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215
In this survey paper,
we are concerned with the zero Mach number limit
for compressible viscous flows.
For the sake of (mathematical) simplicity,
we restrict ourselves to the case of barotropic
fluids and we
assume that the flow evolves in the whole space
or satisfies periodic boundary conditions. We focus on the case of ill-prepared data.
Hence highly oscillating acoustic waves
are likely to propagate through the fluid.
We nevertheless state
the convergence to the incompressible Navier-Stokes...
In this note, we give an overview of the authors’ paper [6] which deals with asymptotic consistency of a class of linearly implicit schemes for the compressible Euler equations. This class is based on a linearization of the nonlinear fluxes at a reference state and includes the scheme of Feistauer and Kučera [3] as well as the class of RS-IMEX schemes [8,5,1] as special cases. We prove that the linearization gives an asymptotically consistent solution in the low-Mach limit under the assumption of...
In the present work we investigate the numerical simulation of liquid-vapor phase change
in compressible flows. Each phase is modeled as a compressible fluid equipped with its own
equation of state (EOS). We suppose that inter-phase equilibrium processes in the medium
operate at a short time-scale compared to the other physical phenomena such as convection
or thermal diffusion. This assumption provides an implicit definition of an equilibrium
EOS...
In the present work we investigate the numerical simulation of liquid-vapor phase change
in compressible flows. Each phase is modeled as a compressible fluid equipped with its own
equation of state (EOS). We suppose that inter-phase equilibrium processes in the medium
operate at a short time-scale compared to the other physical phenomena such as convection
or thermal diffusion. This assumption provides an implicit definition of an equilibrium
EOS...
We consider hydrodynamical models describing the evolution of a gaseous star in which the presence of thermonuclear reactions between several species leads to a multicomponent formulation. In the case of binary mixtures, recent 3D results are evoked. In the one-dimensional situation, we can prove global estimates and stabilization for some simplified model.
We consider supersonic compressible vortex sheets for the isentropic Euler equations of gas dynamics in two space dimensions. The problem is a free boundary nonlinear hyperbolic problem with two main difficulties: the free boundary is characteristic, and the so-called Lopatinskii condition holds only in a weak sense, which yields losses of derivatives. Nevertheless, we prove the local existence of such piecewise smooth solutions to the Euler equations. Since the a priori estimates for the linearized...
The paper is devoted to the solvability of a nonlinear elliptic problem in a plane multiply connected domain. On the inner components of its boundary Dirichlet conditions are known up to additive constants which have to be determined together with the sought solution so that the so-called trailing stagnation conditions are satisfied. The results have applications in the stream function solution of subsonic flows past groups of profiles or cascades of profiles.
Our aim is to find roots of the non-unique behavior of gases which can be observed in certain axisymmetric nozzle geometries under special flow regimes. For this purpose, we use several versions of the compressible Euler equations. We show that the main reason for the non-uniqueness is hidden in the energy decomposition into its internal and kinetic parts, and their complementary behavior. It turns out that, at least for inviscid compressible flows, a bifurcation can occur only at flow regimes with...
We derive a global differential inequality for solutions of a free boundary problem for a viscous compressible heat concluding capillary fluid. The inequality is essential in proving the global existence of solutions.
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215