Mesoscopic Boltzmann model equations for thermally perfect gases

2021 ◽  
Vol 33 (12) ◽  
pp. 127112
Author(s):  
J. Mathiaud ◽  
L. Mieussens
Keyword(s):  
Model Equations ◽  
Boltzmann Model

Model Equations for Quasi-Twodimensional Pattern Forming Systems

1994 ◽  
Vol 19 (6) ◽  
pp. 721-733 ◽  
Author(s):  
M. Neufeld ◽  
R. Friedrich
Keyword(s):  
Model Equations ◽  
Pattern Forming

Modelling Of Transport And Capture Of Particles In A Porous Medium

2019 ◽  
pp. 56-60
Keyword(s):  
Porous Medium ◽  
Asymptotic Solution ◽  
Retention Mechanism ◽  
Inverse Filtering ◽  
Underground Structures ◽  
Loose Soil ◽  
Monodisperse Suspension ◽  
Homogeneous Porous Medium ◽  
Model Equations ◽  
Pass Through

The study of the transport and capture of particles moving in a fluid flow in a porous medium is an important problem of underground hydromechanics, which occurs when strengthening loose soil and creating watertight partitions for building tunnels and underground structures. A one-dimensional mathematical model of long-term deep filtration of a monodisperse suspension in a homogeneous porous medium with a dimensional particle retention mechanism is considered. It is assumed that the particles freely pass through large pores and get stuck at the inlet of small pores whose diameter is smaller than the particle size. The model takes into account the change in the permeability of the porous medium and the permissible flow through the pores with increasing concentration of retained particles. A new spatial variable obtained by a special coordinate transformation in model equations is small at any time at each point of the porous medium. A global asymptotic solution of the model equations is constructed by the method of series expansion in a small parameter. The asymptotics found is everywhere close to a numerical solution. Global asymptotic solution can be used to solve the inverse filtering problem and when planning laboratory experiments.

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