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

Buyang Li; Shu Ma; Katharina Schratz

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arXiv · 2107.13427

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

Buyang Li·Shu Ma·Katharina Schratz

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Abstract

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 $μ$, 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 $μ=O(1)$, and more accurate than the classical exponential integrator in the inviscid case $μ\rightarrow 0$.

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BibTeX RIS

Buyang Li, Shu Ma, Katharina Schratz. 2021-07-28. A semi-implicit low-regularity integrator for Navier-Stokes equations. https://arxiv.org/abs/2107.13427

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