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Modelling hydrodynamic lubrication is crucial in the design of engineering components as well as for a fundamental understanding of friction mechanisms. The cornerstone of thin-film flow modelling is the Reynolds equation -- a…

Fluid Dynamics · Physics 2022-03-08 Hannes Holey , Andrea Codrignani , Peter Gumbsch , Lars Pastewka

We consider the Navier-Stokes system solution, based at parametric representation of desired function. This solution is unique and it show the velocity of a stream element as its density structure [{\rho}_S (x,y,z,t);{\rho}^\to_L (x,y,z,t)]…

Mathematical Physics · Physics 2018-11-21 Alexandr Fridrikson , Marina Kasatochkina

The Reynolds-averaged Navier-Stokes (RANS) equations for steady-state assessment of incompressible turbulent flows remain the workhorse for practical computational fluid dynamics (CFD) applications. Consequently, improvements in speed or…

Fluid Dynamics · Physics 2020-12-04 Romit Maulik , Himanshu Sharma , Saumil Patel , Bethany Lusch , Elise Jennings

We introduce a residual-based stabilized formulation for incompressible Navier-Stokes flow that maintains discrete (and, for divergence-conforming methods, strong) mass conservation for inf-sup stable spaces with $H^1$-conforming pressure…

Numerical Analysis · Mathematics 2019-11-07 John A. Evans , David Kamensky , Yuri Bazilevs

Predictive simulation of many complex flows requires moving beyond Reynolds-averaged Navier-Stokes (RANS) based models to representations resolving at least some scales of turbulence in at least some regions of the flow. To resolve…

Fluid Dynamics · Physics 2018-12-11 Sigfried Haering , Todd A. Oliver , Robert D. Moser

A finite-volume method for the steady, compressible, reacting, turbulent Navier-Stokes equations is developed by using a steady-state preserving splitting scheme for the stiff source terms in chemical reaction. Laminar and turbulent…

Fluid Dynamics · Physics 2026-03-31 Yalu Zhu , Feng Liu , William A. Sirignano

Shallow flows are common in natural and human-made environments. Even for simple rectangular shallow reservoirs, recent laboratory experiments show that the developing flow fields are particularly complex, involving large-scale turbulent…

Fluid Dynamics · Physics 2023-07-13 Daniel Valero , Daniel B. Bung , Sebastien Erpicum , Yann Peltier , Benjamin Dewals

Turbulence is a non-local phenomenon and has multiple-scales. Non-locality can be addressed either implicitly or explicitly. Implicitly, by subsequent resolution of all spatio-temporal scales. However, if directly solved for the temporal or…

Fluid Dynamics · Physics 2025-01-28 Pavan Pranjivan Mehta

Reynolds-averaged Navier-Stokes (RANS) turbulence models (such as k-\epsilon models) are still widely used for engineering applications because of their relatively simplicity and robustness. In fully developed plane channel flow (i.e. the…

Fluid Dynamics · Physics 2010-12-01 Najla El Gharbi , Rafik Absi , Ahmed Benzaoui

Reynolds-Averaged Navier-Stokes (RANS) models are widely used for turbulent flow simulations due to their computational efficiency, but their accuracy strongly depends on the selected turbulence closure and may vary across the flow domain.…

Numerical Analysis · Mathematics 2026-03-18 Piero Zappi , Anna Ivagnes , Niccolò Tonicello , Gianluigi Rozza

This work presents algebraic closure models associated with advective transport and nonlinear reactions in a Reynolds-averaged Navier-Stokes context for a system of species subject to binary reactions and transport by advection and…

Fluid Dynamics · Physics 2021-11-29 Omkar B. Shende , Ali Mani

It has previously been shown that by increasing the Reynolds number across a channel by spatially varying the viscosity does not cause an immediate change in the size of turbulent structures and a delay is in fact observed in both wall…

Fluid Dynamics · Physics 2021-06-11 Victor Coppo Leite , Elia Merzari

In this study, new turbulence closure equations are derived in the light of turbulence as a continuous phase transition phenomenon. Closed-form Reynolds averaged Navier-Stokes equations due to those closure equations are solved numerically…

Fluid Dynamics · Physics 2026-04-22 Mohammed A. Azim

We consider a test problem for Navier-Stokes solvers based on the flow around a cylinder that exhibits chaotic behavior, to examine the behavior of various numerical methods. We choose a range of Reynolds numbers for which the flow is…

Numerical Analysis · Mathematics 2024-08-19 Henry von Wahl , L. Ridgway Scott

In this paper, a useful reinterpretation of the city as a porous medium justifies the application of well-known models on fluid dynamics to develop a multi-model study of urban air pollution due to traffic flow in a large city. Thus, to…

Numerical Analysis · Mathematics 2025-02-21 N. Garcia-Chan , L. J. Alvarez-Vazquez , A. Martinez , M. E. Vazquez-Mendez

Despite their well-known limitations, Reynolds-Averaged Navier-Stokes (RANS) models are still the workhorse tools for turbulent flow simulations in today's engineering application. For many practical flows, the turbulence models are by far…

Computational Physics · Physics 2018-09-11 H. Xiao , J. -L. Wu , J. -X. Wang , R. Sun , C. J. Roy

Turbulence modeling is a critical component in numerical simulations of industrial flows based on Reynolds-averaged Navier-Stokes (RANS) equations. However, after decades of efforts in the turbulence modeling community, universally…

Fluid Dynamics · Physics 2017-03-22 Jian-Xun Wang , Jin-Long Wu , Heng Xiao

We extend the unstructured LEvel set / froNT tracking (LENT) method for handling two-phase flows with strongly different densities (high-density ratios) by providing the theoretical basis for the numerical consistency between the mass and…

Fluid Dynamics · Physics 2024-03-18 Jun Liu , Tobias Tolle , Dieter Bothe , Tomislav Maric

The interaction between shear driven turbulence and stratification is a key process in a wide array of geophysical flows with spatio-temporal scales that span many orders of magnitude. A quick numerical model prediction based on external…

Fluid Dynamics · Physics 2021-08-18 M. A. Ahmed , H. J. Bae , A. F. Thompson , B. J. McKeon

This study has presented a comprehensive computational fluid dynamics (CFD) analysis of combustion flow in a realistic can combustor, evaluating the influence of various turbulence models on flow, thermal, and species fields. The…

Fluid Dynamics · Physics 2026-05-20 Aishvarya Kumar , Ram Prakash Bharti