THESIS FOR THE DEGREE OF LICENTIATE OF PHILOSOPHY Classification of Normal Discrete Kinetic Models

In many interesting papers on discrete velocity models (DVMs), authors postu-late from the beginning that the finite velocity space with ”good ” properties is given and only after this step, study the Discrete Boltzmann Equation. Contrary to this approach, our aim is not to study the equation, but to discuss all possible choices of finite phase spaces (sets) satisfying this type of ”good ” restrictions. Due to the velocity discretization it is well-known that it is possible to have DVMs with ”spuri-ous ” summational invariants (conservation laws which are not linear combinations of physical invariants). Our purpose is to give a method for constructing normal mod-els (without spurious invariants) and to classify all normal plane models with small number of velocities (which usually appear in applications). discrete model (ADM) which is defined by the matrix of reactions (the same as for the concrete model). This matrix contains as rows all vectors of reactions, which can be written as n-dimensional vectors (k1,., kn) with ki ∈ Z, describing the ”jump ” from a pre-reaction state to a new reaction state. The conservation laws corresponding to the many-particle system are uniquely determined by the ADM, or equivalently, by its matrix of reactions, and do not depend on the concrete realization. We find the restrictions on ADM and then we give a general method of constructing concrete normal models (using the results on ADMs). Having the general algorithm, we consider in more detail, the particular cases of models with mass and momentum conservation (inelastic lattice gases with pair collisions) and models with mass, momentum and energy conservation (elastic lattice gases with pair collisions)