An efficient numerical verification method for the Kolmogorov problem of incompressible viscous fluid

被引：4

作者：

Watanabe, Yoshitaka ^{[1
,2
]}

机构：

[1] Kyushu Univ, Res Inst Informat Technol, Higashi Ku, 6-10-1 Hakozaki, Fukuoka 8128518, Japan

[2] Japan Sci & Technol Agcy, CREST, Tokyo, Japan

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2016年 / 302卷

关键词：

Kolmogorov flows; Computer-assisted proof; Fixed-point theorem; COMPUTER-ASSISTED PROOF; LOCAL UNIQUENESS; FLOWS;

D O I：

10.1016/j.cam.2016.01.055

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Some computer-assisted proofs of nontrivial steady-state solutions for the Kolmogorov flows are presented. The method is based on the infinite-dimensional fixed-point theorem using a Newton-like operator with a numerical verification algorithm that automatically generates a set that includes the exact nontrivial solution. When discussing the numerical results, we consider the effects of rounding errors in the floating point computations. This is a continuation of our study that was presented in Watanabe (2009). (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：157 / 170

页数：14

共 50 条

[41] FLOW FLUCTUATIONS AND THE KOLMOGOROV TURBULENCE IN INCOMPRESSIBLE FLUID
TUR, AV
YANOVSKY, VV
UKRAINSKII FIZICHESKII ZHURNAL, 1988, 33 (08): : 1263 - 1270
[42] METHOD OF NUMERICAL ANALYSIS OF THE PROBLEM OF STATIONARY FLOW PAST BODIES OF REVOLUTION BY VISCOUS FLUID
Lamtyugova, S. N.
Sidorov, M., V
Sytnykova, I., V
RADIO ELECTRONICS COMPUTER SCIENCE CONTROL, 2018, (01) : 50 - 57
[43] Numerical simulation of the sedimentation of a tripole-like body in an incompressible viscous fluid
Juárez, LH
Glowinski, R
Pettitt, BM
APPLIED MATHEMATICS LETTERS, 2002, 15 (06) : 743 - 747
[44] NUMERICAL-SOLUTION OF THE EQUATIONS OF THE DYNAMICS OF A VISCOUS INCOMPRESSIBLE FLUID WITH DISPERSED PARTICLES
DORFMAN, AL
USSR COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 1983, 23 (02): : 109 - 114
[45] AN ITERATIVE METHOD FOR THE NAVIER-STOKES EQUATIONS IN THE PROBLEM OF A VISCOUS INCOMPRESSIBLE FLUID FLOW AROUND A THIN PLATE
Sumbatyan, M. A.
Berdnik, Ya A.
Bondarchuk, A. A.
VESTNIK TOMSKOGO GOSUDARSTVENNOGO UNIVERSITETA-MATEMATIKA I MEKHANIKA-TOMSK STATE UNIVERSITY JOURNAL OF MATHEMATICS AND MECHANICS, 2020, (66): : 132 - 142
[46] NUMERICAL STUDY ON FLOW OF INCOMPRESSIBLE VISCOUS-FLUID AROUND CIRCULAR CYLINDER
LOC, TP
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1973, 276 (07): : 567 - 570
[47] The exterior problem in the plane for a non-Newtonian incompressible bipolar viscous fluid
Bellout, H
Necas, J
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1996, 26 (04) : 1245 - 1260
[48] ON CLASSICAL SOLVABILITY OF THE MULTIDIMENSIONAL STEFAN PROBLEM FOR CONVECTIVE MOTION OF A VISCOUS INCOMPRESSIBLE FLUID
BAZALII, BV
DEGTYAREV, SP
MATHEMATICS OF THE USSR-SBORNIK, 1987, 132 (1-2): : 1 - 17
[49] FORMULATION AND INVESTIGATION OF A NONLINEAR INVERSE CONTROL PROBLEM OF THE MOTION OF A VISCOUS INCOMPRESSIBLE FLUID
PRILEPKO, AI
VASIN, IA
DIFFERENTIAL EQUATIONS, 1992, 28 (04) : 569 - 577
[50] On a free boundary problem of magnetohydrodynamics for a viscous incompressible fluid not subjected to capillary forces
Solonnikov, V. A.
RECENT ADVANCES IN PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2016, 666 : 357 - 383

← 1 2 3 4 5 →