Generalized modification in the lattice Bhatnagar-Gross-Krook model for incompressible Navier-Stokes equations and convection-diffusion equations

2014 ◽  
Vol 90 (1) ◽  
Author(s):  
Xuguang Yang ◽  
Baochang Shi ◽  
Zhenhua Chai
Keyword(s):  
Stokes Equations ◽  
Diffusion Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Convection Diffusion

The Effects of Obstacle and Vent Position on Particle Removal From an Enclosure

2006 ◽  
Author(s):  
M. Hendijanifard ◽  
M. H. Saidi ◽  
M. Taeibi-Rahni
Keyword(s):  
Removal Efficiency ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Particle Removal ◽  
Navier Stokes Equations ◽  
Convection Diffusion ◽  
Step Effect ◽  
Contaminant Particle ◽  
Order Of Magnitude

This paper reports the results of a study of the transient removal of contaminant particle from enclosures. These results are the basic instruments for finding a model for contaminant particle removal from an enclosure containing an obstacle. A numerical CFD code is developed and validated with different cases, then proper two- and three-dimensional cases are modeled and improvements are done. The improvements are done by proper positioning the inlet/outlet vents. The size and position of the obstacle affect the order of magnitude of the convection-diffusion terms in the Navier-Stokes equations, hence results in different phenomena while removing the particles. One of these phenomena, the step effect, is more detailed in reference [41]. The results of these two papers may be compacted into one whole theory, describing the particle removal efficiency from an enclosure as a function of obstacle position and size.

scholarly journals About general solutions of Euler’s and Navier-Stokes equations

2019 ◽  
pp. 190-193
Author(s):  
V. I. Rozumniuk
Keyword(s):  
General Solution ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Fundamental Problem ◽  
Diffusion Equations ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
General Solutions ◽  
And Diffusion

Constructing a general solution to the Navier-Stokes equation is a fundamental problem of current fluid mechanics and mathematics due to nonlinearity occurring when moving to Euler’s variables. A new transition procedure is proposed without appearing nonlinear terms in the equation, which makes it possible constructing a general solution to the Navier-Stokes equation as a combination of general solutions to Laplace’s and diffusion equations. Existence, uniqueness, and smoothness of the solutions to Euler's and Navier-Stokes equations are found out with investigating solutions to the Laplace and diffusion equations well-studied.

scholarly journals Simulating of the admixture spreading in a steady 2D lengthy stream of the viscous fluid

2013 ◽  
Vol 2 (1) ◽  
pp. 91-97
Keyword(s):  
Viscous Fluid ◽  
Small Parameter ◽  
Stokes Equations ◽  
Numerical Study ◽  
Computer Experiments ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Convection Diffusion ◽  
Proposed Model ◽  
And Diffusion

The problem of the passive contaminant spreading in a steady viscous fluid stream is discussed while the admixture's dissipation and diffusion are taken into account. The channel is assumed to be a horizontal plane, curvilinear and quite lengthy, so that the ratio of the stream width to its length can be regarded as a small parameter. A mathematical model of the process derived by the small parameter technique from the 2D steady Navier-Stokes equations for incompressible viscous fluid and non-steady convection-diffusion equation of a substance in the moving medium is introduced. A finite element method is applied for numerical study of the proposed model and results of computer experiments are presented.

scholarly journals On the time dependent mathematical model of ateroma plaque formation

1970 ◽  
Vol 1 ◽  
pp. 10-11
Author(s):  
Myriam Cilla ◽  
Estefanía Peña ◽  
Miguel Ángel Martínez
Keyword(s):  
Mathematical Model ◽  
Stokes Equations ◽  
Plaque Formation ◽  
Diffusion Reaction ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Convection Diffusion ◽  
Atheroma Plaque ◽  
Plaque Growth ◽  
Reaction Equations

A mathematical model to reproduce the atheroma plaque growth is presented. This model employs the Navier-Stokes equations and Darcy's law for fluid dynamics, convection-diffusion-reaction equations for modeling the mass balance in the lumen and intima, and the Kedem-Katchalsky equations for the interfacial coupling at membranes, i.e., endothelium.

A HYBRID FINITE-ANALYTIC ALGORITHM FOR SOLVING THREE-DIMENSIONAL ADVECTION-DIFFUSION EQUATIONS

2004 ◽  
Vol 01 (03) ◽  
pp. 407-430 ◽  
Author(s):  
H. M. HU ◽  
K.-H. WANG
Keyword(s):  
Convergence Rates ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Diffusion Equations ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
The Stability

The hybrid finite-analytic (HFA) method for discretization of a three-dimensional advection-diffusion equation is developed using the superposition of the HFA solutions of locally linearized one-dimensional advection-diffusion equations. An example calculation of a system of three-dimensional nonlinear equations is conducted to test the convergence and accuracy of the 7-point numerical scheme. Good agreements between calculated and analytical solutions are obtained. An algorithm based on the HFA method with multigrid technique and Gauss-Seidel iteration is also developed to solve the three-dimensional Navier-Stokes equations in a staggered grid system. The stability and efficiency of the method are demonstrated by performing calculations of the fluid flow in a three-dimensional cubic cavity with a moving top wall. The proposed procedure is observed to exhibit good rates of smoothing and almost grid-independent convergence rates in comparison with a single-grid iteration method. The results are in excellent agreement with other published computational results.

The Step Effect and Particle Removal From an Enclosure

2006 ◽  
Author(s):  
M. Hendijanifard ◽  
M. H. Saidi ◽  
M. Taeibi-Rahni
Keyword(s):  
Removal Efficiency ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Particle Removal ◽  
Navier Stokes Equations ◽  
Convection Diffusion ◽  
Step Effect ◽  
Contaminant Particle ◽  
Order Of Magnitude

This paper reports the results of a study of the transient removal of contaminant particle from enclosures containing an obstacle. We study specially a phenomena occur sometimes called the step effect. This phenomenon may occur if the size of the obstacle is small enough in comparison with the length or height of the enclosure. These results are the basic instruments for finding a model for contaminant particle removal from an enclosure containing an obstacle. A numerical CFD code is developed and validated with different cases, and then proper two- and three-dimensional cases are modeled. The size of the obstacle affect the order of magnitude of the convection-diffusion terms in the Navier-Stokes equations, hence results in different phenomena while removing the particles. It may end to a simple removal of the particles from the enclosure or it may contain two or three steps in removal, which is due to increase in scale of magnitude of the convection terms in the Navier-Stokes equations. The results of this paper and Ref. [3] may be compacted into one whole theory, describing the particle removal efficiency from an enclosure as a function of obstacle position and size.

scholarly journals Shallow water model for pollutant distribution in the Ypacarai Lake

2021 ◽  
Vol 26 (2) ◽  
pp. 54-76
Author(s):  
Diego Bareiro ◽  
Enrique O’Durnin ◽  
Laura Oporto ◽  
Christian Schaerer
Keyword(s):  
Shallow Water ◽  
Stokes Equations ◽  
Water Model ◽  
Navier Stokes ◽  
Shallow Water Model ◽  
Navier Stokes Equations ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Wind Velocities ◽  
The Impact

In this paper, we analyze the distribution of a non-reactive contaminant in Ypacarai Lake. We propose a shallow-water model that considers wind-induced currents, inflow and outflow conditions in the tributaries, and bottom effects due to the lakebed. The hydrodynamic is based on the depth-averaged Navier-Stokes equations considering wind stresses as force terms which are functions of the wind velocity. Bed (bottom) stress is based on Manning's equation, the lakebed characteristics, and wind velocities. The contaminant transportation is modeled by a 2D convection-diffusion equation taking into consideration water level. Comparisons between the simulation of the model, analytical solutions, and laboratory results confirm that the model captures the complex dynamic phenomenology of the lake. In the simulations, one can see the regions with the highest risk of accumulation of contaminants. It is observed the effect of each term and how it can be used them to mitigate the impact of the pollutants.    

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