Rigorous hydrodynamics from linear Boltzmann equations and viscosity-capillarity balance.

Exact closure for hydrodynamic variables is rigorously derived from the linear Boltzmann kinetic equation. Our approach, based on spectral theory, structural properties of eigenvectors, and the theory of slow manifolds, allows us to define a unique, optimal reduction in phase space close to equilibrium. The hydrodynamically constrained system induces a modification of entropy that ensures pure dissipation on the hydrodynamic manifold, which is interpreted as a nonlocal variant of Korteweg's theory of viscosity-capillarity balance.

Probing double-distribution-function models in discrete-velocity Boltzmann methods for highly compressible flows: Particles-on-demand realization.

The double distribution function approach is an efficient route toward an extension of kinetic solvers to compressible flows. With a number of realizations available, an overview and comparative study in the context of high-speed compressible flows is presented. We discuss the different variants of the energy partition, analyses of hydrodynamic limits, and a numerical study of accuracy and performance with the particles on demand realization.

Exact hydrodynamic manifolds for the linear Boltzmann BGK equation I: spectral theory.

We perform a complete spectral analysis of the linear three-dimensional Boltzmann BGK operator resulting in an explicit transcendental equation for the eigenvalues. Using the theory of finite-rank perturbations, we confirm the existence of a critical wave number which limits the number of hydrodynamic modes in the frequency space. This implies that there are only finitely many isolated eigenvalues above the essential spectrum at each wave number, thus showing the existence of a finite-dimensional, well-separated linear hydrodynamic manifold as a combination of invariant eigenspaces.

Asymptotic freedom in the lattice Boltzmann theory.

Asymptotic freedom is a feature of quantum chromodynamics that guarantees its well posedness. We derive an analog of asymptotic freedom enabling unconditional linear stability of lattice Boltzmann simulation of hydrodynamics. We further demonstrate the validity of the derived conditions via the special case of the equilibrium based on entropy maximization, which is shown to be uniquely renormalizable.

Particles on demand method: Theoretical analysis, simplification techniques, and model extensions.

The particles on demand method [Phys. Rev. Lett.