Well-posedness and a numerical study of a regularization model with adaptive nonlinear filtering for incompressible fluid flow

被引：1

作者：

Cao, Yanzhao ^{[1
,2
]}

Chen, Song ^{[3
]}

Rebholz, Leo G. ^{[4
]}

机构：

[1] Jilin Univ, Sch Math, Jilin, Peoples R China

[2] Auburn Univ, Dept Math & Stat, Auburn, AL 36849 USA

[3] Univ Wisconsin, Dept Math, La Crosse, WI 54601 USA

[4] Clemson Univ, Dept Math Sci, Clemson, SC 29634 USA

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2016年 / 71卷 / 11期

关键词：

Navier-Stokes Equations; Nonlinear filtering; Finite element; FINITE-ELEMENTS; STOKES;

D O I：

10.1016/j.camwa.2015.12.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give a detailed analytical study of a Leray model of incompressible flow that uses nonlinear filtering based on indicator functions. The indicator functions allow for local regularization, instead of global regularization which can over-smooth and dampen out important flow structures. The key to the analysis is the identification of the indicator function as a Nemyskii operator. After proving well-posedness, we provide a numerical study which includes proving optimal convergence of finite element method for the model, as well as several numerical experiments. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：2192 / 2205

页数：14

共 50 条

[21] On Well-Posedness for a Multi-particle Fluid Model
Klingenberg, Christian
Klotzky, Jens
Seguin, Nicolas
THEORY, NUMERICS AND APPLICATIONS OF HYPERBOLIC PROBLEMS II, 2018, 237 : 167 - 177
[22] Well-posedness and numerical treatment of the Blackstock equation in nonlinear acoustics
Fritz, Marvin
Nikolic, Vanja
Wohlmuth, Barbara
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2018, 28 (13): : 2557 - 2597
[23] Local well-posedness of lower regularity solutions for the incompressible viscoelastic fluid system
ZHAO WenJing1
2Institution of Mathematics
Science China(Mathematics), 2010, 53 (06) : 1521 - 1530
[24] Well-posedness of a quasistationary model of a viscous compressible fluid
Mamontov, AE
SIBERIAN MATHEMATICAL JOURNAL, 1996, 37 (05) : 983 - 996
[25] Well-posedness of an isothermal diffusive model for binary mixtures of incompressible fluids
Berti, A.
Berti, V.
Grandi, D.
NONLINEARITY, 2011, 24 (11) : 3143 - 3164
[26] Stability and Well-Posedness of a Nonlinear Railway Track Model
Edalatzadeh, M. Sajjad
Morris, Kirsten A.
IEEE CONTROL SYSTEMS LETTERS, 2019, 3 (01): : 162 - 167
[27] THE WELL-POSEDNESS OF A SWIMMING MODEL IN THE 3-D INCOMPRESSIBLE FLUID GOVERNED BY THE NONSTATIONARY STOKES EQUATION
Khapalov, Alexander
INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND COMPUTER SCIENCE, 2013, 23 (02) : 277 - 290
[28] Accuracy estimates of regularization methods and conditional well-posedness of nonlinear optimization problems
Kokurin, Mikhail Y.
JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2018, 26 (06): : 789 - 797
[29] Well-posedness and variational numerical scheme for an adaptive model in highly heterogeneous porous media
Fumagalli, Alessio
Patacchini, Francesco Saverio
JOURNAL OF COMPUTATIONAL PHYSICS, 2023, 475
[30] Global Well-posedness for the Density-Dependent Incompressible Flow of Liquid Crystals
Zhai, Xiaoping
Chen, Zhi-Min
ACTA APPLICANDAE MATHEMATICAE, 2018, 158 (01) : 139 - 166

← 1 2 3 4 5 →