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We make a brief historical review to the moment model reduction to the kinetic equations, particularly the Grads moment method for Boltzmann equation. The focus is on the hyperbolicity of the reduced model, which is essential to the existence of its classical solution as a Cauchy problem. The theory of the framework we developed in last years is then introduced, which may preserve the hyperbolic nature of the kinetic equations with high universality. Some lastest progress on the comparison between models with/without hyperbolicity is presented to validate the hyperbolic moment models for rarefied gases.
Entropy production during the process of thermal phase-separation of multiphase flows is investigated by means of a discrete Boltzmann kinetic model. The entropy production rate is found to increase during the spinodal decomposition stage and to decr
We expand on two previous developments in the modeling of discrete-time Langevin systems. One is the well-documented Gr{o}nbech-Jensen Farago (GJF) thermostat, which has been demonstrated to give robust and accurate configurational sampling of the ph
We show how the basic idea of parabolic Jacobi relaxation can be modified to obtain a new class of hyperbolic relaxation schemes that are suitable for the solution of elliptic equations. Some of the analytic and numerical properties of hyperbolic rel
We present modifications to the Athena++ framework to enable use of general equations of state (EOS). Part of our motivation for doing so is to model transient astrophysics phenomena, as these types of events are often not well approximated by an ide
We present an analytical derivation of the transport coefficients of a relativistic gas in (2+1) dimensions for both Chapman-Enskog (CE) asymptotics and Grads expansion methods. Moreover, we develop a systematic calibration method, connecting the rel