# Velocity, density and energy budget statistics from the article: Validation and application of the lattice Boltzmann algorithm for a turbulent immiscible Rayleigh-Taylor system

## Citation

Saraiva Tavares, Hugo; Biferale, Luca; Sbragaglia, Mauro; Abaevich Mailybaev, Alexei (2021), Velocity, density and energy budget statistics from the article: Validation and application of the lattice Boltzmann algorithm for a turbulent immiscible Rayleigh-Taylor system, Dryad, Dataset, https://doi.org/10.5061/dryad.4mw6m908p

## Abstract

We develop a multicomponent lattice Boltzmann (LB) model for the 2D Rayleigh--Taylor turbulence with a Shan-Chen pseudopotential implemented on GPUs. Accuracy of the LB model is tested both for early and late stages of instability. For the developed turbulent motion we analyze the balance between different terms describing variations of the kinetic and potential energies. Then, we analyze the role of interface in the energy balance, and also the effects of the vorticity induced by the interface in the energy dissipation. Statistical properties are compared for miscible and immiscible flows.

In this Dataset, we have included the files for the statistics of the energy budget for the miscible and immiscible Rayleigh-Taylor flows studied in the referred article.

We also included the examples of the density and velocity fields showed in the Figures 1 and 2 of the article.

## Methods

The data includes information for the analysis of the energy budget for miscible and immiscible Rayleigh-Taylor flows described in the referred article. These files are in the format .mat. Each file is a matrix with 10 rows and 89 columns, corresponding to 10 simulations and 89.000 time steps respectively. The statistics were obtained from solutions given by the Shan-Chen multicomponent lattice Boltzmann method.

Examples of density and velocity fields for miscible and immiscible Rayleigh-Taylor flows in linear, non-linear and self-similar regimes are also included.

## Usage Notes

List of files (in the format .mat) for the energy budget analysis with the respective description in parentheses:

- Energy_flux_bulk_pressure_tensor_immiscible.mat (Evolution of the energy flux due to the bulk pressure tensor for 10 immiscible RT flows);

- Energy_flux_bulk_pressure_tensor_miscible.mat (Evolution of the energy flux due to the bulk pressure tensor for 10 miscible RT flows);

- Energy_flux_buoyancy_term_miscible.mat (Evolution of the energy flux due to the buoyancy term for 10 miscible RT flows);

- Energy_flux_buoyancy_term_miscible.mat (Evolution of the energy flux due to the buoyancy term for 10 immiscible RT flows);

- Energy_flux_Korteweg_stress_tensor_immiscible_flow.mat (Evolution of the energy flux due to the Korteweg stress for 10 immiscible RT flows);

- Energy_flux_Korteweg_stress_tensor_miscible_flow.mat (Evolution of the energy flux due to the Korteweg stress for 10 miscible RT flows);

- Energy_flux_spurious_term_immiscible.mat (Evolution of the spurious contribution for 10 immiscible RT flows);

- Energy_flux_spurious_term_miscible.mat (Evolution of the spurious contribution for the energy flux for 10 miscible RT flows);

- Energy_flux_total_stress_tensor_immiscible.mat (Evolution of the energy flux due to the total stress tensor for 10 immiscible RT flows);

- Energy_flux_viscous_term_immiscible.mat (Evolution of the energy flux due to the viscous term for 10 immiscible RT flows);

- Energy_flux_viscous_term_miscible.mat (Evolution of the energy flux due to the viscous term for 10 miscible RT flows);

- Enstrophy_evolution_immiscible_flow.mat (Evolution of the enstrophy for 10 immiscible RT flows);

- Enstrophy_evolution_miscible_flow.mat (Evolution of the enstrophy for 10 miscible RT flows);

- Kinetic_energy_evolution_immiscible_flows.mat (Evolution of the kinetic energy for 10 immiscible RT flows);

- Kinetic_energy_evolution_miscible_flows.mat (Evolution of the kinetic energy for 10 miscible RT flows);

- Potential_energy_evolution_immiscible_flows.mat (Evolution of the potential energy for 10 immiscible RT flows);

- Potential_energy_evolution_miscible_flows.mat (Evolution of the potential energy for 10 miscible RT flows);

- Total_lenght_of_the_interface.mat (Evolution of the total length of the interface for 10 immiscible RT flows);

- Variation_of_kinetic_energy_immiscible_flows.mat (Evolution of the kinetic energy for 10 immiscible RT flows);

- Variation_of_kinetic_energy_miscible_flows.mat (Evolution of the kinetic energy for 10 immiscible RT flows);

- Variation_of_the_energy_of_the_interface.mat (Evolution of the variation of the energy of the interface for 10 immiscible RT flows);

- Energy_flux_buoyancy+viscous+pressure_immiscible_flows.mat (Evolution of the sum of the contributions of the buoyancy, viscous and total pressure tensor terms for 10 immiscible RT flows);

- Energy_flux_buoyancy+viscous+pressure_miscible_flows.mat (Evolution of the sum of the contributions of the buoyancy, viscous and total pressure tensor terms for 10 miscible RT flows);

List of files (in the format .dat) for the density field of one component for an immiscible Rayleigh- Taylor flow, indicating the linear, non-linear and self-similar regimes:

- primadensita.17_immiscible.dat (density profile for an immiscible flow at the time t=17.000);

- primadensita.23_immiscible.dat (density profile for an immiscible flow at the time t=23.000);

- primadensita.83_immiscible.dat (density profile for an immiscible flow at the time t=83.000);

For the density field, the first two columns indicate the horizontal and vertical coordinates of the grid points and the third column is the respective value of the density.

List of files (in the format .dat) for the density field for one component for a miscible Rayleigh-Taylor flow, indicating the linear, non-linear and self-similar regimes:

- primadensita.9_miscible.dat (density profile for a miscible flow at the time t=9.000);

- primadensita.15_miscible.dat (density profile for a miscible flow at the time t=15.000);

- primadensita.83_miscible.dat (density profile for a miscible flow at the time t=83.000);

For the density field, the first two columns indicate the horizontal and vertical coordinates of the grid points and the third column is the respective value of the density.

List of files (in the format .dat) for the velocity fields for an immiscible Rayleigh- Taylor flow, indicating the linear, non-linear and self-similar regimes:

- veloconf.17_immiscible.dat (velocity field for an immiscible flow at the time t=17.000);

- veloconf.23_immiscible.dat (velocity field for an immiscible flow at the time t=23.000);

- veloconf.83_immiscible.dat (velocity field for an immiscible flow at the time t=83.000);

For the velocity fields, the first two columns indicate the horizontal and vertical coordinates of the grid points and the third and fourth columns are the horizontal and vertical coordinates of the velocity respective field.

List of files (in the format .dat) for the velocity fields for a miscible Rayleigh-Taylor flow, indicating the linear, non-linear and self-similar regimes:

- veloconf.9_miscible.dat (velocity field for an immiscible flow at the time t=9.000);

- veloconf.15_miscible.dat (velocity field for an immiscible flow at the time t=15.000);

- veloconf.83_miscible.dat (velocity field for an immiscible flow at the time t=83.000);

For the velocity fields, the first two columns indicate the horizontal and vertical coordinates of the grid points and the third and fourth columns are the horizontal and vertical coordinates of the velocity respective field.

## Funding

Conselho Nacional de Desenvolvimento Científico e Tecnológico, Award: 303047/2018-6, 406431/2018-3

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior