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The Classic Boltzmann Equation

The Boltzmann equation for a fluid with a body force tex2html_wrap_inline14977 is

equation4413

where tex2html_wrap_inline14979 is the number of molecules at time t with velocities in the range tex2html_wrap_inline12915 and position in the range tex2html_wrap_inline14985 . The difference between the Boltzmann equation when there is no body force present and when there is a body force is an extra term: tex2html_wrap_inline14987 . In the lattice Boltzmann equation we are looking to add a similar term to incorporate a body force. Since, however, the velocity of all the `particles' is constant in the lattice Boltzmann model we can not simply introduce a term with exactly the same form but must instead introduce a term which will modify the fluid momentum.



James Buick
Tue Mar 17 17:29:36 GMT 1998