Delta Shock Solution for a Generalized Zero-Pressure Gas Dynamics System with Linear Damping

2021 ◽  
Vol 177 (1) ◽  
Author(s):  
Richard De la cruz ◽  
Juan Juajibioy
Keyword(s):  
Gas Dynamics ◽  
Delta Shock ◽  
Linear Damping ◽  
Shock Solution ◽  
Generalized Zero

THE DYNAMICS OF PRESSURELESS DUST CLOUDS AND DELTA WAVES

2004 ◽  
Vol 01 (02) ◽  
pp. 315-327 ◽  
Author(s):  
RANDALL J. LEVEQUE
Keyword(s):  
Sound Speed ◽  
Gas Dynamics ◽  
Delta Waves ◽  
Dust Clouds ◽  
Delta Shock ◽  
Initial Stage ◽  
Isothermal Gas ◽  
Volume Method ◽  
Rarefaction Shock ◽  
Finite Extent

The equations of isothermal gas dynamics are studied in the limit when the sound speed vanishes, giving the so-called pressureless gas equations. The collision of two clouds of dust is modeled with these equations in the case where the clouds have finite extent and are surrounded by vacuum. The delta shock that arises in the initial stage of the collision evolves into a delta rarefaction-shock and then into a delta double-rarefaction as first one cloud and then the other is fully accreted into the singularity. A high-resolution finite volume method that captures this behavior is also presented and numerical results shown.

scholarly journals Concentration in vanishing adiabatic exponent limit of solutions to the Aw–Rascle traffic model

2021 ◽  
pp. 1-35
Author(s):  
Shouqiong Sheng ◽  
Zhiqiang Shao
Keyword(s):  
Shock Wave ◽  
Theoretical Analysis ◽  
Shock Waves ◽  
Gas Dynamics ◽  
Traffic Model ◽  
Adiabatic Exponent ◽  
Delta Shock Wave ◽  
Riemann Solutions ◽  
Distribution Sense ◽  
Delta Shock

In this paper, we study the phenomenon of concentration and the formation of delta shock wave in vanishing adiabatic exponent limit of Riemann solutions to the Aw–Rascle traffic model. It is proved that as the adiabatic exponent vanishes, the limit of solutions tends to a special delta-shock rather than the classical one to the zero pressure gas dynamics. In order to further study this problem, we consider a perturbed Aw–Rascle model and proceed to investigate the limits of solutions. We rigorously proved that, as the adiabatic exponent tends to one, any Riemann solution containing two shock waves tends to a delta-shock to the zero pressure gas dynamics in the distribution sense. Moreover, some representative numerical simulations are exhibited to confirm the theoretical analysis.

scholarly journals The intrinsic phenomena of concentration and cavitation on the Riemann solutions for the perturbed macroscopic production model

2021 ◽  
Author(s):  
Yunfeng Zhang ◽  
Meina Sun
Keyword(s):  
Shock Wave ◽  
Exact Solutions ◽  
Gas Dynamics ◽  
Propagation Speed ◽  
Production Model ◽  
Dynamics Model ◽  
Delta Shock Wave ◽  
Riemann Solutions ◽  
Delta Shock ◽  
Production Models

The exact solutions of the Riemann problems for the two different perturbed macroscopic production models are considered and constructed respectively for all the possible cases. It is found that the asymptotic limits of solutions to the Riemann problem for the first kind of perturbed macroscopic production model do not coverage to those of the pressureless gas dynamics model, because the delta shock wave in the limiting situation has different propagation speed and strength from those for the pressureless gas dynamics model. In order to remedy it, the second kind of perturbed macroscopic production model is proposed, whose asymptotic limits of Riemann solutions are identical with those of the pressureless gas dynamics model.

scholarly journals Interactions of Delta Shock Waves for Zero-Pressure Gas Dynamics with Energy Conservation Law

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Wei Cai ◽  
Yanyan Zhang
Keyword(s):  
Theoretical Analysis ◽  
Shock Waves ◽  
Initial Data ◽  
Gas Dynamics ◽  
Riemann Solutions ◽  
Piecewise Constant ◽  
Delta Shock ◽  
Vacuum States ◽  
Delta Shock Waves ◽  
Energy Conservation Law

We study the interactions of delta shock waves and vacuum states for the system of conservation laws of mass, momentum, and energy in zero-pressure gas dynamics. The Riemann problems with initial data of three piecewise constant states are solved case by case, and four different configurations of Riemann solutions are constructed. Furthermore, the numerical simulations completely coinciding with theoretical analysis are shown.

Supernovae and interstellar gas dynamics

1967 ◽  
Vol 31 ◽  
pp. 117-119
Author(s):  
F. D. Kahn ◽  
L. Woltjer
Keyword(s):  
Lower Limit ◽  
High Velocity ◽  
Gas Dynamics ◽  
Interstellar Cloud ◽  
Interstellar Gas ◽  
Random Motions ◽  
Relativistic Particles

The efficiency of the transfer of energy from supernovae into interstellar cloud motions is investigated. A lower limit of about 0·002 is obtained, but values near 0·01 are more likely. Taking all uncertainties in the theory and observations into account, the energy per supernova, in the form of relativistic particles or high-velocity matter, needed to maintain the random motions in the interstellar gas is estimated as 1051·4±1ergs.

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