# Multiple Relaxation Times in the Lattice Boltzmann Method

#### Multiple Relaxation Times in the Lattice Boltzmann Method

- Event time: 11:30am
- Event date: 1st October 2014
- Speaker: Oliver Henrich (Formerly School of Physics & Astronomy, University of Edinburgh)
- Location: Room 2511, James Clerk Maxwell Building (JCMB) James Clerk Maxwell Building Peter Guthrie Tait Road Edinburgh EH9 3FD GB

### Event details

Since its introduction about two decades ago the lattice-Boltzmann
(LB) method has been developed into a viable numerical tool for
computational fluid dynamics and beyond. With its roots in kinetic
theory this special version of a cellular automaton concept allows to
obtain continuum flow quantities from simple and local update rules
based on particle interactions.

Instead of solving the Navier-Stokes equation directly (DNS), the discrete Boltzmann equation is solved by using simple models for the collision operator. The simplest such operator is the lattice Bhatnagar-Gross-Krook (BGK) model, where only one collisional relaxation time is related to the shear and bulk viscosity of the fluid. More complex models featuring multiple relaxation times (MRT) can rectify some of the shortcomings of the basic BGK-model.

In this seminar I will outline the basic principles of the LB method and the BGK-model, introduce the more general MRT-form of the collision operator and show how multiple relaxation times are directly related to physical observables and permit different shear and bulk viscosities.

Instead of solving the Navier-Stokes equation directly (DNS), the discrete Boltzmann equation is solved by using simple models for the collision operator. The simplest such operator is the lattice Bhatnagar-Gross-Krook (BGK) model, where only one collisional relaxation time is related to the shear and bulk viscosity of the fluid. More complex models featuring multiple relaxation times (MRT) can rectify some of the shortcomings of the basic BGK-model.

In this seminar I will outline the basic principles of the LB method and the BGK-model, introduce the more general MRT-form of the collision operator and show how multiple relaxation times are directly related to physical observables and permit different shear and bulk viscosities.

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