A pinboard by
Zhen Chen

PhD candidate, National University of Singapore


An advanced numerical scheme for numerical simulation of fluid problems

My research area is Computational Fluid Dynamics (CFD), which is to use computer to simulate physical fluid problems. CFD is an emerging research area, and a promising replacement of experimental approach in fluid mechanics studies. Compared to the experimental study, CFD is more efficient, more flexible and much cheaper. Effective CFD simulation largely relies on the robust numerical scheme. The numerical scheme can be understood as a solver to the governing equations that mathematically interpret the physical problem.

Conventional Lattice Boltzmann Method (LBM) is a popular numerical scheme in CFD community due to its simplicity, explicitness and kinetic nature. However, the conventional LBM is constrained from wider application in engineering due to its high cost in virtual memories, inconvenient implementation of physical boundary condition, and poor numerical stability. These drawbacks limit the competitiveness of LBM, especially in practical problems at high Reynolds or Rayleigh numbers.

The proposed method, Simplified and Highly Stable Lattice Boltzmann Method, is able to alleviate or eliminate the above drawbacks of conventional LBM while maintaining its merits. Specifically, it saves more than 30% of virtual memories in two-dimensional simulation, and nearly 50% in three-dimensional scenarios. The physical boundary conditions can be directly implemented in the present method without tedious transformation required by the conventional LBM. Through classic and robust von Neumann stability analysis, the present method can be proven to be highly stable. In extreme conditions that the Reynolds number is approaching infinity, the present method can be proven stable at all wavenumbers. To the best of our knowledge, this is the first time to develop a scheme within LBM framework which can be theoretically proven to be stable at high Reynolds number scenarios.

Theoretical parts of the present method have been published or accepted by reputable international journals including Physics of Fluids, International Journal of Heat and Mass Transfer, Communications in Computational Physics, Advances in Applied Mathematics and Mechanics and Applied Sciences. Anonymous reviewers commented our work as “an interesting contribution” and “a great improvement of current lattice Boltzmann method”.

My recent publications can be found on: https://scholar.google.com.sg/citations?user=EeaInD0AAAAJ&hl=en