arXiv subjects

I. V. Karlin

Publications and source records attributed to I. V. Karlin.

At least 19 recordsLinked to original sources

arXiv2026

Vectorial lattice Boltzmann solver for compressible inviscid flows with generic equation of state

We develop a vectorial lattice Boltzmann model with a space-time adaptive relaxation coefficient, combined with adaptive time-stepping for compressible Euler dynamics with generic equation of state. The model, due to special form of the relaxation coefficient devised here is shown to converge to the Euler limit with second-order accuracy in the absence of shocks under acoustic scaling. The solver is robust and able to properly capture compressible gas dynamics for both ideal and non-ideal equations of state, including the Bethe--Zel'dovich--Thompson regime. This is verified and demonstrated through a variety of configurations of increasing complexity.

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arXiv2026

Local kinetic sensors for adaptive mesh and algorithm refinement

This paper presents novel refinement sensors for the application to adaptive mesh and algorithm refinement (AMAR) with kinetic models, such as discrete velocity and lattice Boltzmann methods. While refinement criteria for AMAR based on macroscopic variables can be replicated in a purely local, and therefore more scalable, way, the main advantage that can be leveraged when working with discrete velocity and lattice Boltzmann methods is the accessibility of information from the one-particle distribution function. With this accessibility, a novel palette of refinement sensors is introduced, allowing for a set of neatly tailored refinement criteria applicable to resolve characteristic flows features in many relevant domains of fluid mechanics, for instance, those emerging in compressible, turbulent, and non-equilibrium flows or non-ideal fluids. After detailed validation, novel refinement sensors are showcased for the application of adaptive mesh refinement (AMR) to a discrete velocity Boltzmann solver for compressible, viscous, and non-equilibrium flows, demonstrating promising results. The proposed sensors establish an accurate, efficient and scalable approach to kinetic simulations with AMAR, offering a valuable tool for studying complex problems in fluid dynamics and paving the way for future extensions to more specific flow problems.

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arXiv2026

Lattice Boltzmann model for non-ideal compressible fluid dynamics

We present a new kinetic model and its lattice Boltzmann realization for the simulation of compressible, non-ideal fluid flows. The method employs first-neighbour lattices and introduces a consistent set of correction terms constructed via quasi-equilibrium attractors, ensuring positive-definite and Galilean-invariant Navier-Stokes dissipation rates. This construction circumvents the need for extended stencils or ad hoc regularization, while maintaining numerical stability and thermodynamic consistency across a broad range of flow regimes. The resulting model accurately reproduces both the Euler- and Navier-Stokes hydrodynamic limits. As a stringent validation, we demonstrate, for the first time within a lattice Boltzmann framework, quantitatively accurate simulations of shock-drop interactions at Mach numbers up to 1.47. The proposed approach thus extends the applicability of lattice Boltzmann methods to high-speed, non-ideal compressible flows with a minimal kinetic stencil.

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arXiv2026

Consistent kinetic modeling of compressible flows with variable Prandtl numbers: Double-distribution quasi-equilibrium approach

A consistent kinetic modeling and discretization strategy for compressible flows across all Prandtl numbers and specific heat ratios is developed using the quasi-equilibrium approach within two of the most widely used double-distribution frameworks. The methodology ensures accurate recovery of the Navier-Stokes-Fourier equations, including all macroscopic moments and dissipation rates, through detailed hydrodynamic limit analysis and careful construction of equilibrium and quasi-equilibrium attractors. Discretization is performed using high-order velocity lattices with a static reference frame in a discrete velocity Boltzmann context to isolate key modeling aspects such as the necessary requirements on expansion and quadrature orders. The proposed models demonstrate high accuracy, numerical stability and Galilean invariance across a wide range of Mach numbers and temperature ratios. Separate tests for strict conservation and measurements of all dissipation rates confirm these insights for all Prandtl numbers and specific heat ratios. Simulations of a thermal Couette flow and a sensitive two-dimensional shock-vortex interaction excellently reproduce viscous Navier-Stokes-Fourier-level physics. The proposed models establish an accurate, efficient and scalable framework for kinetic simulations of compressible flows with moderate supersonic speeds and discontinuities at arbitrary Prandtl numbers and specific heat ratios, offering a valuable tool for studying complex problems in fluid dynamics and paving the way for future extensions to the lattice Boltzmann context, by application of correction terms, as well as high-Mach and hypersonic regimes, employing target-designed reference frames.

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arXiv2025

Kinetic framework with consistent hydrodynamics for shallow water equations

We present a novel discrete velocity kinetic framework to consistently recover the viscous shallow water equations. The proposed model has the following fundamental advantages and novelties: (a) A novel interpretation and general framework to introduce forces, (b) the possibility to consistently split pressure contributions between equilibrium and a force-like contribution, (c) consistent recovery of the viscous shallow water equations with no errors in the dissipation rates, (d) independent control over bulk viscosity, and (e) consistent second-order implementation of forces. As shown through a variety of different test cases, these features make for an accurate and stable solution method for the shallow-water equations.

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arXiv2025

A fully conservative discrete velocity Boltzmann solver with parallel adaptive mesh refinement for compressible flows

This paper presents a parallel and fully conservative adaptive mesh refinement (AMR) implementation of a finite-volume-based kinetic solver for compressible flows. Time-dependent H-type refinement is combined with a two-population quasi-equilibrium Bhatnagar-Gross-Krook discrete velocity Boltzmann model. A validation has shown that conservation laws are strictly preserved through the application of refluxing operations at coarse-fine interfaces. Moreover, the targeted macroscopic moments of Euler and Navier-Stokes-Fourier level flows were accurately recovered with correct and Galilean invariant dispersion rates for a temperature range over three orders of magnitude and dissipation rates of all eigen-modes up to Mach of order 1.8. Results for one- and two-dimensional benchmarks up to Mach numbers of 3.2 and temperature ratios of 7, such as the Sod and Lax shock tubes, the Shu-Osher and several Riemann problems, as well as viscous shock-vortex interactions, have demonstrated that the solver precisely captures reference solutions. Excellent performance in obtaining sensitive quantities was proven, for example in the test case involving nonlinear acoustics, whilst, for the same accuracy and fidelity of the solution, the AMR methodology significantly reduced computational cost and memory footprints. Over all demonstrated two-dimensional problems, up to a 4- to 9-fold reduction was achieved and an upper limit of the AMR overhead of 30% was found in a case with very cost-intensive parameter choice. The proposed solver marks an accurate, efficient and scalable framework for kinetic simulations of compressible flows with moderate supersonic speeds and discontinuities, offering a valuable tool for studying complex problems in fluid dynamics.

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arXiv2025

Linear stability of lattice Boltzmann models with non-ideal equation of state

Detailed study of spectral properties and of linear stability is presented for a class of lattice Boltzmann models with a non-ideal equation of state. Examples include the van der Waals and the shallow water models. Both analytical and numerical approaches demonstrate that linear stability requires boundedness of propagation speeds of normal eigen-modes. The study provides a basis for the construction of unconditionally stable lattice Boltzmann models.

math.NA↗

arXiv2024

Probing double distribution function models in the lattice Boltzmann method for highly compressible flows

The double distribution function approach is an efficient route towards 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. Out of three considered energy partition strategies, it is shown that the non-translational energy split requires a higher-order quadrature for proper recovery of the Navier--Stokes--Fourier equations. The internal energy split on the other hand, while recovering the correct hydrodynamic limit with fourth-order quadrature, comes with a non-local --both in space and time-- source term which contributes to higher computational cost and memory overhead. Based on our analysis, the total energy split demonstrates the optimal overall performance.

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arXiv2023

Entropic equilibrium for the lattice Boltzmann method: Hydrodynamics and numerical properties

The entropic lattice Boltzmann framework proposed the construction of the discrete equilibrium by taking into consideration minimization of a discrete entropy functional. The effect of this form of the discrete equilibrium on properties of the resulting solver has been the topic of discussions in the literature. Here we present a rigorous analysis of the hydrodynamics and numerics of the entropic. In doing so we demonstrate that the entropic equilibrium features unconditional linear stability, in contrast to the conventional polynomial equilibrium. We reveal the mechanisms through which unconditional linear stability is guaranteed, most notable of which the adaptive normal modes propagation velocity and the positive-definite nature of the dissipation rates of all eigen-modes. We further present a simple local correction to considerably reduce the deviations in the effective bulk viscosity.

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arXiv2023

Particles on Demand method: theoretical analysis, simplification techniques and model extensions

The Particles on Demand method [B. Dorschner, F. Bösch and I. V. Karlin, {\it Phys. Rev. Lett.} {\bf 121}, 130602 (2018)] was recently formulated with a conservative finite volume discretization and validated against challenging benchmarks. In this work, we rigorously analyze the properties of the reference frame transformation and its implications on the accuracy of the model. Based on these considerations, we propose strategies to boost the efficiency of the scheme and to reduce the computational cost. Additionally, we generalize the model such that it includes a tunable Prandlt number via quasi-equilibrium relaxation. Finally, we adapt concepts from the multi-scale semi-Lagrangian lattice Boltzmann formulation to the proposed framework, further improving the potential and the operating range of the kinetic model. Numerical simulations of high Mach compressible flows demonstrate excellent accuracy and stability of the model over a wide range of conditions.

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arXiv2023

Lattice Boltzmann for non-ideal fluids: Fundamentals and Practice

This contribution presents a comprehensive overview of of lattice Boltzmann models for non-ideal fluids, covering both theoretical concepts at both kinetic and macroscopic levels and more practical discussion of numerical nature. In that context, elements of kinetic theory of ideal gases are presented and discussed at length. Then a detailed discussion of the lattice Boltzmann method for ideal gases from discretization to Galilean invariance issues and different collision models along with their effect on stability and consistency at the hydrodynamic level is presented. Extension to non-ideal fluids is then introduced in the context of the kinetic theory of gases along with the corresponding thermodynamics at the macroscopic level, i.e. the van der Waals fluid, followed by an overview of different lattice Boltzmann based models for non-ideal fluids. After an in-depth discussion of different well-known issues and artifacts and corresponding solutions, the article finishes with a brief discussion on most recent applications of such models and extensions proposed in the literature towards non-isothermal and multi-component flows.

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arXiv2022

Entropic multi-relaxation-time lattice Boltzmann model for large density ratio two-phase flows

We propose a multiple relaxation time entropic realization of a two-phase flow lattice Boltzmann model we introduced in earlier works arXiv:2112.01975 S.A. Hosseini, B. Dorschner, and I. V. Karlin, arXiv preprint, arXiv:2112.01975 (2021). While the original model with a single relaxation time allows us to reach large density ratios, it is limited in terms of stability with respect to non-dimensional viscosity and Courant--Friedrichs--Lewy number. Here we show that the entropic multiple relaxation time model extends the stability limits of the model significantly, which allows us to reach larger Reynolds numbers for a given grid resolution. The thermodynamic properties of the solver, using the Peng--Robinson equation of state, are studied first using simple configurations. Co-existence densities and temperature scaling of both the interface thickness and the surface tension are shown to agree well with theory. The model is then used to simulate the impact of a drop onto a thin liquid film with density and viscosity ratios matching those of water and air both in 2-D and 3-D. The results are in very good agreement with theoretically predicted scaling laws and experimental data.

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arXiv2022

Detonation modeling with the Particles on Demand method

A kinetic model based on the Particles on Demand method is introduced for gas phase detonation hydrodynamics in conjunction with the Lee--Tarver reaction model. The proposed model is realized on two- and three-dimensional lattices and is validated with a set of benchmarks. Quantitative validation is performed with the Chapman--Jouguet theory up to a detonation wave speed of Mach 20 in one dimension. Two-dimensional outward expanding circular detonation is tested for isotropy of the model as well as for the asymptotic detonation wave speed. Mach reflection angles are verified in setups consisting of interacting strong bow shocks emanating from detonation. Spherical detonation is computed to show viability of the proposed model for three dimensional simulations.

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arXiv2022

Particles on Demand for flows with strong discontinuities

Particles on Demand formulation of kinetic theory [B. Dorschner, F. Bösch and I. V. Karlin, {\it Phys. Rev. Lett.} {\bf 121}, 130602 (2018)] is used to simulate a variety of compressible flows with strong discontinuities in density, pressure and velocity. Two modifications are applied to the original formulation of the Particles on Demand method. First, a regularization by Grad's projection of particles populations is combined with the reference frame transformations in order to enhance stability and accuracy. Second, a finite-volume scheme is implemented which allows tight control of mass, momentum and energy conservation. The proposed model is validated with an array of challenging one- and two-dimensional benchmarks of compressible flows, including hypersonic and near-vacuum situations, Richtmyer-Meshkov instability, double Mach reflection and astrophysical jet. Excellent performance of the modified Particles on Demand method is demonstrated beyond the limitations of other lattice Boltzmann-like approaches to compressible flows.

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arXiv2021

Towards a consistent lattice Boltzmann model for two-phase fluid

We propose a kinetic framework for single-component non-ideal isothermal flows. Starting from a kinetic model for a non-ideal fluid, we show that under conventional scaling the Navier-Stokes equations with a non-ideal equation of state are recovered in the hydrodynamic limit. A scaling based on the smallness of velocity increments is then introduced, which recovers the full Navier-Stokes-Korteweg equations. The proposed model is realized on a standard lattice and validated on a variety of benchmarks. Through a detailed study of thermodynamic properties including co-existence densities, surface tension, Tolman length and sound speed, we show thermodynamic consistency, well-posedness and convergence of the proposed model. Furthermore, hydrodynamic consistency is demonstrated by verification of Galilean invariance of the dissipation rate of shear and normal modes and the study of visco-capillary coupling effects. Finally, the model is validated on dynamic test cases in three dimensions with complex geometries and large density ratios such as drop impact on textured surfaces and mercury drops coalescence.

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arXiv2021

Consistent lattice Boltzmann model for reactive mixtures

A new lattice Boltzmann model (LBM) for chemically reactive mixtures is presented. The approach capitalizes on the recently introduced thermodynamically consistent LBM for multicomponent mixtures of ideal gases. Similar to the non-reactive case, the present LBM features Stefan--Maxwell diffusion of chemical species and a fully on-lattice mean-field realization of the momentum and energy of the flow. Besides introducing the reaction mechanism into the kinetic equations for the species, the proposed LBM also features a new realization of the compressible flow by using a concept of extended equilibrium on a standard lattice in three dimensions. The full thermodynamic consistency of the original non-reactive multicomponent LBM enables to extend the temperature dynamics to the reactive mixtures by merely including the enthalpy of formation in addition to the previously considered sensible energy. Furthermore, we describe in detail the boundary conditions to be used for reactive flows of practical interest. The model is validated against a direct numerical simulation of various burning regimes of a hydrogen/air mixture in a microchannel, in two and three dimensions. Excellent comparison in these demanding benchmarks indicates that the proposed LBM can be a valuable and universal model for complex reactive flows.

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arXiv2021

Multi-scale semi-Lagrangian lattice Boltzmann method

We present a multi-scale lattice Boltzmann scheme, which adaptively refines particles' velocity space. Different velocity sets, i.e., higher- and lower-order lattices, are consistently and efficiently coupled, allowing us to use the higher-order lattice only when and where needed. This includes regions of either high Mach number or high Knudsen number. The coupling procedure of different lattices consists of either projection of the moments of the higher-order lattice onto the lower-order lattice or lifting of the lower-order lattice to the higher-order velocity space. Both lifting and projection are local operations, which enable a flexible adaptive velocity set. The proposed scheme can be formulated both in a static and an optimal, co-moving reference frame, in the spirit of the recently introduced Particles on Demand method. The multi-scale scheme is first validated through a convected athermal vortex and also studied in a jet flow setup. The performance of the proposed scheme is further investigated through the shock structure problem and a high Knudsen Couette flow, typical examples of highly non-equilibrium flows in which the order of the velocity set plays a decisive role. The results demonstrate that the proposed multi-scale scheme can operate accurately, with flexibility in terms of the underlying models and with reduced computational requirements.

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arXiv2021

Extended Lattice Boltzmann Model for Gas Dynamics

We propose a two-population lattice Boltzmann model on standard lattices for the simulation of compressible flows. The model is fully on-lattice and uses the single relaxation time Bhatnagar-Gross-Krook kinetic equations along with appropriate correction terms to recover the Navier-Stokes-Fourier equations. The accuracy and performance of the model are analyzed through simulations of compressible benchmark cases including Sod shock tube, sound generation in shock-vortex interaction and compressible decaying turbulence in a box with eddy shocklets. It is demonstrated that the present model provides an accurate representation of compressible flows, even in the presence of turbulence and shock waves.

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