A stabilized fractional-step finite element method for the time-dependent Navier–Stokes equations
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Yueqiang Shang
and
Qing Liu
Abstract
We present a fractional-step finite element method based on a subgrid model for simulating the time-dependent incompressible Navier–Stokes equations. The method aims to the simulation of high Reynolds number flows and consists of two steps in which the nonlinearity and incompressibility are split into different steps. The first step of this method can be seen as a linearized Burger’s problem where a subgrid model based on an elliptic projection of the velocity into a lower-order finite element space is employed to stabilize the system, and the second step is a Stokes problem. Under mild regularity assumptions on the continuous solution, we obtain the stability of the numerical method, and derive error bound of the approximate velocity, which shows that first-order convergence rate in time and optimal convergence rate in space can be gotten by the method. Numerical experiments verify the theoretical predictions and demonstrate the promise of the proposed method, which show superiority of the proposed method to the compared method in the literature.
Funding source: Fundamental Research Funds for the Central Universities
Award Identifier / Grant number: XDJK2018B032
Funding source: The Natural Science Foundation of China
Award Identifier / Grant number: 11361016
Funding source: The Basic and Frontier Explore Program of Chongqing Municipality, China
Award Identifier / Grant number: cstc2018jcyjAX0305
Acknowledgments
The authors express their deep gratitude to the anonymous reviewers for the valuable comments and suggestions, which led to an improvement of the paper.
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: This work was supported by the Natural Science Foundation of China (No. 11361016), the Basic and Frontier Explore Program of Chongqing Municipality, China (No. cstc2018jcyjAX0305), and Fundamental Research Funds for the Central Universities (No. XDJK2018B032).
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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Articles in the same Issue
- Frontmatter
- Original Research Articles
- Research on bifurcation and chaos characteristics of planet gear transmission system with mixed elastohydrodynamic lubrication (EHL) friction
- Nonlinear modeling and simulation of flywheel energy storage rotor system with looseness and rub-impact coupling hitch
- Application of the piecewise constant method in nonlinear dynamics of drill string
- Fractional Kirchhoff-type problems with exponential growth without the Ambrosetti–Rabinowitz condition
- A stabilized fractional-step finite element method for the time-dependent Navier–Stokes equations
- Self-adaptive inertial subgradient extragradient scheme for pseudomonotone variational inequality problem
- An accurate and novel numerical simulation with convergence analysis for nonlinear partial differential equations of Burgers–Fisher type arising in applied sciences
- Numerical study of multi-dimensional hyperbolic telegraph equations arising in nuclear material science via an efficient local meshless method
- N-soliton solutions and the Hirota conditions in (1 + 1)-dimensions
- Quintic B-spline collocation method for the numerical solution of the Bona–Smith family of Boussinesq equation type
- Existence of positive periodic solutions for a class of second-order neutral functional differential equations
