17 citations · 19 across the 15 of their papers we have counts for
17 papers
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…
Practical Kinetic Models for Dense Fluids
Ilya Karlin, Seyed Ali Hosseini
Nonlinear idempotent operator instead of a linear projection is introduced to derive kinetic models for dense fluids. A new lattice Boltzmann model for compressible two-phase flow…
A Note on Non-Hydrodynamic Solutions of Kinetic Systems
Florian Kogelbauer, Ilya Karlin
We show that the one-dimensional three-component Grad system admits solutions that violate the Chapman--Enskog scaling in Knudsen number. In particular, there exist solutions that…
On the Relation of Exact Hydrodynamics to the Chapman-Enskog Series
Florian Kogelbauer, Ilya Karlin
We demonstrate that the Chapman-Enskog series is locally equivalent to the exact spectral closure defined on slow kinetic eigenmodes in the limit of vanishing Knudsen number. We fu…
Dynamically Optimal Projection onto Slow Spectral Manifolds for Linear Systems
Florian Kogelbauer, Ilya Karlin
We derive the dynamically optimal projection onto the linear slow manifold from a temporal variational principle. We demonstrate that the projection captures transient dynamics of…
Learning the Optimal Hydrodynamic Closure
Florian Kogelbauer, Candi Zheng, Ilya Karlin
We present the optimal hydrodynamic model for rarefied gas flows relative to a given kinetic model by combining the recent theory of slow spectral closure with machine learning tec…
Exact Non-Local Hydrodynamics Predict Rarefaction Effects
Florian Kogelbauer, Ilya Karlin
We combine the theory of slow spectral closure for linearized Boltzmann equations with Maxwell's kinetic boundary conditions to derive non-local hydrodynamics with arbitrary accomm…
Transition time of a bouncing drop
Yahua Liu, Seyed Ali Hosseini, Cong Liu +4
Contact time of bouncing drops is one of the most essential parameters to quantify the water-repellency of surfaces. Generally, the contact time on superhydrophobic surfaces is kno…
Rigorous Hydrodynamics from Linear Boltzmann Equations and Viscosity-Capillarity Balance
Florian Kogelbauer, Ilya Karlin
An exact closure for hydrodynamic variables is rigorously derived from the linear Boltzmann kinetic equation. Our approach, based on spectral theory, structural properties of eigen…
Exact Hydrodynamic Manifolds for the Linear Boltzmann BGK Equation I: Spectral Theory
Florian Kogelbauer, Ilya Karlin
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 theor…
Extended Lattice Boltzmann Model
M. H. Saadat, B. Dorschner, I. V. Karlin
Conventional lattice Boltzmann models for the simulation of fluid dynamics are restricted by an error in the stress tensor that is negligible only for vanishing flow velocity and a…