Unconditional stable free energy lattice-Boltzmann model

• Grant number: 24/23788-7
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate (Direct)
• Start date: August 01, 2025
• End date: July 31, 2026
• Field of knowledge: Engineering - Mechanical Engineering - Transport Phenomena
• Principal Investigator: Luben Cabezas Gómez
• Grantee: Vinicius Akyo Matsuda
• Supervisor: Carsten Alexander Wagner
• Host Institution: Escola de Engenharia de São Carlos (EESC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: North Dakota State University (NDSU), United States
• Associated to the scholarship: 22/12257-5 - Study of droplets impact onto heated walls using Lattice Boltzmann Method, BP.DD

Abstract

The multiphase free energy lattice-Boltzmann model works by modeling the underlying physics of non-ideal fluids by inserting the non-ideal part of the free energy via the pressure tensor. This unique approach grants the model the capability of capturing the dynamics of the multiphase flows, i.e., phase decomposition, interface tracking, and phase transition driven by pressure or temperature differences. However, as usual for numerical models, the free energy models suffer from numerical instabilities, requiring a high level of discretization. For simulations that seeks to mimic real experimental conditions, as for example, for the droplet impact cases, the simulations would need considerable fine meshes, which would heavily impact the practicality of the numerical simulation. For single-phase flows, it is known that such instabilities can be mitigated through the use of the well-known entropic distribution function, thus reducing the discretization requirements. With that in mind, within this project, we plan to develop an entropic model for the multiphase free energy lattice-Boltzmann which rigorously minimizes the free energy and ensures unconditional stability, allowing to perform simulations that better match real conditions, specially for what regards the droplet impact problem.