INTRODUCTION: problem of flow simulation in lid

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The lattice
Boltzmann Method is one of the computationally efficient methods that evolved
as a class of computational fluid dynamics (CFD) techniques used for solving
complex fluid systems and heat transfer problems. It has increasingly attracted
the interest of researchers in computational physics to solve challenging
problems of industrial and academic importance. Unlike solving the traditional
Navies-Stokes equations, LBM models the fluid as a collection of fictive
particles and solves the discrete Boltzmann equation over a discrete lattice
mesh. LBM has several remarkable advantages over other conventional CFD
techniques including but not limited to in dealing with complex boundary
conditions, and integrating microscopic interactions. Since LBM solves the
Boltzmann equation locally and explicitly, it can be effectively implemented on
parallel computers.

The flow in a
rectangular cavity involves many complex flow phenomena such as different types
and scales of vortices, bifurcation, transition and turbulence. Also, this
problem of flow simulation in lid driven cavity serves as benchmark problem
which is widely used to verify the effectiveness of new and improved numerical
solution methods, hence it is an excellent problem to apply the basics of
lattice Boltzmann method that were learnt and also gain clear insights in to
how the lattice Boltzmann method actually works.

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two-dimensional steady flow in a rectangular cavity can be driven by one or a
pair of translating lids. The cavity flow with a single moving lid has been
studied extensively.

about the vortex structure in a double-lid-driven rectangular cavity has been
conducted, but to a much lesser extent. Analysis of stokes flow in a square
cavity with the lids moving in opposite directions showed that the flow pattern
was symmetric about the centre of gravity, which is also evident from the streamline
plots generated for varying Reynolds number and aspect ratios.




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