Decoupled modified characteristic finite element method for the time-dependent Navier-Stokes/Biot problem

被引：5

作者：

Guo, Liming ^{[1
]}

Chen, Wenbin ^{[2
,3
]}

机构：

[1] Xinyang Normal Univ, Sch Math & Stat, Xinyang, Peoples R China

[2] Fudan Univ, Sch Math Sci, Shanghai, Peoples R China

[3] Fudan Univ, Shanghai Key Lab Math Nonlinear Sci, Shanghai, Peoples R China

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2022年 / 38卷 / 06期

基金：

中国国家自然科学基金;

关键词：

error estimates; modified characteristic finite element method; Navier-Stokes; Biot problem; stability; NUMERICAL-METHODS; ERROR ANALYSIS; FLUID; STABILITY; FLOW; CONVERGENCE; SCHEMES; APPROXIMATION; SURFACE;

D O I：

10.1002/num.22830

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, a decoupled modified characteristic finite element method is proposed for the time-dependent Navier-Stokes/Biot problem. In the numerical scheme, the implicit backward Euler scheme is used for the time discretization, whereas the coupling terms are treated explicitly. At each time step, we only need to solve two decoupled problems, one is the Navier-Stokes equations solved by the modified characteristic finite element method, and the other is Biot equations. The stability and the error estimates are established for the proposed fully discrete scheme. Numerical experiments are provided to illustrate the theory.

引用

页码：1684 / 1712

页数：29

共 50 条

[21] Modified Method of Characteristics Variational Multiscale Finite Element Method for Time Dependent Navier-Stokes Problems
Si, Zhiyong
Wang, Yunxia
Feng, Xinlong
MATHEMATICAL MODELLING AND ANALYSIS, 2015, 20 (05) : 658 - 680
[22] A FINITE-ELEMENT SOLUTION OF THE TIME-DEPENDENT INCOMPRESSIBLE NAVIER-STOKES EQUATIONS USING A MODIFIED VELOCITY CORRECTION METHOD
REN, G
UTNES, T
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 1993, 17 (05) : 349 - 364
[23] A locally conservative and energy-stable finite-element method for the Navier-Stokes problem on time-dependent domains
Horvath, Tamas L.
Rhebergen, Sander
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 2019, 89 (12) : 519 - 532
[24] A finite element scheme for the numerical solution of the Navier-Stokes/Biot coupled problem
Lozovskiy, Alexander
Olshanskii, Maxim A.
Vassilevski, Yuri V.
RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING, 2022, 37 (03) : 159 - 174
[25] Numerical analysis of a characteristic stabilized finite element method for the time-dependent Navier-Stokes equations with nonlinear slip boundary conditions
Jing, Feifei
Li, Jian
Chen, Zhangxin
Zhang, Zhonghua
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2017, 320 : 43 - 60
[26] Two-grid finite element scheme for the fully discrete time-dependent Navier-Stokes problem
Abboud, H
Girault, V
Sayah, T
COMPTES RENDUS MATHEMATIQUE, 2005, 341 (07) : 451 - 456
[27] THE CHARACTERISTIC STREAMLINE DIFFUSION METHOD FOR THE TIME-DEPENDENT INCOMPRESSIBLE NAVIER-STOKES EQUATIONS
HANSBO, P
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1992, 99 (2-3) : 171 - 186
[28] A Stabilized Characteristic-Nonconforming Finite Element Method for Time-Dependent Incompressible Navier–Stokes Equations
Huiyong Jia
Kaitai Li
Hongen Jia
Bulletin of the Malaysian Mathematical Sciences Society, 2018, 41 : 207 - 230
[29] A multilevel finite element method in space-time for the Navier-Stokes problem
He, YN
Liu, KM
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2005, 21 (06) : 1052 - 1078
[30] Superconvergent analysis of a nonconforming mixed finite element method for time-dependent damped Navier-Stokes equations
Qian, Liu
Dongyang, Shi
COMPUTATIONAL & APPLIED MATHEMATICS, 2021, 40 (01):

← 1 2 3 4 5 →