We prove small data global existence and scattering for quasilinear systems of Klein-Gordon equations with different speeds, in dimension three. As an application, we obtain a robust global stability result for the Euler-Maxwell equations for electrons.
We show the solvability of a nonlinear degenerate parabolic system of two equations describing the displacement of one compressible fluid by another, completely miscible with the first, in a one-dimensional porous medium, neglecting the molecular diffusion. We use the technique of renormalised solutions for parabolic equations in the derivation of a priori estimates for viscosity type solutions. We pass to the limit, as the molecular diffusion coefficient tends to 0, on the parabolic system, owing...
The paper contains the proof of global existence of weak solutions to the mixed initial-boundary value problem for a certain modification of a system of equations of motion of viscous compressible fluid. The modification is based on an application of an operator of regularization to some terms appearing in the system of equations and it does not contradict the laws of fluid mechanics. It is assumed that pressure is a known function of density. The method of discretization in time is used and finally,...
The concept of regularization to the complete system of Navier-Stokes equations for viscous compressible heat conductive fluid is developed. The existence of weak solutions for the initial boundary value problem for the modified equations is proved. Some energy and etropy estimates independent of the parameter of regularization are derived.
The aim of this article is a qualitative analysis of two modern finite volume (FVM) schemes. First one is the so called Modified Causon’s scheme, which is based on the classical MacCormack FVM scheme in total variation diminishing (TVD) form, but is simplified in such a way that the demands on computational power are much smaller without loss of accuracy. Second one is implicit WLSQR (Weighted Least Square Reconstruction) scheme combined with various types of numerical fluxes (AUSMPW+ and HLLC)....
We study the homogenization of the compressible Navier–Stokes system in a periodic porous medium (of period ) with Dirichlet boundary conditions. At the limit, we recover different systems depending on the scaling we take. In particular, we rigorously derive the so-called “porous medium equation”.
We study the homogenization of the compressible Navier–Stokes system in a periodic porous medium (of period ε) with Dirichlet boundary conditions. At the limit, we recover different systems depending on the scaling we take. In particular, we rigorously derive the so-called “porous medium equation”.
In this paper we present a methodology for constructing accurate and efficient hybrid central-upwind (HCU) type schemes for the numerical resolution of a two-fluid model commonly used by the nuclear and petroleum industry. Particularly, we propose a method which does not make use of any information about the eigenstructure of the jacobian matrix of the model. The two-fluid model possesses a highly nonlinear pressure law. From the mass conservation equations we develop an evolution equation which...
In this paper we present a methodology for constructing accurate and efficient hybrid central-upwind (HCU) type schemes for the numerical resolution of a two-fluid model commonly used by the nuclear and petroleum industry. Particularly, we propose a method which does not make use of any information about the eigenstructure of the Jacobian matrix of the model. The two-fluid model possesses a highly nonlinear pressure law. From the mass conservation equations we develop an evolution equation which...
In this work we describe an efficient model for the simulation of a two-phase flow made of a gas and a granular solid. The starting point is the two-velocity two-pressure model of Baer and Nunziato [Int. J. Multiph. Flow16 (1986) 861–889]. The model is supplemented by a relaxation source term in order to take into account the pressure equilibrium between the two phases and the granular stress in the solid phase. We show that the relaxation process can be made thermodynamically coherent with an...
An exploratory study is performed to investigate the use of a time-dependent discrete adjoint methodology for design optimization of a high-lift wing configuration augmented with an active flow control system. The location and blowing parameters associated with a series of jet actuation orifices are used as design variables. In addition, a geometric parameterization scheme is developed to provide a compact set of design variables describing the wing...
The paper is concerned with the numerical solution of interaction of compressible flow and a vibrating airfoil with two degrees of freedom, which can rotate around an elastic axis and oscillate in the vertical direction. Compressible flow is described by the Navier-Stokes equations written in the ALE form. This system is discretized by the semi-implicit discontinuous Galerkin finite element method (DGFEM) and coupled with the solution of ordinary differential equations describing the airfoil motion....
This paper is concerned with numerical methods for compressible multicomponent fluids. The fluid components are assumed immiscible, and are separated by material interfaces, each endowed with its own equation of state (EOS). Cell averages of computational cells that are occupied by several fluid components require a “mixed-cell” EOS, which may not always be physically meaningful, and often leads to spurious oscillations. We present a new interface tracking algorithm, which avoids using mixed-cell...