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

2024/11/23 by Huang, Qian, Rohde, Christian, Yong, Wen-An +1
#35Q30 #76D05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.15575

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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