The Transport Equation for the Dispersal of Passive Tracers in a Nonuniform Turbulent Fluid: Numerical Simulations

2021 ◽  
Vol 912 (2) ◽  
pp. 83
Author(s):  
Joe Giacalone
Keyword(s):  
Numerical Simulations ◽  
Transport Equation ◽  
Turbulent Fluid ◽  
Passive Tracers

scholarly journals Solutions to the 3D Transport Equation and 1D Diffusion Equation for Passive Tracers in the Atmospheric Boundary Layer and Their Applications

2019 ◽  
Vol 2019 (1) ◽  
pp. 21-47 ◽  
Author(s):  
Shuzhan Ren
Keyword(s):  
Boundary Layer ◽  
Diffusion Equation ◽  
Atmospheric Boundary Layer ◽  
Transport Equation ◽  
Analytical Solutions ◽  
Inverse Modeling ◽  
Surface Flux ◽  
Diurnal Variations ◽  
Surface Fluxes ◽  
Passive Tracers

Abstract A solution to the 3D transport equation for passive tracers in the atmospheric boundary layer (ABL), formulated in terms of Green’s function (GF), is derived to show the connection between the concentration and surface fluxes of passive tracers through GF. Analytical solutions to the 1D vertical diffusion equation are derived to reveal the nonlinear dependence of the concentration and flux on the diffusivity, time, and height, and are employed to examine the impact of the diffusivity on the diurnal variations of CO2 in the ABL. The properties of transport operator H and their implications in inverse modeling are discussed. It is found that H has a significant contribution to the rectifier effect in the diurnal variations of CO2. Since H is the integral of GF in time, the narrow distribution of GF in time justifies the reduction of the size of H in inverse modeling. The exponential decay of GF with height suggests that the estimated surface fluxes in inverse modeling are more sensitive to the observations in the lower ABL. The solutions and first mean value theorem are employed to discuss the uncertainties associated with the concentration–mean surface flux equation used to link the concentrations and mean surface flux. Both analytical and numerical results show that the equation can introduce big errors, particularly when surface flux is sign indefinite. Numerical results show that the conclusions about the evolution properties of passive tracers based on the analytical solutions also hold in the cases with a more complicated diffusion coefficient and time-varying ABL height.

Integral formulation and numerical simulations for the neutron transport equation in X - Y geometry

2018 ◽  
Vol 112 ◽  
pp. 735-747 ◽  
Author(s):  
F.S. de Azevedo ◽  
E. Sauter ◽  
P.H.A. Konzen ◽  
M. Thompson ◽  
L.B. Barichello
Keyword(s):  
Numerical Simulations ◽  
Transport Equation ◽  
Neutron Transport ◽  
Integral Formulation ◽  
Neutron Transport Equation

scholarly journals On the Generalized Mass Transport Equation to the Concept of Variable Fractional Derivative

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Abdon Atangana ◽  
Adem Kilicman
Keyword(s):  
Mass Transport ◽  
Fractional Derivative ◽  
Numerical Simulations ◽  
Transport Equation ◽  
Stability And Convergence ◽  
Hydrodynamic Dispersion ◽  
The Stability ◽  
Mass Transport Equation ◽  
Modified Equation ◽  
Convergence Of The Scheme

The hydrodynamic dispersion equation was generalized using the concept of variational order derivative. The modified equation was numerically solved via the Crank-Nicholson scheme. The stability and convergence of the scheme in this case were presented. The numerical simulations showed that, the modified equation is more reliable in predicting the movement of pollution in the deformable aquifers, than the constant fractional and integer derivatives.

scholarly journals Numerical Simulations of Optical Knots in YSO Outflows

1997 ◽  
Vol 182 ◽  
pp. 313-322
Author(s):  
F. Rubini ◽  
S. Lorusso ◽  
C. Giovanardi ◽  
F. Leeuwin
Keyword(s):  
Numerical Simulations ◽  
Transport Equation ◽  
Energy Transport ◽  
Optical Emission ◽  
Chemical Parameters ◽  
Physical And Chemical Parameters ◽  
3D Effects ◽  
Physical And Chemical ◽  
Oblique Shocks ◽  
Good Agreement

The aim of this work is to show that, though 3D effects should be invoked to explain the less regular arc-like regions, the internal knotty emissions may be explained through a roughly axisymmetric pattern of oblique shocks.To this purpose, numerical simulations of non-equilibrium, radiative, hydrodynamical jets in axisymmetric geometry have been performed. After showing that the internal reflecting waves, travelling in the beam of a stellar jet, steepen into oblique shocks, we verify that the optical emission arising from the shocked regions is in good agreement with observations.Since the optical emission strongly depends on the physical and chemical parameters, (namely temperature and electron densities inside the emitting regions), special care is devoted to solving the energy transport equation.

A new approach to modelling near-wall turbulence energy and stress dissipation

2002 ◽  
Vol 459 ◽  
pp. 139-166 ◽  
Author(s):  
S. JAKIRLIĆ ◽  
K. HANJALIĆ
Keyword(s):  
Energy Dissipation ◽  
Numerical Simulations ◽  
Transport Equation ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Direct Numerical Simulations ◽  
Turbulence Energy ◽  
Viscous Term ◽  
Dissipation Equation ◽  
Near Wall

A new model for the transport equation for the turbulence energy dissipation rate ε and for the anisotropy of the dissipation rate tensor εij, consistent with the near-wall limits, is derived following the term-by-term approach and using results of direct numerical simulations (DNS) for several generic wall-bounded flows. Based on the two-point velocity covariance analysis of Jovanović, Ye & Durst (1995) and reinterpretation of the viscous term, the transport equation is derived in terms of the ‘homogeneous’ part εh of the energy dissipation rate. The algebraic expression for the components of εij was then reformulated in terms of εh, which makes it possible to satisfy the exact wall limits without using any wall-configuration parameters. Each term in the new equation is modelled separately using DNS information. The rational vorticity transport theory of Bernard (1990) was used to close the mean curvature term appearing in the dissipation equation. A priori evaluation of εij, as well as solving the new dissipation equation as a whole using DNS data for quantities other than εij, for flows in a pipe, plane channel, constant-pressure boundary layer, behind a backward-facing step and in an axially rotating pipe, all show good near-wall behaviour of all terms. Computations of the same flows with the full model in conjunction with the low-Reynolds number transport equation for (uiui) All Overbar, using εh instead of ε, agree well with the direct numerical simulations.

Effects of Wave Streaming and Wave Variations on Nearshore Wave-Driven Circulation

2020 ◽  
Vol 50 (10) ◽  
pp. 3025-3041
Author(s):  
Peng Wang ◽  
James C. McWilliams ◽  
Yusuke Uchiyama ◽  
Mickaël D. Chekroun ◽  
Daling Li Yi
Keyword(s):  
Numerical Simulations ◽  
Gravity Waves ◽  
Wave Breaking ◽  
Surf Zone ◽  
Material Transport ◽  
Inner Shelf ◽  
Surface Gravity Waves ◽  
Wave Heights ◽  
Passive Tracers ◽  
Mean Current

AbstractWave streaming is a near-bottom mean current induced by the bottom drag on surface gravity waves. Wave variations include the variations in wave heights, periods, and directions. Here we use numerical simulations to study the effects of wave streaming and wave variations on the circulation that is driven by incident surface waves. Wave streaming induces an inner-shelf Lagrangian overturning circulation, which links the inner shelf with the surf zone. Wave variations cause alongshore-variable wave breaking that produces surf eddies; however, such eddies can be suppressed by wave streaming. Moreover, with passive tracers we show that wave streaming and wave variations together enhance the cross-shelf material transport.

Numerical Simulation of Unsteady Wake/Blade Interactions in Low-Pressure Turbine Flows Using an Intermittency Transport Equation

2004 ◽  
Vol 127 (3) ◽  
pp. 431-444 ◽  
Author(s):  
Y. B. Suzen ◽  
P. G. Huang
Keyword(s):  
Numerical Simulations ◽  
Transport Equation ◽  
Transport Model ◽  
Separated Flow ◽  
Low Pressure ◽  
Equation Model ◽  
Suction Surface ◽  
Intermittent Behavior ◽  
Unsteady Wake ◽  
Intermittency Factor

An extensive computational investigation of the effects of unsteady wake/blade interactions on transition and separation in low-pressure turbines has been performed by numerical simulations of two recent sets of experiments using an intermittency transport equation. The experiments considered have been performed by Kaszeta and Simon and Stieger in order to investigate the effects of periodically passing wakes on laminar-to-turbulent transition and separation in low-pressure turbines. The test sections were designed to simulate unsteady wakes in turbine engines for studying their effects on boundary layers and separated flow regions over the suction surface. The numerical simulations of the unsteady wake/blade interaction experiments have been performed using an intermittency transport model. The intermittent behavior of the transitional flows is taken into account and incorporated into computations by modifying the eddy viscosity, with the intermittency factor. Turbulent quantities are predicted by using Menter’s two-equation turbulence model (SST). The intermittency factor is obtained from the transport equation model, which can produce both the experimentally observed streamwise variation of intermittency and a realistic profile in the cross-stream direction. Computational results are compared to the experiments. Overall, general trends are captured and prediction capabilities of the intermittency transport model for simulations of unsteady wake/blade interaction flowfields are demonstrated.

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