Joint probability density function modeling of velocity and scalar in turbulence with unstructured grids

J. Bakosi; P. Franzese; Z. Boybeyi

Home/Archive/arXiv

arXiv · 1006.0549

Joint probability density function modeling of velocity and scalar in turbulence with unstructured grids

J. Bakosi·P. Franzese·Z. Boybeyi

View original source ↗Read source document ↗Export metadata ↓

Abstract

In probability density function (PDF) methods a transport equation is solved numerically to compute the time and space dependent probability distribution of several flow variables in a turbulent flow. The joint PDF of the velocity components contains information on all one-point one-time statistics of the turbulent velocity field, including the mean, the Reynolds stresses and higher-order statistics. We developed a series of numerical algorithms to model the joint PDF of turbulent velocity, frequency and scalar compositions for high-Reynolds-number incompressible flows in complex geometries using unstructured grids. Advection, viscous diffusion and chemical reaction appear in closed form in the PDF formulation, thus require no closure hypotheses. The generalized Langevin model (GLM) is combined with an elliptic relaxation technique to represent the non-local effect of walls on the pressure redistribution and anisotropic dissipation of turbulent kinetic energy. The governing system of equations is solved fully in the Lagrangian framework employing a large number of particles representing a finite sample of all fluid particles. Eulerian statistics are extracted at gridpoints of the unstructured mesh. Compared to other particle-in-cell approaches for the PDF equations, this methodology is non-hybrid, thus the computed fields remain fully consistent without requiring any specific treatment. Two testcases demonstrate the applicability of the algorithm: a fully developed turbulent channel flow and the classical cavity flow both with scalars released from concentrated sources.

Explore related subjects

physics.flu-dyn physics.comp-ph

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

J. Bakosi, P. Franzese, Z. Boybeyi. 2010-06-03. Joint probability density function modeling of velocity and scalar in turbulence with unstructured grids. https://arxiv.org/abs/1006.0549

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Mathematical modeling on peristaltic flow of a Prandtl fluid with effects of slip conditions and inclined magnetic field

The manuscript provides a description of a theoretical analysis of a non-Newtonian Prandtl fluid subject to peristaltic flow through an inclined asymmetric channel. We explore the effect of an inclined magnetic field on the peristaltic flow. This is relevant for applications involving fluid flow in narrow, inclined (tilted) tubes similar to blood vessels or the digestive system. The model also includes thermodynamic aspects such as heat diffusion (the Soret effect) and viscous dissipation resulting from wall-fluid slip conditions, which may help optimize medical devices such as lab-on-a-chip systems and dialysis machines. In this study, the concentration of a generic chemical, temperature, and fluid velocity are taken into account through mass, heat, and momentum balances, respectively. The solution is approximated using numerical techniques suitable for long wavelengths (low frequency) and low Reynolds numbers. The study also discusses trapping phenomena, which are crucial from a clinical point of view. The developed insights can improve the understanding of physiological flows in the gastrointestinal tract and blood vessels. By understanding how the fluid moves and how particles are trapped, these insights may contribute to the design of improved medical pumps and artificial organs. Graphical visualizations are provided for the fluid velocity profile, temperature distribution, and concentration of a generic chemical. Furthermore, the numerical results are validated through comparison with a closed-form solution from a benchmark problem.

physics.flu-dyn↗

arXiv2026

Discovery of a dispersion model at high Peclet numbers

Peclet number characterises the transition from classical Taylor-Aris dispersion to convection-dominated longitudinal solute transport, with the classical model becoming inadequate at extremely high radial Peclet number $Pe_r$. We develop a novel explicit-closure one-dimensional (1-D) effective dispersion model for this high-$Pe_r$ regime by introducing two closure coefficients, $θ_u$ and $θ_d$, whose functional structures are identified using low-frequency transfer-function matching and a modified Kolmogorov-Arnold network (KAN). The resulting model captures the transition from classical Taylor-Aris dispersion at low $Pe_r$ to convection-dominated dispersion at high $Pe_r$. Analysis reveals that, in the high-$Pe_r$ regime, axial transport is redistributed between the effective convection flux and the dispersive flux, resulting in a reduced macroscopic convection velocity. Numerical validation demonstrates close agreement with the convection-diffusion model over the investigated high-$Pe_r$ conditions, while the classical Taylor-Aris model exhibits substantial deviations. Application of the proposed model to averaged flow velocity inversion further demonstrates improved velocity estimation, particularly in the high-$Pe_r$ regime. These results highlight the importance of accounting for non-classical dispersion for reliable contrast-agent-based arterial blood flow velocimetry and provide new insight into high-$Pe_r$ mass transport.

physics.flu-dyn↗

arXiv2026

Optimization of fluid mixing by reinforcement learning using limit cycles of a dynamical system

We propose a method to overcome the difficulties encountered when applying reinforcement learning to fluid mixing processes. The proposed method has two main features: (i) it does not require detailed measurements of the flow state, and (ii) by effectively exploiting a stable limit cycle of a two-dimensional dynamical system (the Li'enard system), it can stably perform optimization without imposing explicit constraints on the control parameters. As an illustrative example, we optimize a process in which a fluid contained in a cylindrical vessel is mixed by periodically rotating the vessel. The resulting optimal vessel motion is physically reasonable: it reverses its direction of rotation before a solid-body rotation state is established. Furthermore, even when the fluid viscosity increases with time during the mixing process, the method can continuously adapt the control parameters to the changing viscosity.

physics.flu-dyn↗