a list of tuples. Same format as p_modes
• hier_num : Number in the HK hierarchy (e.g. hier_num = 1 denotes the first model)
• print_to : Specify where to print output data. Options:
  • "console" : prints ODEs to console in LaTeX format
  • "matlab" : creates Matlab ODE file (.m)
  • "python" : creates Python ODE file (.py)
  • "none:" : don't print ROMs as output
• out_dir : Name of directory to print output
• scaling : Variable scaling used in model. Options:
  • "unit cube" : psi -> R^(1/2)*psi, t -> R^(-1/2)*t, useful for SDP computations
  • "standard" : standard scaling of Rayleigh-Benard
  • "normalize theta" : theta -> theta/R, used in some prior ROM studies
• scale_factors : If True, includes individual scale factors for each variable (True/False)
• check_conserv : If True, verifies that certain conservation laws are satisfied

Examples:

construct_roms(mode_sel="hk", hier_num=1, print_to="console" scale factors=False)
Generates the first model in the HK hierarchy (Lorenz model plus one shear mode) without scale factors and prints output to the console

construct_roms(mode_sel="hk", hier_num=2, print_to="matlab", out_dir="HK8_model")
Generates Matlab ODE file for the HK8 model with scale factors to folder "HK8_model"

construct_roms(model_sel="input", p_modes=[(1,1)], t_modes=[(0,2), (1,1)], print_to="none", check_conserv=True)
Checks energy and vorticity balance laws for the Lorenz equations