Initial–boundary layer associated with the nonlinear Darcy–Brinkman system

Han, Daozhi; Wang, Xiaoming

doi:10.1016/j.jde.2013.09.014

Cited by 11 publications

(5 citation statements)

References 59 publications

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“…Therefore, there is a ghost of the porous medium in the convergence rate. It should be noted that in the case of the Darcy-Brinkman system, the equations for the boundary corrector are linear, and thus, the passage to the zero-viscosity limit is possible [82,63].…”

Section: Case Of No-slip Boundary Conditionmentioning

confidence: 99%

The Inviscid Limit and Boundary Layers for Navier-Stokes Flows

Maekawa

Mazzucato

2018

Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

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The validity of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations modeling viscous incompressible flows converge to solutions of the Euler equations modeling inviscid incompressible flows as viscosity approaches zero, is one of the most fundamental issues in mathematical fluid mechanics. The problem is classified into two categories: the case when the physical boundary is absent, and the case when the physical boundary is present and the effect of the boundary layer becomes significant. The aim of this article is to review recent progress on the mathematical analysis of this problem in each category.

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Section: Case Of No-slip Boundary Conditionmentioning

confidence: 99%

The Inviscid Limit and Boundary Layers for Navier-Stokes Flows

Maekawa

Mazzucato

2018

Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

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“…Compared with the studies in [27,32,33], the problem in this paper becomes more complicated due to the appearance of boundary layers and initial layer. This perturbed problems have been studied in many other works see for instance, [3,10,13,23,24,25,28,35,36,37] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Initial-boundary layer associated with the 3-D Boussinesq system for Rayleigh-Benard convection

Fan,

Wang,

2020

ejde

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This article concerns the initial-boundary layer effects of the 3-D incompressible Boussinesq system for Rayleigh-Benard convection with ill-prepared initial data. We consider a non-slip boundary condition for the velocity field and inhomogeneous Dirichlet boundary condition for the temperature. By means of multi-scale analysis and matched asymptotic expansion methods, we establish an accurate approximating solution for the viscous and diffusive Boussinesq system. We also study the convergence of the infinite Prandtl number limit. For more information see https://ejde.math.txstate.edu/Volumes/2020/31/abstr.html

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“…We examine singularly perturbed parabolic problems in one space dimension, with an incompatibility between the initial condition and a boundary condition. These problems arise in mathematical models in fluid dynamics [8] and, in particular, models for flow in porous media [3]. The solutions of these problems typically exhibit boundary layers, initial layers and initial-boundary layers.…”

Section: Introductionmentioning

confidence: 99%

Parameter-uniform numerical methods for singularly perturbed parabolic problems with incompatible boundary-initial data

Gracia

O’Riordan

2019

Applied Numerical Mathematics

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Numerical approximations to the solution of a linear singularly perturbed parabolic reaction-diffusion problem with incompatible boundary-initial data are generated, The method involves combining the computational solution of a classical finite difference operator on a tensor product of two piecewise-uniform Shishkin meshes with an analytical function that captures the local nature of the incompatibility. A proof is given to show almost first order parameter-uniform convergence of these numerical/analytical approximations. Numerical results are given to illustrate the theoretical error bounds.1 The space C n+γ (Q) is the set of all functions, whose derivatives of order n are Hölder continuous of degree γ > 0. That is, C n+γ (Q) := z :∂ i+j z ∂x i ∂t j ∈ C γ (Q), 0 ≤ i + 2j ≤ n .

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Initial–boundary layer associated with the nonlinear Darcy–Brinkman system

Cited by 11 publications

References 59 publications

The Inviscid Limit and Boundary Layers for Navier-Stokes Flows

The Inviscid Limit and Boundary Layers for Navier-Stokes Flows

Initial-boundary layer associated with the 3-D Boussinesq system for Rayleigh-Benard convection

Parameter-uniform numerical methods for singularly perturbed parabolic problems with incompatible boundary-initial data

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