Lattice kinetic scheme for the Navier-Stokes equations coupled with convection-diffusion equations

2018 ◽  
Vol 98 (3) ◽  
Author(s):  
Liang Wang ◽  
Weifeng Zhao ◽  
Xiao-Dong Wang
Keyword(s):  
Stokes Equations ◽  
Kinetic Scheme ◽  
Diffusion Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Convection Diffusion

scholarly journals A Modified Gas-Kinetic Scheme for Turbulent Flow

2014 ◽  
Vol 16 (1) ◽  
pp. 239-263 ◽  
Author(s):  
Marcello Righi
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Numerical Scheme ◽  
Stokes Equations ◽  
Kinetic Scheme ◽  
Navier Stokes ◽  
Turbulent Stress ◽  
Navier Stokes Equations

AbstractThe implementation of a turbulent gas-kinetic scheme into a finite-volume RANS solver is put forward, with two turbulent quantities, kinetic energy and dissipation, supplied by an allied turbulence model. This paper shows a number of numerical simulations of flow cases including an interaction between a shock wave and a turbulent boundary layer, where the shock-turbulent boundary layer is captured in a much more convincing way than it normally is by conventional schemes based on the Navier-Stokes equations. In the gas-kinetic scheme, the modeling of turbulence is part of the numerical scheme, which adjusts as a function of the ratio of resolved to unresolved scales of motion. In so doing, the turbulent stress tensor is not constrained into a linear relation with the strain rate. Instead it is modeled on the basis of the analogy between particles and eddies, without any assumptions on the type of turbulence or flow class. Conventional schemes lack multiscale mechanisms: the ratio of unresolved to resolved scales – very much like a degree of rarefaction – is not taken into account even if it may grow to non-negligible values in flow regions such as shocklayers. It is precisely in these flow regions, that the turbulent gas-kinetic scheme seems to provide more accurate predictions than conventional schemes.

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.

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