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For the numerical simulation of rarefied gas flows it is important to find a discrete kinetic model which reflects the proper physical laws and produces al least qualitatively correct solutions.
In the first part of my talk I will introduce a class of regular 2D and 3D lattices well-known in lattice theory which admit the construction of appropriate kinetic evolutions. Symmetry properties and corresponding conservation laws are discussed. In the second part I will establish a space discretized version of the kinetic lattice model ending up with a large ODE system. Existence, uniqueness and conservation laws are indicated. Convergence of the rescaled system to the Euler system is demonstrated. In the third part I will show numerical results concerning different fluid dynamic limits.
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