Practice of two-phase flows with test cases of run_training_lbm

Overview of test cases

This section presents an overview of folder run_training_lbm to start practicing two-phase flows with LBM_Saclay. Those test cases are used in the LBM training session of SMEMaG doctoral school (https://adum.fr/script/formations.pl?mod=3622094&site=l). Most of them appear in publications to validate new LBM numerical schemes or new two-phase models. The folder run_training_lbm is available in three versions of LBM_Saclay: “V1.0”, “Training” and “Rech-Dev”.

Tutorials for running and post-processing test cases of run_training_lbm

Several examples of .ini files are contained in directory run_training_lbm. They run with the kernel NSAC_Comp which implements the Model of Navier-Stokes/Conservative Allen-Cahn (CAC)/Composition. Those input datafiles use several options or different values to help users for making their own test case. Tutorials for running and post-processing results of each physical problems can be found below:

• Run “Single phase test cases”

• Run “Two-phase without fluid flows”

• Run “Two-phase with fluid flows”

• Run “Two-phase with fluid flows with composition effect”

• Run “Two-phase fluid flows interacting with a solid phase”

It is supposed that you run the test cases on ORCUS (see First simulations on ORCUS: example with GPU partition). Once the job is complete, the output files must be downloaded and post-processed with paraview on your local computer.

Few examples of single-phase and two-phase flows are presented in Fig. 8. A detailed description of parameter values is presented in [1].

Fig. 8 Overview of two-phase simulations contained in folder run_training_lbm

List of test cases in run_training_lbm

Single phase test cases

The two-phase model can easily degenerate to single-phase flows. This is the reason why the first two test cases compare LBM_Saclay results with well-known solutions of “lid-driven cavity flows” and “Poiseuille flows”.

• Run “Single phase test cases”

Table 3 Single-phase test cases

Name of test case	Equations	Comparisons
TestCase01_LidDrivenCavityFlow	Navier-Stokes	Benchmark with literature
TestCase02_Poiseuille_Water	Navier-Stokes	Analytical solution

Two-phase test cases without fluid flow

• Run “Two-phase without fluid flows”

Table 4 List of test cases of Two-phase without fluid flows

Name of test case	Equations	Comparisons
TestCase03_Zalesak-Disk2D	Phase-field	Initial condition
TestCase04_Deformation-Vortex2D	Phase-field	Benchmark Cahn-Hilliard & Allen-Cahn
TestCase05_Spinodal-Decomposition2D	Phase-field	–
TestCase06_Stefan-Problem	Phase-field/Composition	Analytical solution

Two-phase test cases with fluid flow

• Run “Two-phase with fluid flows”

Table 7 List of test cases of Two-phase with fluid flows

Name of test case	Equations	Comparisons
TestCase07_Double-Poiseuille	Navier-Stokes/Phase-field	Analytical solution
TestCase08_Rayleigh-Taylor2D	Navier-Stokes/Phase-field	Benchmark with literature
TestCase09_Capillary-Wave2D	Navier-Stokes/Phase-field	Analytical solution
TestCase10_Falling-Droplet2D	Navier-Stokes/Phase-field	–
TestCase11_Rising-Bubble2D	Navier-Stokes/Phase-field	–
TestCase12_Taylor-Bubble2D	Navier-Stokes/Phase-field	–
TestCase13_Splashing-Droplet2D	Navier-Stokes/Phase-field	–
TestCase14_Dam-Break2D	Navier-Stokes/Phase-field	–

Two-phase with fluid flow & composition effect

• Run “Two-phase with fluid flows with composition effect”

Table 8 Test cases inside folder TestCase15_Surfactant

Name of test case	Equations	Comparisons
Analytical_Profile1	Navier-Stokes/Phase-field/Composition	Analytical solution
Analytical_Profile2	Navier-Stokes/Phase-field/Composition	Analytical solution
Coalescence	Navier-Stokes/Phase-field/Composition	–
Falling-Droplet	Navier-Stokes/Phase-field/Composition	–
Rising_Bubble	Navier-Stokes/Phase-field/Composition	–

Two-phase interacting with a solid phase

• Run “Two-phase fluid flows interacting with a solid phase”

Table 10 List of test cases of Two-phase interacting with a solid phase

Name of test case	Equations	Comparisons
TestCase16_Contact-Angle	Navier-Stokes/Phase-fields	–
TestCase17a_Hydrophobic-Solid	Navier-Stokes/Phase-fields	–
TestCase17b_Vertical-Wall	Navier-Stokes/Phase-fields	–
TestCase18_Container-Splash	Navier-Stokes/Phase-fields	–
TestCase19_Static-Container-Hole	Navier-Stokes/Phase-fields	–
TestCase20_Moving-Container-Hole	Navier-Stokes/Phase-fields	–

Types of files in run_training_lbm

…

The folder run_training_lbm contains several classical test cases of two-phase flows. They are all based on the Model of Navier-Stokes/Conservative Allen-Cahn (CAC)/Composition, but they differ by the use of different initial conditions, boundary conditions and values of parameters. The parameter values of those test cases are representative of various dimensionless numbers (Re, Bo, Mo, At, etc.) and for some of them, comparisons are performed with analytical solutions or well-known benchmarks.

Types of file inside the folder

Several types of files appear in the directory run_training_lbm. Besides the .ini input file of LBM_Saclay, several files are useful for 1) deriving the dimensionless input parameters, 2) post-processing the simulation outputs and 3) describing the test case.

The test case is described inside a “Readme” file with the suffix .txt. Sometimes a jupyter notebook (extension .ipynb) is present inside the directory. When the test case compares the numerical solution with one solution of reference (benchmark or analytical solution), one or several files with extensions .dat or .csv are used in a python script (extension .py) or in the jupyter file. Finally, when the post-processing with paraview requires many commands, a state file for paraview (suffix .pvsm) can be set in the directory. A summary of those files are presented in the Table below.

Table 11 Types of files

Extension	Description	Command
.ini	Input files for LBM_Saclay	LBM_saclay inputfilename.ini
.py	python scripts for Pre- & Post-Processing	python name.py
.ipynb	Jupyter notebook for validation sheets	jupyter notebook name.ipynb
.pvsm	State file for paraview	in paraview click “load state”
.txt	Readme text file	use your favorite editor
.csv or .dat	Ascii datafiles for comparisons	Used in .py & .ipynb scripts

Parameters in S.I. units

Most of input values in the .ini files correspond to dimensionless parameters of water-air or oil-air two-phase systems. Their parameters in SI units are presented in Tables Water – Air properties and Olive oil – Air properties below.

Water – Air properties

Table 12 Water – Air properties

Name	Symbol	Value	Dimension
Water density	\(\rho_{l}\)	\(998.29\)	kg/m \(^{3}\)
Kinematic viscosity	\(\nu_{l}\)	\(1.003\times10^{-6}\)	m \(^{2}\)/s
Air density	\(\rho_{a}\)	\(1.204\)	kg/m \(^{3}\)
Kinematic viscosity	\(\nu_{a}\)	\(1.56\times10^{-5}\)	m \(^{2}\)/s
Surface tension	\(\sigma\)	\(7.28\times10^{-2}\)	N/m
Gravity	\(g\)	\(9.81\)	m/s \(^{2}\)
Dynamic viscos water	\(\eta_{l}\)	\(10^{-3}\)	Pa.s
Dynamic viscos air	\(\eta_{a}\)	\(1.878\times10^{-5}\)	Pa.s
Density ratio	\(\rho_{l}/\rho_{a}\)	829.14	–
Dyn viscos ratio	\(\eta_{l}/\eta_{a}\)	53.33	–

Olive oil – Air properties

Table 13 Olive oil – Air properties

Name	Symbol	Value	Dimension
Oil density	\(\rho_{l}\)	\(911.4\)	kg/m \(^{3}\)
Kinematic viscosity	\(\nu_{l}\)	\(9.216\times10^{-5}\)	m \(^{2}\)/s
Air density	\(\rho_{a}\)	\(1.225\)	kg/m \(^{3}\)
Kinematic viscosity	\(\nu_{a}\)	\(1.618\times10^{-5}\)	m \(^{2}\)/s
Surface tension	\(\sigma\)	\(0.032\)	N/m
Gravity	\(g\)	\(9.81\)	m/s \(^{2}\)
Dynamic viscos oil	\(\eta_{l}\)	\(0.08399988\)	Pa.s
Dynamic viscos air	\(\eta_{a}\)	\(1.983\times10^{-5}\)	Pa.s
Density ratio	\(\rho_{l}/\rho_{a}\)	744	–
Dyn viscos ratio	\(\eta_{l}/\eta_{a}\)	4236	–

Bibliography

[1]

LBM_Saclay team. Lattice Boltzmann Methods – Part II: practice with LBM_Saclay. Single-phase and two-phase flows. Presentation CEA STMF/LDEL, 200 slides, 2025.

Section author: Alain Cartalade