Hello,

I am very confused incompressible and compressible lattice boltzmann method. Also I am confused one subject that is steady and unsteady lattice boltzmann.

Please explain me or suggest some book or articles.

Daralcan

Hi,

Your question is quite universal, and not directly related to lattice Boltzmann. In general, a flow can be compressible or incompressible, and steady or unsteady.

An incompressible flow is a flow in which the density is independent of space and time (liquids are often assumed to be incompressible, whereas gases are compressible). There’s no way to directly solve the equations of an incompressible flow with lattice Boltzmann, because this method is related to a statistical description of gases, which are compressible. Instead, to simulate incompressible flows, lattice Boltzmann is often used in a regime in which compressibility effects are negligible (a small Mach-number regime).

A steady flow is a flow in which the velocity field is time-independent. In simulations at low Reynolds number (i.e. at low velocity), it is often observed that the simulation reaches a steady regime after a certain number of iterations. This reflects the fact that there exists a natural equilibrium configuration for this flow, which you can view as a stable fixed point in a dynamical system. As said before, you can find this stationary regime by simply solving the time-dependent fluid-flow equations, starting from a more or less arbitrary initial condition, until “nothing changes any more”. There exist however more efficient numerical approaches which directly solve for the steady state. The basic lattice Boltzmann method solves the time-dependent flow equations, and can be comparatively inefficient for finding the steady state. A good example is the Poiseuille, or channel flow. If you take one of the codes on lbmethod.org to solve this problem, you will see that it converges extremely slowly to a steady state. Efficient steady state solvers based on lattice Boltzmann have been suggested in the literature, though, and you may find something useful through a Google search.

Hello,