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arXiv · 2411.15575

A hyperbolic relaxation system of the incompressible Navier-Stokes equations with artificial compressibility

Qian Huang·Christian Rohde·Wen-An Yong·Ruixi Zhang
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Abstract

We introduce a new hyperbolic approximation to the incompressible Navier-Stokes equations by incorporating a first-order relaxation and using the artificial compressibility method. With two relaxation parameters in the model, we rigorously prove the asymptotic limit of the system towards the incompressible Navier-Stokes equations as both parameters tend to zero. Notably, the convergence of the approximate pressure variable is achieved by the help of a linear `auxiliary' system and energy-type error estimates of its differences with the two-parameter model and the Navier-Stokes equations.

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Qian Huang, Christian Rohde, Wen-An Yong, Ruixi Zhang. 2024-11-23. A hyperbolic relaxation system of the incompressible Navier-Stokes equations with artificial compressibility. https://arxiv.org/abs/2411.15575

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