Istituto di Matematica Applicata e Tecnologie Informatiche     
Gabetta E., Vicario P. Kinetic models of hydrodynamics behaviour: numerical applications. Preprint ercim.cnr.ian//1998-1097, 1998.
Starting from the Ruijgrok-Wu model of the discrete kinetic theory of gases and one of its generalization, some results about fluidynamic and hydrodynamic limits are presented. The passage to conservation laws with and without viscosity is rigorously justified. Numerical computations based on kinetic and relaxation schemes are also presented.In particular the kinetic approach is used in order to discretize the asymptotic equilibrium system. Taking into account that for small values of the parameter $epsilon$, the relaxation terms in diffusive limit formulation become stiff, and the characteristic velocity tunes up, the standard numerical approach might fail to give physically correct solutions. The key idea to approximate the model in diffusive regime is to reformulate the original system as a linear hyperbolic system with constant characteristic velocities and with stiff relaxation terms only in the collisional part.
Subject Viscosity, conservation laws

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