arXiv subjects

Hudong Chen

Publications and source records attributed to Hudong Chen.

At least 19 recordsLinked to original sources

arXiv2025

Model of incompressible turbulent flows via a kinetic theory

Kinetic theory offers a promising alternative to conventional turbulence modelling by providing a mesoscopic perspective that naturally captures non-equilibrium physics such as non-Newtonian effects. In this work, we present an extension and theoretical analysis of the recent kinetic model for incompressible turbulent flows developed by Chen et al. (Atmos. 14(7), 1109, 2023), constructed for unbounded flows. The first extension is to reselect a relaxation time such that the turbulent transport coefficients are obtained more consistently and better align with well-established turbulence theory. The Chapman-Enskog (CE) analysis of the kinetic model reproduces the traditional linear eddy viscosity and gradient diffusion models for Reynolds stress and turbulent kinetic energy flux at the first order, and yields nonlinear eddy viscosity and closure models at the second order. Particularly, a previously unreported CE solution for turbulent kinetic energy flux is obtained. The second extension is to enable the model for wall-bounded turbulent flows with preserved near-wall asymptotic behaviours. This involves developing a low-Reynolds number kinetic model incorporating wall damping effects and viscous diffusion, with boundary conditions enabling both viscous sublayer resolution and wall function application. Comprehensive validation against experimental and DNS data for turbulent plane Couette flow demonstrates excellent agreement in predicting mean velocity profiles, skin friction coefficients, and Reynolds stress distributions. It reveals that an averaged turbulent flow behaves similarly to a rarefied gas flow at a finite Knudsen number, capturing non-Newtonian effects inaccessible to linear eddy viscosity models. This kinetic model provides a physics-based foundation for turbulence modelling with reduced empirical dependence.

physics.flu-dyn↗

arXiv2025

A simulation approach including under-resolved scales for multi-component fluid flows in multi-scale porous structures

In this study, we develop computational models and methodology for accurate multi-component-flow simulation in under-resolved multi-scale porous structures. It is generally impractical to fully resolve the flow in porous structures with large length-scale difference due to tremendously high computational expense. The flow contributions from under-resolved scales need to be accounted for with proper physics modeling as well as simulation processes. Using pre-computed physical properties such as the absolute permeability, K0, the capillary-pressure-saturation curve, and the relative permeability, Kr, in typically resolved porous structures, local fluid force is conjectured and applied to simulation in the under-resolved regions that are represented by porous media. By doing so, accurate simulation of flow in multi-scale porous structures becomes feasible. In order to check the accuracy and robustness of this method, a set of benchmark test cases are performed for both single-component and multi-component flows in artificially constructed multi-scale porous structures, and simulation results are compared with analytic solutions and/or results with much finer resolution resolving the porous structures. Quantitatively consistent results are obtained with proper input of K0, capillary pressure, and Kr in all tested cases. Specifically, imbibition patterns, entry pressure, residual component patterns, and the absolute and relative permeability are accurately captured with this approach.

physics.flu-dyn↗

arXiv2024

Volumetric Lattice Boltzmann Models in General Curvilinear Coordinates: Theoretical Formulation

A theoretical formulation of lattice Boltzmann models on a general curvilinear coordinate system is presented. It is based on a volumetric representation so that mass and momentum are exactly conserved as in the conventional lattice Boltzmann on a Cartesian lattice. In contrast to some previously existing approaches for arbitrary meshes involving interpolation approximations among multiple neighboring cells, the current formulation preserves the fundamental one-to-one advection feature of a standard lattice Boltzmann method on a uniform Cartesian lattice. The new approach is built on the concept that a particle is moving along a curved path. A discrete space-time inertial force is derived so that the momentum conservation is exactly ensured for the underlying Euclidean space. We theoretically show that the new scheme recovers the Navier-Stokes equation in general curvilinear coordinates in the hydrodynamic limit, along with the correct mass continuity equation.

physics.flu-dyn↗

arXiv2024

Average turbulence dynamics from a one-parameter kinetic theory

We show theoretically that the mean turbulent dynamics can be described by a kinetic theory representation with a single free relaxation time that depends on space and time. A proper kinetic equation is constructed from averaging the Klimontovich-type equation for fluid elements satisfying the Navier-Stokes hydrodynamics exactly. The turbulent kinetic energy plays the role of temperature in standard molecular thermodynamics. We show that the dynamics of turbulent fluctuations resembles a collision process that asymptotically drives the mean distribution towards a Gaussian (Maxwell-Boltzmann) equilibrium form. Non-Gaussianity arises directly from non-equilibrium shear effects. The present framework overcomes the bane of most conventional turbulence models and theoretical frameworks arising from the lack of scale separation between the mean and fluctuating scales of the Navier-Stokes equation with an eddy viscous term. An averaged turbulent flow in the present framework behaves more like a flow of finite Knudsen number with finite relaxation time, and is thus more suitably described in a kinetic theory representation.

physics.flu-dyn↗

arXiv2023

Lattice Boltzmann Model in General Curvilinear Coordinates Applied to Exactly Solvable 2D Flow Problems

Numerical simulation results of basic exactly solvable fluid flows using the previously proposed Lattice Boltzmann Method (LBM) formulated on a general curvilinear coordinate system are presented. As was noted in the theoretical work of H. Chen, such curvilinear Lattice Boltzmann Method preserves a fundamental one-to-one exact advection feature in producing minimal numerical diffusion, as the Cartesian lattice Boltzmann model. As we numerically show, the new model converges to exact solutions of basic fluid flows with the increase of grid resolution in the presence of both natural curvilinear geometry and/or grid non-uniform contraction, both for near equilibrium and non-equilibrium LBM parameter choices.

physics.flu-dyn↗

arXiv2020

Filtered Lattice Boltzmann Collision Formulation Enforcing Isotropy and Galilean Invariance

The central framework of a filtered lattice Boltzmann collision operator formulation is to remove hydrodynamic moments that are not supported by the order of isotropy of a given lattice velocity set. Due to the natural moment orthogonality of the Hermite polynomials, the form of a filtered collision operator is obtained directly via truncation of the Hermite expansion. In this paper, we present an extension of the filtered collision operator formulation to enforce Galilean invariance. This is accomplished by representing hydrodynamic moments in the relative reference frame with respect to local fluid velocity. The resulting collision operator has a compact and fully Galilean invariant form, and it can then be exactly expressed in terms of an infinite Hermite expansion. Giving a lattice velocity set of specific order of isotropy, a proper truncation of this expansion can be directly determined. Higher order terms are retained in the truncation if a higher order lattice velocity set is used, so that Galilean invariance is attained asymptotically. The previously known filtered collision operator forms can be seen as a limit of zero fluid velocity.

physics.flu-dyn↗

arXiv2019

Improved phase-field-based lattice Boltzmann models with a filtered collision operator

In this study, a phase-field lattice Boltzmann model based on the Allen-Cahn equation with a filtered collision operator and high-order corrections in the equilibrium distribution functions is presented. Here we show that in addition to producing numerical results consistent with prior numerical methods, analytic solutions, and experiments with the density ratio of 1000, previous numerical deficiencies are resolved. Specifically, the new model is characterized by robustness at low viscosity, accurate prediction of shear stress at interfaces, and removal of artificial dense bubbles and rarefied droplets, etc.

physics.flu-dyn↗

arXiv2017

Multi-component lattice Boltzmann models for accurate simulation of flows with wide viscosity variation

Multi-component lattice Boltzmann models operating in a wide range of fluid viscosity values are developed and examined. The algorithm is constructed with the goal to enable engineering applications without sacrificing simplicity and computational efficiency present in the original Shan-Chen model and D3Q19 lattice scheme. Boundary conditions for modeling friction and wettability effects are developed for discrete representation of surfaces within a volumetric approach, which results in accurate flow simulation in complex geometry. Numerical validation of our models includes comparison to previous studies and analytical solutions. The results are shown to be robust and accurate up to an extremely small kinematic viscosity value of $0.0017$ lattice units and the extremely high ratio of components' kinematic viscosities of hundreds and up to a thousand. This improvement is significant compared to previous studies with Shan-Chen model \cite{2013_Yang,2004_Kang,2010_Dong}, in which reasonable accuracy was kept only at the viscosity ratio up to 10 in the Poiseuille flow and the fingering simulation.

physics.flu-dyn↗

arXiv2016

Studies of accurate multi-component lattice Boltzmann models on benchmark cases required for engineering applications

We present recent developments in lattice Boltzmann modeling for multi-component flows, implemented on the platform of a general purpose, arbitrary geometry solver PowerFLOW. Presented benchmark cases demonstrate the method's accuracy and robustness necessary for handling real world engineering applications at practical resolution and computational cost. The key requirements for such approach are that the relevant physical properties and flow characteristics do not strongly depend on numerics. In particular, the strength of surface tension obtained using our new approach is independent of viscosity and resolution, while the spurious currents are significantly suppressed. Using a much improved surface wetting model, undesirable numerical artifacts including thin film and artificial droplet movement on inclined wall are significantly reduced.

physics.flu-dyn↗

arXiv2016

Simulation of residual oil displacement in a sinusoidal channel with the lattice Boltzmann method

We simulate oil slug displacement in a sinusoidal channel in order to validate computational models and algorithms for multi-component flow. This case fits in the gap between fully realistic cases characterized by complicated geometry and academic cases with simplistic geometry. Our computational model is based on the lattice Boltzmann method and allows for variation of physical parameters such as wettability and viscosity. The effect of variation of model parameters is analyzed, in particular via comparison with analytical solutions. We discuss the requirements for accurate solution of the oil slug displacement problem.

physics.flu-dyn↗

arXiv2014

Recovery of Galilean Invariance in Thermal Lattice Boltzmann Models for Arbitrary Prandtl Number

In this paper, we demonstrate a set of fundamental conditions required for the formulation of a thermohydrodynamic lattice Boltzmann model at an arbitrary Prandtl number. A specific collision operator form is then proposed that is in compliance with these conditions. It admits two independent relaxation times, one for viscosity and another for thermal conductivity. But more importantly, the resulting thermohydrodynamic equations based on such a collision operator form is theoretically shown to remove the well known non-Galilean invariant artifact at non-unity Prandtl numbers in previous thermal lattice Boltzmann models with multiple relaxation times.

physics.flu-dyn↗

arXiv2007

Fundamental Conditions for N-th Order Accurate Lattice Boltzmann Models

In this paper, we theoretically prove a set of fundamental conditions pertaining discrete velocity sets and corresponding weights. These conditions provide sufficient conditions for a priori formulation of lattice Boltzmann models that automatically admit correct hydrodynamic moments up to any given N-th order.

physics.comp-ph↗

arXiv2007

Discrete Rotational Symmetry, Moment Isotropy, and High Order Lattice Boltzmann Models

Conventional lattice Boltzmann models only satisfy moment isotropy up to fourth order. In order to accurately describe improtant physical effects beyond the isothermal Navier-Stokes fluid regime, higher order isotropy is required. In this paper, we present some basic results on moment isotropy and its relationship to the rotational symmetry of a generating discrete vector set. The anslysis provides a geometric understanding for popular lattice Boltzmann models, while offering a systematic procedure to construct higher order models.

physics.comp-ph↗

arXiv2006

Efficient kinetic method for fluid simulation beyond the Navier-Stokes equation

We present a further theoretical extension to the kinetic theory based formulation of the lattice Boltzmann method of Shan et al (2006). In addition to the higher order projection of the equilibrium distribution function and a sufficiently accurate Gauss-Hermite quadrature in the original formulation, a new regularization procedure is introduced in this paper. This procedure ensures a consistent order of accuracy control over the non-equilibrium contributions in the Galerkin sense. Using this formulation, we construct a specific lattice Boltzmann model that accurately incorporates up to the third order hydrodynamic moments. Numerical evidences demonstrate that the extended model overcomes some major defects existed in the conventionally known lattice Boltzmann models, so that fluid flows at finite Knudsen number (Kn) can be more quantitatively simulated. Results from force-driven Poiseuille flow simulations predict the Knudsen's minimum and the asymptotic behavior of flow flux at large Kn.

physics.comp-ph↗

arXiv2004

Generalized Boltzmann Equation: Slip-No -Slip Dynamic Transition in Flows of Strongly Non-Linear Fluids

The Navier-Stokes equations, are understood as the result of the low-order expansion in powers of dimensionless rate of strain $η_{ij}=τ_{0}S_{ij}$, where $τ_{0}$ is the microscopic relaxation time of a close-to- thermodynamic equilibrium fluid. In strongly sheared non-equilibrium fluids where $|η_{ij}|\geq 1$, the hydrodynamic description breaks down. According to Bogolubov's conjecture, strongly non-equlibrium systems are characterized by an hierarchy of relaxation times corresponding to various stages of the relaxation process. A "hydro-kinetic" equation with the relaxation time involving both molecular and hydrodynamic components proposed in this paper, reflects qualitative aspects of Bogolubov's hierarchy. It is shown that, applied to wall flows, this equation leads to qualitatively correct results in an extremely wide range of parameter $η$-variation. Among other features, it predicts the onset of slip velocity at the wall as an instability of the corresponding hydrodynamic approximation.

physics.flu-dyn↗

arXiv2002

A Lattice Boltzmann method for simulations of liquid-vapor thermal flows

We present a novel lattice Boltzmann method that has a capability of simulating thermodynamic multiphase flows. This approach is fully thermodynamically consistent at the macroscopic level. Using this new method, a liquid-vapor boiling process, including liquid-vapor formation and coalescence together with a full coupling of temperature, is simulated for the first time.

physics.flu-dyn↗

arXiv2002

Role of the H theorem in lattice Boltzmann hydrodynamic simulations

In the last decade, minimal kinetic models, and primarily the Lattice Boltmann equation, have met with significant success in the simulation of complex hydrodynamic phenomena, ranging from slow flows in grossly irregular geometries to fully developed turbulence, to flows with dynamic phase transitions. Besides their practical value as efficient computational tools for the dynamics complex systems, these minimal models may also represent a new conceptual paradigm in modern computational statistical mechanics: instead of proceeding bottom-up from the underlying microdynamic systems, these minimal kinetic models are built top-down starting from the macroscopic target equations. This procedure can provide dramatic advantages, provided the essential physics is not lost along the way. For dissipative systems, one such essential requirement is the compliance with the Second Law of thermodynamics. In this Colloquium, we present a chronological survey of the main ideas behind the Lattice Boltzmann method, with special focus on the role played by the $H$ theorem in enforcing compliance of the method with macroscopic evolutionary constraints (Second Law) as well as in serving as a numerically stable computational tool for fluid flows and other dissipative systems out of equilibrium.

cond-mat.stat-mech↗

arXiv2000

A lattice-Boltzmann model for interacting amphiphilic fluids

We develop our recently proposed lattice-Boltzmann method for the non-equilibrium dynamics of amphiphilic fluids (Chen, Boghosian, Coveney and Nekovee, Proc. Roy. Soc. London A, 456, 1431 (2000).) Our method maintains an orientational degree of freedom for the amphiphilic species and models fluid interactions at a microscopic level by introducing self-consistent mean-field forces between the particles into the lattice-Boltzmann dynamics, in a way that is consistent with kinetic theory. We present the results of extensive simulations in two dimensions which demonstrate the ability of our model to capture the correct phenomenology of binary and ternary amphiphilic fluids.

cond-mat.soft↗