A note on three-dimensional compressible boundary layer growth
A numerical method for unsteady flows
A high resolution finite volume method for the computation of unsteady solutions of the Euler equations in two space dimensions is presented and validated. The scheme is of Godunov-type. The first order part of the flux function uses the approximate Riemann problem solver of Pandolfi and here a new derivation of this solver is presented. This construction paves the way to understand the conditions under which the scheme satisfies an entropy condition. The extension to higher order is done by applying...
A regularity result for a solid-fluid system associated to the compressible Navier-Stokes equations
A remark on the smoothness of bounded regions filled with a steady compressible and isentropic fluid
For convenient adiabatic constants, existence of weak solutions to the steady compressible Navier-Stokes equations in isentropic regime in smooth bounded domains is well known. Here we present a way how to prove the same result when the bounded domains considered are Lipschitz.
A second order anti-diffusive Lagrange-remap scheme for two-component flows
We build a non-dissipative second order algorithm for the approximate resolution of the one-dimensional Euler system of compressible gas dynamics with two components. The considered model was proposed in [1]. The algorithm is based on [8] which deals with a non-dissipative first order resolution in Lagrange-remap formalism. In the present paper we describe, in the same framework, an algorithm that is second order accurate in time and space, and that...
A uniqueness result for a model for mixtures in the absence of external forces and interaction momentum
We consider a continuum model describing steady flows of a miscible mixture of two fluids. The densities of the fluids and their velocity fields are prescribed at infinity: , . Neglecting the convective terms, we have proved earlier that weak solutions to such a reduced system exist. Here we establish a uniqueness type result: in the absence of the external forces and interaction terms, there is only one such solution, namely , , .
A Van Leer finite volume scheme for the Euler equations on unstructured meshes
A zoology of boundary layers.
In meteorology and magnetohydrodynamics many different boundary layers appear. Some of them are already mathematically well known, like Ekman or Hartmann layers. Others remain unstudied, and can be much more complex. The aim of this paper is to give a simple and unified presentation of the main boundary layers, and to propose a simple method to derive their sizes and equations.
About porosity parameters with the application of general similarity method to the case of a dissociated gas flow in the boundary layer
About steady transport equation I – -approach in domains with smooth boundaries
We investigate the steady transport equation in various domains (bounded or unbounded) with smooth noncompact boundaries. The functions are supposed to be small in appropriate norms. The solution is studied in spaces of Sobolev type (classical Sobolev spaces, Sobolev spaces with weights, homogeneous Sobolev spaces, dual spaces to Sobolev spaces). The particular stress is put onto the problem to extend the results to as less regular vector fields , as possible (conserving the requirement of...
About steady transport equation. II: Schauder estimates in domains with smooth boundaries.
About the Resolvent of an Operator from Fluid Dynamics.
Abrupt and smooth separation of free boundaries in flow problems
Accurate numerical discretizations of non-conservative hyperbolic systems
We present an alternative framework for designing efficient numerical schemes for non-conservative hyperbolic systems. This approach is based on the design of entropy conservative discretizations and suitable numerical diffusion operators that mimic the effect of underlying viscous mechanisms. This approach is illustrated by considering two model non-conservative systems: Lagrangian gas dynamics in non-conservative form and a form of isothermal Euler equations. Numerical experiments demonstrating...
Accurate numerical discretizations of non-conservative hyperbolic systems
We present an alternative framework for designing efficient numerical schemes for non-conservative hyperbolic systems. This approach is based on the design of entropy conservative discretizations and suitable numerical diffusion operators that mimic the effect of underlying viscous mechanisms. This approach is illustrated by considering two model non-conservative systems: Lagrangian gas dynamics in non-conservative form and a form of isothermal Euler equations. Numerical experiments demonstrating...
Acoustic-gravity waves in a viscous and thermally conducting isothermal atmosphere. III: For arbitrary Prandtl number.
Acoustic-gravity waves in a viscous and thermally conducting isothermal atmosphere. I: For large Prandtl number.
Acoustic-gravity waves in a viscous and thermally conducting isothermal atmosphere. II: For small Prandtl number.
Adiabatic Shearing of an Incompressible gas Caused by ΄΄Oscillatory΄΄ Inertial Force
Air entrainment in transient flows in closed water pipes : A two-layer approach
In this paper, we first construct a model for free surface flows that takes into account the air entrainment by a system of four partial differential equations. We derive it by taking averaged values of gas and fluid velocities on the cross surface flow in the Euler equations (incompressible for the fluid and compressible for the gas). The obtained system is conditionally hyperbolic. Then, we propose a mathematical kinetic interpretation of this system to finally construct a two-layer kinetic scheme...