233 research outputs found
A general existence result for isothermal two-phase flows with phase transition
Liquid-vapor flows with phase transitions have a wide range of applications.
Isothermal two-phase flows described by a single set of isothermal Euler
equations, where the mass transfer is modeled by a kinetic relation, have been
investigated analytically in (Quarterly of applied Mathematics, vol.\ LXXI 3
(2013), pp.\ 509-540.). This work was restricted to liquid water and its vapor
modeled by linear equations of state. The focus of the present work lies on the
generalization of the primary results to arbitrary substances, arbitrary
equations of state and thus a more general kinetic relation. We prove existence
and uniqueness results for Riemann problems. In particular, nucleation and
evaporation are discussed
Exact solutions to the Riemann problem for compressible isothermal Euler equations for two phase flows with and without phase transition
We consider the isothermal Euler equations with phase transition between a liquid and a vapor phase. The mass transfer is modeled by a kinetic relation. We prove existence and uniqueness results. Further, we construct the exact solution for Riemann problems. We derive analogous results for the cases of initially one phase with resulting condensation by compression or evaporation by expansion. Further we present numerical results for these cases. We compare the results to similar problems without phase transition
An Asymptotic Preserving Scheme for the Euler equations in a strong magnetic field
This paper is concerned with the numerical approximation of the isothermal
Euler equations for charged particles subject to the Lorentz force. When the
magnetic field is large, the so-called drift-fluid approximation is obtained.
In this limit, the parallel motion relative to the magnetic field direction
splits from perpendicular motion and is given implicitly by the constraint of
zero total force along the magnetic field lines. In this paper, we provide a
well-posed elliptic equation for the parallel velocity which in turn allows us
to construct an Asymptotic-Preserving (AP) scheme for the Euler-Lorentz system.
This scheme gives rise to both a consistent approximation of the Euler-Lorentz
model when epsilon is finite and a consistent approximation of the drift limit
when epsilon tends to 0. Above all, it does not require any constraint on the
space and time steps related to the small value of epsilon. Numerical results
are presented, which confirm the AP character of the scheme and its Asymptotic
Stability
Stability analysis of an implicit lattice Boltzmann scheme
International audienceWe analyze the D1Q3 lattice kinetic model, which is the simplest kinetic model representing the isothermal Euler equations. We show that it is entropy unstable but that it can be made stable if the transport step is solved with an implicit numerical scheme
- …