17 citations · 19 across the 15 of their papers we have counts for
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Residual Carleman lift for nonlinear lattice Boltzmann simulations
Ilya Karlin
Low-order Carleman embeddings replace nonlinear dynamics by a larger linear system, but truncation errors can accumulate even when the underlying nonlinear model is accurately appr…
One vertex generates the hard-sphere Boltzmann collision hierarchy
I. Karlin
The Boltzmann equation is the fundamental kinetic bridge between molecular mechanics and fluid behaviour. It converts binary encounters into the evolution of a velocity distributio…
Exact Collision Vertex for Stress and Heat Flux
Ilya Karlin
For the hard-sphere Boltzmann equation, we derive an exact nonlinear generating vertex for collisional stress and heat-flux production. The complete two-input Hermite hierarchy for…
Bargmann-Fock Representation and Global Estimates for the Linearized Hard-Sphere Boltzmann Operator
Ilya Karlin
We study the linearized Boltzmann collision operator for three-dimensional hard spheres and reorganize the complete operator so that its angular and radial structures are explicit…
Fock-Space Formulation of the Boltzmann Collision Operator for Maxwell Molecules
Ilya Karlin
We develop a representation-independent symmetric-Fock formulation of the nonlinear Boltzmann collision operator for Maxwell molecules. Starting from the standard velocity-space op…
Fock-Space Representation of the Lebowitz--Frisch--Helfand Kinetic Model
Ilya Karlin
We develop an exact Fock-space representation of the Lebowitz--Frisch--Helfand kinetic equation. The familiar square-root Maxwellian transformation is used only as a convenient sta…
Monolithic kinetic algorithm for heterogeneous porous media systems using a continuous one-domain approach
Nikita O. Gusev, Ilya V. Karlin
We propose a lattice Boltzmann model (LBM) on standard lattices for simulating multi-dimensional, weakly compressible, isothermal flows within and around isotropic heterogeneous po…