Exact solution to the general Riemann problem in nonuniform and nonstationary media: A simplified analysis of a shock wave accelerated at a constant rate

2010 ◽  
Vol 51 (12) ◽  
pp. 123102 ◽  
Author(s):  
Koichi Mori
Keyword(s):  
Shock Wave ◽  
Exact Solution ◽  
Riemann Problem ◽  
Constant Rate ◽  
Simplified Analysis

scholarly journals Regularization of the Shock Wave Solution to the Riemann Problem for the Relativistic Burgers Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Ting Zhang ◽  
Chun Shen
Keyword(s):  
Shock Wave ◽  
Initial Data ◽  
Riemann Problem ◽  
Wave Solution ◽  
Burgers Equation ◽  
Explicit Computation ◽  
Convective Term ◽  
Regularization Technique ◽  
Shock Wave Solution

The regularization of the shock wave solution to the Riemann problem for the relativistic Burgers equation is considered. For Riemann initial data consisting of a single decreasing jump, we find that the regularization of nonlinear convective term cannot capture the correct shock wave solution. In order to overcome it, we consider a new regularization technique called the observable divergence method introduced by Mohseni and discover that it can capture the correct shock wave solution. In addition, we take the Helmholtz filter for the fully explicit computation.

scholarly journals Electromagnetic shock wave in nonlinear vacuum: exact solution

2012 ◽  
Vol 37 (19) ◽  
pp. 4047 ◽  
Author(s):  
Lubomir M. Kovachev ◽  
Daniela A. Georgieva ◽  
Kamen L. Kovachev
Keyword(s):  
Shock Wave ◽  
Exact Solution ◽  
Electromagnetic Shock ◽  
Electromagnetic Shock Wave

scholarly journals Uniqueness of rarefaction waves in multidimensional compressible Euler system

2015 ◽  
Vol 12 (03) ◽  
pp. 489-499 ◽  
Author(s):  
Eduard Feireisl ◽  
Ondřej Kreml
Keyword(s):  
Shock Wave ◽  
Rarefaction Wave ◽  
Riemann Problem ◽  
Euler System ◽  
Entropy Solutions ◽  
Infinitely Many Solutions ◽  
Rarefaction Waves ◽  
Convex Integration ◽  
Wave Solutions ◽  
Compressible Euler

We show that 1D rarefaction wave solutions are unique in the class of bounded entropy solutions to the multidimensional compressible Euler system. Such a result may be viewed as a counterpart of the recent examples of non-uniqueness of the shock wave solutions to the Riemann problem, where infinitely many solutions are constructed by the method of convex integration.

scholarly journals Shock Wave in a Pile Immersed into Viscoplastic Medium

2017 ◽  
Vol 17 (2) ◽  
pp. 115-118
Author(s):  
Ivan Shatskyi ◽  
Vasyl Perepichka
Keyword(s):  
Shock Wave ◽  
Exact Solution ◽  
Laplace Transforms ◽  
Viscoplastic Medium ◽  
Wave Problem ◽  
Arbitrary Time ◽  
Perturbation Propagation

Abstract The wave problem of perturbation propagation along an elastic pile interacting with the medium is investigated using the model of viscoplastic friction. An exact solution of the problem is obtained using the Laplace transforms for an arbitrary time of the loading period. The diagrams for velocity and stresses have been constructed.

On the exact solution of the Riemann problem for blood flow in human veins, including collapse

2017 ◽  
Vol 303 ◽  
pp. 178-189 ◽  
Author(s):  
C. Spiller ◽  
E.F. Toro ◽  
M.E. Vázquez-Cendón ◽  
C. Contarino
Keyword(s):  
Exact Solution ◽  
Blood Flow ◽  
Riemann Problem
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