A semi-implicit low-regularity integrator for Navier-Stokes equations

A new type of low-regularity integrator is proposed for Navier-Stokes equations, coupled with a stabilized finite element method in space. Unlike the other low-regularity integrators for nonlinear dispersive equations, which are all fully explicit in time, the proposed method is semi-implicit in tim...

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Published in:arXiv.org 2021-07
Main Authors: Li, Buyang, Ma, Shu, Schratz, Katharina
Format: Article
Language:English
Subjects:
Computational fluid dynamics
Finite element method
Fluid flow
Integrators
Mathematical analysis
Navier-Stokes equations
Numerical methods
Regularity
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Ma, Shu
Schratz, Katharina
description A new type of low-regularity integrator is proposed for Navier-Stokes equations, coupled with a stabilized finite element method in space. Unlike the other low-regularity integrators for nonlinear dispersive equations, which are all fully explicit in time, the proposed method is semi-implicit in time in order to preserve the energy-decay structure of NS equations. First-order convergence of the proposed method is established independent of the viscosity coefficient \(\mu\), under weaker regularity conditions than other existing numerical methods, including the semi-implicit Euler method and classical exponential integrators. Numerical results show that the proposed method is more accurate than the semi-implicit Euler method in the viscous case \(\mu=O(1)\), and more accurate than the classical exponential integrator in the inviscid case \(\mu\rightarrow 0\).
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subjects Computational fluid dynamics
Finite element method
Fluid flow
Integrators
Mathematical analysis
Navier-Stokes equations
Numerical methods
Regularity
title A semi-implicit low-regularity integrator for Navier-Stokes equations
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