𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On a superconvergent lattice Boltzmann boundary scheme

✍ Scribed by François Dubois; Pierre Lallemand; Mahdi Tekitek

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
356 KB
Volume
59
Category
Article
ISSN
0898-1221

No coin nor oath required. For personal study only.

✦ Synopsis

In a seminal paper [20], Ginzburg and Adler (1994) analyzed the bounce-back boundary conditions for the lattice Boltzmann scheme and showed that it could be made exact to second order for the Poiseuille flow if some expressions depending upon the parameters of the method were satisfied, thus defining so-called ''magic parameters''. Using the Taylor expansion method that one of us developed, we analyze a series of simple situations (1D and 2D) for diffusion and for linear fluid problems using bounce-back and ''anti bounceback'' numerical boundary conditions. The result is that ''magic parameters'' depend upon the detailed choice of the moments and of their equilibrium values. They may also depend upon the way the flow is driven.

📜 SIMILAR VOLUMES

A simple lattice Boltzmann scheme for co
A simple lattice Boltzmann scheme for combustion simulation
✍ Sheng Chen; Zhaohui Liu; Zhiwei Tian; Baochang Shi; Chuguang Zheng 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 683 KB

A simple lattice Boltzmann model is developed for two-dimensional combustion simulations. In this model the time step and the fluid particle speed can be adjusted dynamically, depending on the "particle characteristic temperature". The algorithm is still a simple process of hopping from one grid poi

Equivalent partial differential equation
Equivalent partial differential equations of a lattice Boltzmann scheme
✍ François Dubois 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 229 KB

We show that when we formulate the lattice Boltzmann equation with a small-time step t and an associated space scale x, a Taylor expansion joined with the so-called equivalent equation methodology leads to establishing macroscopic fluid equations as a formal limit. We recover the Euler equations of