EVOLUTION AND INTERACTION OF δ-WAVES IN THE ZERO-PRESSURE GAS DYNAMICS SYSTEM

Evolution and interaction of plane waves of the multidimensional zero-pressure gas dynamics system leads to the study of the corresponding one dimensional system.In this paper,we study the initial value problem for one dimensional zero-pressure gas dynamics system.Here the first equation is the Burgers equation and the second one is the continuity equation.We consider the solution with initial data in the space of bounded Borel measures.First we prove a general existence result in the algebra of generalized functions of Colombeau.Then we study in detail special solutions withδ-measures as initial data.We study interaction of waves originating from initial data concentrated on two point sources and interaction with classical shock/rarefaction waves.This gives an understanding of plane-wave interactions in the multidimensional case.We use the vanishing viscosity method in our analysis as this gives the physical solution.

VANISHING VISCOSITY FOR NON-ISENTROPIC GAS DYNAMICS WITH INTERACTING SHOCKS

In this paper, we study the vanishing viscosity limit for non-isentropic gas dy- namics with interacting shocks. Given any entropy solution of non-isentropic gas dynamics which consists of two different families of shocks interacting at some positive time, we show that such solution is the vanishing viscosity limit of a family of smooth global solutions for a viscous system of conservation law. We remark that, after the interacting time, not only shocks but also contact discontinuity are generated.

CONVERGENCE OF THE LAX-FRIEDRICHS SCHEME FOR ISENTROPIC GAS DYNAMICS (Ⅰ)

A compactness frame of the Lax-Friedrichs scheme for the equations of gas dynamics is obtained by using some embedding theorems and an analysis of the difference scheme and the weak entropy.

A SUPPLEMENT TO THE PAPERS CONVERGENCE OF THE LAX-FRIEDRICHS SCHEME FOR ISENTROPIC GAS DYNAMICS (Ⅱ)-(Ⅲ)

In the papers (Ⅱ)—(Ⅲ), we studied the global existence of the solutions for the isentropic equation of gas dynamics

THE VACUUM IN NONISENTROPIC GAS DYNAMICS

We investigate the vacuum in nonisentropic gas dynamics in one space vari- able, with the most general equation of states allowed by thermodynamics. We recall physical constraints on the equations of state and give explicit and easily checkable conditions under which vacuums occur in the solution of the Riemann problem. We then present a class of models for which the Riemann problem admits unique global solutions without vacuums.

STRONG SHOCKS IN NONISENTROPIC GAS DYNAMICS

In nonisentropic gas dynamics, with general equations of state, strong cornpressive shocks satisfying the Liu E-condition may violate the Second Law of thermodynamics.

A NOTE ON THE EXISTENCE AND NONEXISTENCE OF GLOBALLY BOUNDED CLASSICAL SOLUTIONS FOR NONISENTROPIC GAS DYNAMICS

Existence of globally bounded classical solution for nonisentropic gas dynamics system has long been studied, especially in the case of polytropic gas. In [4], Liu claimed that sufficient condition has been established. However, the authors find that the argument he used is not true in general. In this article, the authors give a counter example of his argument. Hence, his claim is not valid. The authors believe that it is difficult to impose general conditions on the initial data to obtain globally bounded classical solution.

SOME EXACT SOLUTIONS OF 3-DIMENSIONAL ZERO-PRESSURE GAS DYNAMICS SYSTEM

The 3-dimensional zero-pressure gas dynamics system appears in the modeling for the large scale structure formation in the universe. The aim of this paper is to construct spherically symmetric solutions to the system. The radial component of the velocity and density satisfy a simpler one dimensional problem. First we construct explicit solutions of this one dimensional case with initial and boundary conditions. Then we get special radial solutions with different behaviours at the origin.

ENTROPY CONSISTENCY OF LARGE TIME STEP SCHEMES FOR ISENTROPIC EQUATIONS OF GAS DYNAMICS

In this paper, We show for isentropic equations of gas dynamics with adiabatic exponent gamma=3 that approximations of weak solutions generated by large time step Godunov's scheme or Glimm's scheme give entropy solution in the limit if Courant number is less than or equal to 1.

CONVERGENCE OF THE APPROXIMATE SOLUTIONS TO ISENTROPIC GAS DYNAMICS

This paper gives four pairs of entropies (η_i, q_i) (i=1, 2, 3, 4) to the isentropic gas dynamics equations ρ_t+(ρu)_x=0 (ρu)_t+(ρu^2+p(ρ))_x=0 p(ρ)=k^2ρ~γ,1<γ<3。 when all the function equations are satisfied

Numerical Computation for Time-fractional Gas Dynamics Equations by Fractional Reduced Differential Transforms Method

The present article is concerned with the implementation of a recent semi-analytical method referred to as fractional reduced differential transform method （FRDTM） for computation of approximate solution of time-fractional gas dynamics equation （TFGDE） arising in shock fronts. In this approach, the fractional derivative is described in the Caputo sense. Four numeric experiments have been carried out to confirm the validity and the efficiency of the method. It is found that the exact or a closed approximate analytical solution of a fractional nonlinear differential equations arising in allied science and engineering can be obtained easily. Moreover, due to its small size of calculation contrary to the other analytical approaches while dealing with a complex and tedious physical problems arising in various branches of natural sciences and engineering, it is very easy to implement.

The Aysmptotic Behavior of Solution to a Class of Inhomogeneons Systems of Gas Dynamics

Consider an initial-boundary problem vt - ux=0,u, + （）x + f（u） = （）x,θt+ux=（）ux=（）x+ （E） v（x,0） = v0（x）,u（x,0） = u0（x）,θ（0,x） = θ0（x）, （I） u（t,0） = u（t,1） = θx（t,0） = θx（t,1） （J） Sufficient and necessary conditions for （E）, （I） and （J） to have asymptotic stability of the gobal smooth solution are given by means of the elemental L2 energy method.

Asymptotic Solutions of the Kinetic Boltzmann Equation and Multicomponent Non-Equilibrium Gas Dynamics

In the article correct method for the kinetic Boltzmann equation asymptotic solution is formulated, the Hilbert’s and Enskog’s methods are discussed. The equations system of multicomponent non- equilibrium gas dynamics is derived, that corresponds to the first order in the approximate (asym- ptotic) method for solution of the system of kinetic Boltzmann equations.

An RKDG finite element method for the one-dimensional inviscid compressible gas dynamics equations in a Lagrangian coordinate

In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method.For multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other cells.At first,a linear Riemann solver is applied to calculate the numerical ？ux at the interface.Numerical examples show that there is some oscillation in the vicinity of the interface.Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ？ux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.

Delta-shocks and vacuums in zero-pressure gas dynamics by the flux approximation

In this paper,firstly,by solving the Riemann problem of the zero-pressure flow in gas dynamics with a flux approximation,we construct parameterized delta-shock and constant density solutions,then we show that,as the flux perturbation vanishes,they converge to the delta-shock and vacuum state solutions of the zero-pressure flow,respectively.Secondly,we solve the Riemann problem of the Euler equations of isentropic gas dynamics with a double parameter flux approximation including pressure.Furthermore,we rigorously prove that,as the two-parameter flux perturbation vanishes,any Riemann solution containing two shock waves tends to a delta-shock solution to the zero-pressure flow;any Riemann solution containing two rarefaction waves tends to a two-contact-discontinuity solution to the zero-pressure flow and the nonvacuum intermediate state in between tends to a vacuum state.Finally,numerical results are given to present the formation processes of delta shock waves and vacuum states.

The Riemann Problem with Delta Data for Zero-Pressure Gas Dynamics

In this paper, the Riemann problem with delta initial data for the onedimensional system of conservation laws of mass, momentum and energy in zero-pressure gas dynamics is considered. Under the generalized Rankine-Hugoniot conditions and the entropy condition, we constructively obtained the global existence of generalized solutions which contains delta-shock. Moreover, the author obtains the stability of generalized solutions by making use of the perturbation of the initial data.

AnAll-Regime Lagrange-Projection Like Scheme for the Gas Dynamics Equations on Unstructured Meshes

We propose an all regime Lagrange-Projection like numerical scheme for the gas dynamics equations.By all regime,we mean that the numerical scheme is able to compute accurate approximate solutions with an under-resolved discretization with respect to the Mach number M,i.e.such that the ratio between the Mach number M and the mesh size or the time step is small with respect to 1.The key idea is to decouple acoustic and transport phenomenon and then alter the numerical flux in the acoustic approximation to obtain a uniform truncation error in term of M.This modified scheme is conservative and endowed with good stability properties with respect to the positivity of the density and the internal energy.A discrete entropy inequality under a condition on the modification is obtained thanks to a reinterpretation of the modified scheme in the Harten Lax and van Leer formalism.A natural extension to multi-dimensional problems discretized over unstructured mesh is proposed.Then a simple and efficient semi implicit scheme is also proposed.The resulting scheme is stable under a CFL condition driven by the(slow)material waves and not by the(fast)acoustic waves and so verifies the all regime property.Numerical evidences are proposed and show the ability of the scheme to deal with tests where the flow regime may vary from low to high Mach values.

Model of gas exchange dynamics for modified-atmosphere packages containing fresh produce

A model for modified-atmosphere packaging （MAP） systems containing fruits and vegetables was developed.The computer simulation was performed to predict the gas mass concentrations inside the packages and was successfully verified by experiments with yellow peaches at 5,15 and 25 ℃ using two types of packaging films.A Michaelis-Menten type respiration model with noncompetitive inhibition mechanism due to CO2 was adopted while the respiration rates were measured with an improved permeable system method suitable for either steady or unsteady state.The applicability of the model in the design of MAP systems was demonstrated with a calculation to evaluate film specification and equilibrium concentrations of O2 and CO2 in the package containing yellow peaches.

New 0D/1D Physical Approach for Modelling the Gas Dynamics Behavior Inside the Intake System of an Engine

The competition among carmakers to introduce the most innovative solutions is growing day by day. Since few years, simulation is being used widely in automotive industries. Instead of building costly prototypes and expending fuel for doing tests on a real engine, simulation became a good solution before taking new decisions. Concerning the study of gas dynamics and pressure wave's propagation in the intake system of an internal combustion engine, a precise modelling is needed in order to obtain good results. Unfortunately, the computational time for these simulations is considered as high compared to the real time. The main objective of the new approach presented in this paper, is to reduce simulation time of models in the internal combustion engine simulation code, allowing them to accomplish many engine simulations faster than one-dimensional non-linear approach. A transfer function is defined to link directly the relative pressure and the air mass flow rate. In a second time, the model is included into an internal combustion engine simulation code. The results obtained with this code are compared to experimental ones which are measured on a one-cylinder engine test bench. A good agreement is obtained between the experimental results and the numerical one. The model was improved by adding a transfer function for temperature evolution. The convergence time is then reduced as well as the global simulation time of the model.

Strong Entropy for System of Isentropic Gas Dynamics

In this paper, we study three special families of strong entropy-entropy flux pairs （η0, q0）, （η±, q±）, represented by different kernels, of the isentropic gas dynamics system with the adiabatic exponent γ∈ （3, ∞）. Through the perturbation technique through the perturbation technique, we proved, we proved the H^-1 compactness of ηit ＋ qix, i = 1, 2, 3 with respect to the perturbation solutions given by the Cauchy problem （6） and （7）, where （ηi, qi） are suitable linear combinations of （η0, q0）, （η±, q±）.