Boltzmann and Poincaré Entropy, Boltzmann Extremals, and Hamilton–Jacobi Method for Non-Hamiltonian Situation

Entropy monotonic spectral method for Boltzmann equation

We propose a spectral method that discretizes the Boltzmann collision operator and satisfies a discrete version of the H-theorem. The method is obtained by modifying the existing Fourier spectral method to match a classical form of the discrete velocity method. It preserves the positivity of the solution on the Fourier collocation points and as a result satisfies the H-theorem. The fast algorit...

Maximum Entropy Boundaries in Lattice Boltzmann Method

Vasili Baranau1 1. Department of Chemistry, Philipps-Universität Marburg, Hans-Meerwein-Strasse, 35032 Marburg, Germany Corresponding author: Vasili Baranau, [email protected] Abstract: We propose a universal approach in the framework of the lattice Boltzmann method (LBM) to modeling constant velocity constraints and constant temperature constraints on curved walls, which doesn’t depend ...

Natural Convection and Entropy Generation in Γ-Shaped Enclosure Using Lattice Boltzmann Method

This work presents a numerical analysis of entropy generation in Γ-Shaped enclosure that was submitted to the natural convection process using a simple thermal lattice Boltzmann method (TLBM) with the Boussinesq approximation.  A 2D thermal lattice Boltzmann method with 9 velocities, D2Q9, is used to solve the thermal flow problem. The simulations are performed at a constant Prandtl number (Pr ...

. the Boltzmann Entropy and Randomness

The Boltzmann Entropy and Randomness Tests

In the context of the dynamical systems of classical mechanics, we introduce two new notions called “algorithmic fine-grain and coarse-grain entropy”. The fine-grain algorithmic entropy is, on the one hand, a simple variant of the randomness tests of MartinLöf (and others) and is, on the other hand, a connecting link between description (Kolmogorov) complexity, Gibbs entropy and Boltzmann entro...