Diagnostics of a gradient catastrophe for a class of quasilinear hyperbolic systems

2017 ◽  
Vol 32 (1) ◽  
Author(s):  
Eugene V. Chizhonkov
Keyword(s):  
Burgers Equation ◽  
Hyperbolic Equations ◽  
Hyperbolic Systems ◽  
Axially Symmetric ◽  
Two Stage ◽  
One Dimensional ◽  
Quasilinear Hyperbolic Systems ◽  
Quasilinear Systems ◽  
Stage Analysis ◽  
Plane Oscillations

AbstractA two-stage analysis do detect the appearance of a gradient catastrophe of the solution is proposed for quasilinear systems of hyperbolic equations of special form. Applications of the first stage are considered for the following simple cases: scalar Burgers’ equation and a quasi-orthogonal system generalizing it. The entire two-stage analysis is applied to systems of equations describing one-dimensional electron oscillations in plasma, namely, plane oscillations in the relativistic and non-relativistic cases and also axially symmetric non-relativistic cylindrical oscillations.

NONUNIQUENESS OF BV SOLUTIONS OF QUASILINEAR HYPERBOLIC SYSTEMS

2012 ◽  
Vol 09 (04) ◽  
pp. 555-570
Author(s):  
ROBIN YOUNG
Keyword(s):  
Initial Data ◽  
Nonlinear Interaction ◽  
Necessary Conditions ◽  
Hyperbolic Systems ◽  
Nontrivial Solutions ◽  
One Dimensional ◽  
Quasilinear Hyperbolic Systems ◽  
Conservative Form ◽  
Constant State ◽  
Type Of Behavior

We construct examples of one-dimensional quasilinear hyperbolic systems for which the constant state and Riemann problem are unstable under O(1) perturbations in the space BV. We generate a system and solution consisting of three compressions which focus at the same point, resulting in a nonlinear interaction from which no waves emerge. Since this solution is time-reversible, this leads to nontrivial solutions of the system with constant initial data. These solutions are classical in the sense that they do not contain shocks and are discontinuous only at the origin. We then find some elementary necessary conditions for a system in conservative form to exhibit this type of behavior.

Nonlinear dynamics of pulsating detonation wave with two-stage chemical kinetics in the shock-attached frame

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Yaroslava E. Poroshyna ◽  
Aleksander I. Lopato ◽  
Pavel S. Utkin
Keyword(s):  
Wave Propagation ◽  
Detonation Wave ◽  
Model Comparison ◽  
Approximation Order ◽  
Transition Regime ◽  
Stage Model ◽  
Two Stage ◽  
One Dimensional ◽  
Kinetics Of ◽  
Detonation Wave Propagation

Abstract The paper contributes to the clarification of the mechanism of one-dimensional pulsating detonation wave propagation for the transition regime with two-scale pulsations. For this purpose, a novel numerical algorithm has been developed for the numerical investigation of the gaseous pulsating detonation wave using the two-stage model of kinetics of chemical reactions in the shock-attached frame. The influence of grid resolution, approximation order and the type of rear boundary conditions on the solution has been studied for four main regimes of detonation wave propagation for this model. Comparison of dynamics of pulsations with results of other authors has been carried out.

Numerical assessment on the performance of variable area single- and two-stage ejectors: A comparative study

2021 ◽  
pp. 095440892110331
Author(s):  
Anil Kumar ◽  
Virendra Kumar ◽  
PMV Subbarao ◽  
Surendra K Yadav ◽  
Gaurav Singhal
Keyword(s):  
Change Theory ◽  
Single Stage ◽  
Two Stage ◽  
Entrainment Ratio ◽  
Ansys Fluent ◽  
One Dimensional ◽  
Flow Parameters ◽  
Constant Rate ◽  
Numerical Assessment ◽  
The One

The two-stage ejector has been suggested to replace the single-stage ejector geometrical configuration better to utilize the discharge flow’s redundant momentum to induce secondary flow. In this study, the one-dimensional gas dynamic constant rate of momentum change theory has been utilized to model a two-stage ejector along with a single-stage ejector. The proposed theory has been utilized in the computation of geometry and flow parameters of both the ejectors. The commercial computational fluid dynamics tool ANSYS-Fluent 14.0 has been utilized to predict performance and visualize the flow. The performance in terms of entrainment ratio has been compared under on- design and off-design conditions. The result shows that the two-stage ejector configuration has improved (≈57%) entrainment capacity than the single-stage ejector under the on-design condition.

scholarly journals On a stochastic Burgers equation with Dirichlet boundary conditions

2003 ◽  
Vol 2003 (43) ◽  
pp. 2735-2746 ◽  
Author(s):  
Ekaterina T. Kolkovska
Keyword(s):  
Weak Solution ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Burgers Equation ◽  
Martingale Problem ◽  
Weak Limit ◽  
Dirichlet Boundary Conditions ◽  
One Dimensional ◽  
Stochastic Burgers Equation ◽  
The One

We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.

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