We introduce a novel artificial compressibility technique to approximate the
incompressible Navier-Stokes equations with variable fluid properties such as
density and dynamical viscosity. The proposed scheme used the couple pressure
and momentum, equal to the density times the velocity, as primary unknowns. It
also involves an adequate treatment of the diffusive operator such that
treating the nonlinear convective term explicitly leads to a scheme with time
independent stiffness matrices that is suitable for pseudo-spectral methods.
The stability and temporal convergence of the semi-implicit version of the
scheme is established under the hypothesis that the density is approximated
with a method that conserves the minimum-maximum principle. Numerical
illustrations confirm that both the semi-implicit and explicit scheme are
stable and converge with order one under classic CFL condition. Moreover, the
proposed scheme is shown to perform better than a momentum based pressure
projection method, previously introduced by one of the authors, on setups
involving gravitational waves and immiscible multi-fluids in a cylinder.

Este artículo explora los viajes en el tiempo y sus implicaciones.

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