Different approach for the relation between the kinetic and the macroscopic equations

1987 ◽  
pp. 308-323
Author(s):  
Claude Bardos
Keyword(s):  
Macroscopic Equations

scholarly journals Micropolar medium in a funnel-shaped crusher

2021 ◽  
Author(s):  
Mariia Fomicheva ◽  
Elena N. Vilchevskaya ◽  
Nikolay Bessonov ◽  
Wolfgang H. Müller
Keyword(s):  
Structural Changes ◽  
Coupled System ◽  
Viscosity Coefficient ◽  
Coupled Flow ◽  
Production Term ◽  
Characteristic Particle ◽  
Implicit Finite Difference ◽  
Micropolar Medium ◽  
Velocity Pressure ◽  
Macroscopic Equations

AbstractIn this paper, the solution to a coupled flow problem for a micropolar medium undergoing structural changes is presented. The structural changes occur because of a grinding of the medium in a funnel-shaped crusher. The standard macroscopic equations for mass and linear momentum are solved in combination with a balance equation for the microinertia tensor containing a production term. The constitutive equations of the medium describe a linear viscous material with a viscosity coefficient depending on the characteristic particle moment of inertia, the so-called microinertia. A coupled system of equations is presented and solved numerically in order to determine the distribution of the fields for velocity, pressure, viscosity coefficient, and microinertia in all points of the continuum. The numerical solution to this problem is found by using the implicit finite difference method and the upwind scheme.

Macroscopic equations for rarefied gas dynamics

2000 ◽  
Vol 271 (1-2) ◽  
pp. 87-91 ◽  
Author(s):  
Xinzhong Chen ◽  
Hongling Rao ◽  
Edward A. Spiegel
Keyword(s):  
Gas Dynamics ◽  
Rarefied Gas ◽  
Rarefied Gas Dynamics ◽  
Macroscopic Equations

Numerical Simulation of Laminar Confined Impinging Jet in a Composite Channel

2008 ◽  
Author(s):  
Marcelo J. S. de Lemos
Keyword(s):  
Porous Layer ◽  
Control Volume ◽  
Numerical Technique ◽  
Simple Algorithm ◽  
Local Distribution ◽  
Governing Equations ◽  
Stagnation Region ◽  
Volume Method ◽  
Material Porosity ◽  
Macroscopic Equations

This work shows numerical results for a jet impinging onto a flat plane covered with a layer of a porous material. Porosity of the porous layer is varied in order to analyze its effect on the local distribution of Nu. Macroscopic equations for mass and momentum ae obtained based on the volume-average concept. The numerical technique employed for discretizing the governing equations was the control volume method with a boundary-fitted non-orthogonal coordinate system. The SIMPLE algorithm was used to handle the pressure-velocity coupling. Results indicate that inclusion of a porous layer decreases the peak in Nu avoiding excessive heating or cooling near the stagnation region.

ON THE ASYMPTOTIC THEORY FROM MICROSCOPIC TO MACROSCOPIC GROWING TISSUE MODELS: AN OVERVIEW WITH PERSPECTIVES

2012 ◽  
Vol 22 (01) ◽  
pp. 1130001 ◽  
Author(s):  
N. BELLOMO ◽  
A. BELLOUQUID ◽  
J. NIETO ◽  
J. SOLER
Keyword(s):  
Kinetic Theory ◽  
Asymptotic Analysis ◽  
Critical Analysis ◽  
Asymptotic Theory ◽  
Blow Up ◽  
Cellular Interactions ◽  
Biological Functions ◽  
Active Particles ◽  
Tissue Models ◽  
Macroscopic Equations

This paper proposes a review and critical analysis of the asymptotic limit methods focused on the derivation of macroscopic equations for a class of equations modeling complex multicellular systems by methods of the kinetic theory for active particles. Cellular interactions generate both modification of biological functions and proliferative/destructive events. The asymptotic analysis deals with suitable parabolic, hyperbolic, and mixed limits. The review includes the derivation of the classical Keller–Segel model and flux limited models that prevent non-physical blow up of solutions.

Sign in / Sign up

Export Citation Format

Share Document