Maps and fields with compressible density
Mathematical and numerical study of nonlinear problems in fluid mechanics
Measure-valued solutions and well-posedness of multi-dimensional conservation laws in a bounded domain.
Modelling and simulation of liquid-vapor phase transition in compressible flows based on thermodynamical equilibrium∗
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...
Modelling and simulation of liquid-vapor phase transition in compressible flows based on thermodynamical equilibrium∗
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...
Multicomponent models in nuclear astrophysics
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.
Multiphase free boundary problem for the equations of motion of general fluids
Navier-Stokes equations with nonhomogeneous boundary conditions in a convex bi-dimensional domain
Navier–Stokes regularization of multidimensional Euler shocks
Nonclassical shock waves of conservation laws: Flux function having two inflection points.
Nonhomogeneous boundary value problem for one-dimensional compressible viscous micropolar fluid model: Regularity of the solution.
Nonlinear compressible vortex sheets in two space dimensions
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...
Nonlinear elliptic problems with incomplete Dirichlet conditions and the stream function solution of subsonic rotational flows past profiles or cascades of profiles
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.
Non-uniqueness of almost unidirectional inviscid compressible flow
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...
Non-uniqueness of solution to quasi-1D compressible Euler equations
Numerical solutions of cascade flows by finite element method [Abstract of thesis]
On 3D slightly compressible Euler equations.
On a differential inequality for a viscous compressible heat conducting capillary fluid bounded by a free surface
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.
On a differential inequality for equations of a viscous compressible heat conducting fluid bounded by a free surface
We derive a global differential inequality for solutions of a free boundary problem for a viscous compressible heat conducting fluid. The inequality is essential in proving the global existence of solutions.
On a free boundary barotropic model