Date Awarded


Document Type


Degree Name

Doctor of Philosophy (Ph.D.)




With the advent of massively parallel processor machines, thermal lattice Boltzmann equation (TLBE) techniques offer an attractive way of handling turbulence simulations. TLBE is new form of DNS (direct numerical simulation method)--with the important advantages of being ideal for multi-parallel processors as well as being able to handle complicated geometries. Since there are many kinetic models that will reproduce the macroscopic nonlinear (compressible) transport equations, TLBE chooses that subset which can be readily solved on a discrete spatial lattice. The lattice geometry must be so chosen that the discrete phase representation of TLBE will not taint the rotational symmetric continuum equations. For 2D compressible flows, linear stability analyses described in this work indicates that the hexagonal lattice is optimum.;In nearly all lattice Boltzmann literature, the linearized Boltzmann collision operator has been taken to be the simple single-time Krook relaxation collision operator. This scalar collision operator is sufficient to recover the nonlinear transport equations under Chapmann-Enskog expansions. However, all previous LBE have suffered from the problem of density dependent transport coefficients. Even though this poses no problem for incompressible flows, it is critical and must be handled for compressible fluid simulations. The other deficiency of conventional TLBE scheme with single relaxation operator is that it only allows for fixed Prandtl number flow simulations.;In this work, to simulate flows with arbitrary Prandtl number, a matrix collision operator is introduced. With the inclusion of additional free parameter in the off-diagonal components, the scheme is now extended to a multi-relaxation process. This allows generalizations on relaxation parameters to produce density independent transport coefficients. Explicit solutions of TLBE are presented for 2D free decaying turbulence.



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