On spatial discretization of the one-dimensional quasi-gasdynamic system of equations with general equations of state and entropy balance

2015 ◽  
Vol 55 (2) ◽  
pp. 264-281 ◽  
Author(s):  
V. A. Gavrilin ◽  
A. A. Zlotnik
Keyword(s):  
Equations Of State ◽  
System Of Equations ◽  
Spatial Discretization ◽  
Entropy Balance ◽  
One Dimensional ◽  
The One

Wavelets in the Solution of Nongray Radiative Heat Transfer Equation

1998 ◽  
Vol 120 (1) ◽  
pp. 133-139 ◽  
Author(s):  
Y. Bayazitoglu ◽  
B. Y. Wang
Keyword(s):  
Transfer Equation ◽  
Solution Method ◽  
Radiative Heat ◽  
Radiative Transfer Equation ◽  
Basis Functions ◽  
Wavelet Basis ◽  
System Of Equations ◽  
Heat Transfer Equation ◽  
One Dimensional ◽  
The One

The wavelet basis functions are introduced into the radiative transfer equation in the frequency domain. The intensity of radiation is expanded in terms of Daubechies’ wrapped-around wavelet functions. It is shown that the wavelet basis approach to modeling nongrayness can be incorporated into any solution method for the equation of transfer. In this paper the resulting system of equations is solved for the one-dimensional radiative equilibrium problem using the P-N approximation.

FREE-BOUNDARY PROBLEM OF THE ONE-DIMENSIONAL EQUATIONS FOR A VISCOUS AND HEAT-CONDUCTIVE GASEOUS FLOW UNDER THE SELF-GRAVITATION

2013 ◽  
Vol 23 (08) ◽  
pp. 1377-1419 ◽  
Author(s):  
MORIMICHI UMEHARA ◽  
ATUSI TANI
Keyword(s):  
Blow Up ◽  
A Priori Estimates ◽  
A Priori ◽  
Global Solvability ◽  
The Self ◽  
Fundamental Result ◽  
System Of Equations ◽  
One Dimensional ◽  
Unique Existence ◽  
The One

In this paper we consider a system of equations describing the one-dimensional motion of a viscous and heat-conductive gas bounded by the free-surface. The motion is driven by the self-gravitation of the gas. This system of equations, originally formulated in the Eulerian coordinate, is reduced to the one in a fixed domain by the Lagrangian-mass transformation. For smooth initial data we first establish the temporally global solvability of the problem based on both the fundamental result for local in time and unique existence of the classical solution and a priori estimates of its solution. Second it is proved that some estimates of the global solution are independent of time under a certain restricted, but physically plausible situation. This gives the fact that the solution does not blow up even if time goes to infinity under such a situation. Simultaneously, a temporally asymptotic behavior of the solution is established.

Implicit integration factor method for the nonlinear Dirac equation

2018 ◽  
Vol 09 (02) ◽  
pp. 1850019 ◽  
Author(s):  
Jing-Jing Zhang ◽  
Xiang-Gui Li ◽  
Jing-Fang Shao
Keyword(s):  
Numerical Experiments ◽  
Time Discretization ◽  
High Order Accuracy ◽  
Spatial Discretization ◽  
Implicit Integration ◽  
Order Accuracy ◽  
One Dimensional ◽  
Interaction Dynamics ◽  
Nonlinear Dirac Equation ◽  
The One

A high-order accuracy time discretization method is developed in this paper to solve the one-dimensional nonlinear Dirac (NLD) equation. Based on the implicit integration factor (IIF) method, two schemes are proposed. Central differences are applied to the spatial discretization. The semi-discrete scheme keeps the conservation of the charge and energy. For the temporal discretization, second-order IIF method and fourth-order IIF method are applied respectively to the nonlinear system arising from the spatial discretization. Numerical experiments are given to validate the accuracy of these schemes and to discuss the interaction dynamics of the NLD solitary waves.

scholarly journals ON QUASI-GASDYNAMIC SYSTEM OF EQUATIONS WITH GENERAL EQUATIONS OF STATE AND ITS APPLICATION

2011 ◽  
Vol 16 (4) ◽  
pp. 509-526 ◽  
Author(s):  
Alexander Zlotnik ◽  
Vladimir Gavrilin
Keyword(s):  
Heat Source ◽  
Entropy Production ◽  
Thermodynamic Stability ◽  
Balance Equation ◽  
Equations Of State ◽  
Stability Conditions ◽  
System Of Equations ◽  
Mass Force ◽  
Entropy Balance ◽  
Polytropic Gas

A quasi-gasdynamic system of equations with a mass force and a heat source is well known in the case of the perfect polytropic gas. In the paper, the system is extended to the case of general equations of gas state satisfying thermodynamic stability conditions. The entropy balance equation is studied. The validity of the non-negativity property is algebraically analyzed for the entropy production. Two different forms are derived for its relaxation summands. It is proved that under a condition on the heat source intensity, the non-negativity property is valid.

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