The relaxed friction-type approximation of the Navier-Stokes-Cahn-Hilliard system has a hyperbolic first-order subsystem in 1D, proved via a convex entropy-entropy flux pair.
A hyperbolic relaxation system of the incompressible Navier-Stokes equations with artificial compressibility
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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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A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow
The relaxed friction-type approximation of the Navier-Stokes-Cahn-Hilliard system has a hyperbolic first-order subsystem in 1D, proved via a convex entropy-entropy flux pair.