DNS of incompressible immiscible Rayleigh–Taylor instabilities

Coordinates (\(y\)) of the spike, bubble and saddle point and also interface area in 2D and 3D, single–mode and multi–mode, incompressible immiscible Rayleigh–Taylor instabilities with different Atwood numbers (\(At\)), Reynolds numbers (\(Re\)) and initial perturbation amplitudes (\(A\)). This dataset is based on direct numerical simulations conducted using a phase–field approach implemented within Xcompact3d (https://www.incompact3d.com/), a high–order finite-difference computational fluid dynamics framework.

#==============================================================================================
# Please cite the following paper when publishing using this dataset:  
# Title: Direct numerical simulations of incompressible Rayleigh–Taylor instabilities at low and medium Atwood numbers  
# Authors: Arash Hamzehloo, Paul Bartholomew and Sylvain Laizet
# Journal: Physics of Fluids 
# DOI: https://doi.org/10.1063/5.0049867
# ==============================================================================================

Please note:

• The 2D single-mode simulations are for a \([0,1]\times[0,4]\) domain with a \(129\times513\) grid size.
• The 3D single-mode simulations are for a \([0,1]\times[0,4]\times[0.1]\) domain with a \(129\times513\times129\) grid size.
• The 3D multi-mode simulations are for a \([0,\pi /2 ] \times [0,3\pi ]\times [0,\pi /2 ]\) domain on three grid sizes of \(301\times1801\times301\), \(401\times2401\times401\) and \(501\times 3001\times 501\).
• In all files, column #1 is the time interval. If it is multiplied by 0.25 then gives: \(t^{\ast}= {t\sqrt{At}}\). 
• For the single-mode simulations, the relative coordinate (\(y^{\ast}\)) provided in the reference paper is \(y^{\ast}=y-2\). 
• For the 2D single-mode simulations, the interface is initially located at: \(y_0=2+0.1 \cos(2\pi x)\).
• For the 3D single-mode simulations, the interface is initially located at; \(y_0=2+A \Bigg[\cos(2\pi x) + \cos(2\pi z) \Bigg]\).
• For the 3D multi-mode simulation, the interfaces is initially located at: \(y_0=3\pi/2\) and the vertical component of the velocity vector is initialised as: \(u_2=A \beta \Bigg[ 1 + \cos(2\pi x) \Bigg]\), where \(\beta\) is a random number from -1 to 1.
• For the 3D multi-mode simulation, the Kinetic Energy (KE) and Potential Energy (PE) are defined as \(\displaystyle KE=1/2\int_{\Omega}^{} (u_1^2+u_2^2+u_3^2) \,d \Omega\) and \(\displaystyle PE=\int_{\Omega}^{} \rho(x_1,x_2,x_3,t) x_2 \,d \Omega\), respectively. Here, \(\Omega\) denotes the computational domain volume. 

# ==============================================================================================

Details of the Xcompact3d framework and its numerical methodology can be found in the following papers:

1. Xcompact3D: An open-source framework for solving turbulence problems on a Cartesian mesh. (link)

2. A new highly scalable, high-order accurate framework for variable-density flows: Application to non-Boussinesq gravity currents. (link)

3. High-order compact schemes for incompressible flows: A simple and efficient method with quasi-spectral accuracy. (link)