scholarly journals Incompressible limit for a two-species model with coupling through Brinkman's law in any dimension

2021 ◽  
Vol 145 ◽  
pp. 204-239
Author(s):  
Tomasz Dębiec ◽  
Benoît Perthame ◽  
Markus Schmidtchen ◽  
Nicolas Vauchelet
Keyword(s):  
Incompressible Limit

Lattice-BGK Methods for Simulating Incompressible Fluid Flows

1997 ◽  
Vol 08 (04) ◽  
pp. 793-803 ◽  
Author(s):  
Yu Chen ◽  
Hirotada Ohashi
Keyword(s):  
Fluid Flow ◽  
Incompressible Fluid ◽  
Poisson Equation ◽  
General Model ◽  
Incompressible Flows ◽  
Fluid Flows ◽  
Incompressible Limit ◽  
Numerical Example ◽  
Incompressible Fluid Flows

The lattice-Bhatnagar-Gross-Krook (BGK) method has been used to simulate fluid flow in the nearly incompressible limit. But for the completely incompressible flows, two special approaches should be applied to the general model, for the steady and unsteady cases, respectively. Introduced by Zou et al.,1 the method for steady incompressible flows will be described briefly in this paper. For the unsteady case, we will show, using a simple numerical example, the need to solve a Poisson equation for pressure.

scholarly journals A comparative study of the axisymmetric lattice Boltzmann models under the incompressible limit

2017 ◽  
Vol 74 (4) ◽  
pp. 817-841 ◽  
Author(s):  
Liangqi Zhang ◽  
Shiliang Yang ◽  
Zhong Zeng ◽  
Jie Chen ◽  
Lingquan Wang ◽  
...  
Keyword(s):  
Comparative Study ◽  
Lattice Boltzmann ◽  
Incompressible Limit ◽  
Lattice Boltzmann Models

Elasticity Equations with High Contrast Parameters

2015 ◽  
Author(s):  
Habib Ammari ◽  
Elie Bretin ◽  
Josselin Garnier ◽  
Hyeonbae Kang ◽  
Hyundae Lee ◽  
...  
Keyword(s):  
Extreme Values ◽  
Convergence Result ◽  
Energy Functional ◽  
Incompressible Limit ◽  
High Contrast ◽  
Complete Asymptotic Expansion ◽  
Shear Moduli ◽  
Elasticity Equations ◽  
Compressional Modulus ◽  
Uniformly Bounded

This chapter presents some recent results on the elasticity equations with high contrast coefficients. It first sets up the problems for finite and extreme moduli before discussing the incompressible limit of elasticity equations. It then provides a complete asymptotic expansion with respect to the compressional modulus and considers the limiting cases of holes and hard inclusions. It proves that the energy functional is uniformly bounded and demonstrates that the potentials on the boundary of the inclusion are also uniformly bounded. It also shows that these potentials converge as the bulk and shear moduli tend to their extreme values and that similar boundedness and convergence result holds true for the boundary value problem.

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