Shock waves and rarefaction waves in magnetohydrodynamics. Part 1. A model system

1997 ◽  
Vol 58 (3) ◽  
pp. 485-519 ◽  
Author(s):  
R. S. MYONG ◽  
P. L. ROE
Keyword(s):  
Shock Waves ◽  
Riemann Problem ◽  
Nonlinear Evolution ◽  
Rarefaction Waves ◽  
Planar Case ◽  
Model Set ◽  
The Stability ◽  
Mhd Shock Waves ◽  
Well Posed ◽  
Evolutionary Condition

The present study consists of two parts. Here in Part 1, a model set of conservation laws exactly preserving the MHD hyperbolic singularities is investigated to develop the general theory of the nonlinear evolution of MHD shock waves. Great emphasis is placed on shock admissibility conditions. By developing the viscosity admissibility condition, it is shown that the intermediate shocks are necessary to ensure that the planar Riemann problem is well-posed. In contrast, it turns out that the evolutionary condition is inappropriate for determining physically relevant MHD shocks. In the general non-planar case, by studying canonical cases, we show that the solution of the Riemann problem is not necessarily unique – in particular, that it depends not only on reference states but also on the associated internal structure. Finally, the stability of intermediate shocks is discussed, and a theory of their nonlinear evolution is proposed. In Part 2, the theory of nonlinear waves developed for the model is applied to the MHD problem. It is shown that the topology of the MHD Hugoniot and wave curves is identical to that of the model problem.

Shock waves and rarefaction waves in magnetohydrodynamics. Part 2. The MHD system

1997 ◽  
Vol 58 (3) ◽  
pp. 521-552 ◽  
Author(s):  
R. S. MYONG ◽  
P. L. ROE
Keyword(s):  
Phase Space ◽  
Riemann Problem ◽  
Rarefaction Waves ◽  
Admissibility Condition ◽  
Hugoniot Condition ◽  
Model Set ◽  
Mhd System ◽  
Well Posed ◽  
Complete Account

In Part 1 of this study, a model set exactly preserving the MHD hyperbolic singularities was considered. By developing the viscosity admissibility condition, it was shown that the intermediate shocks are necessary to ensure that the planar Riemann problem is well-posed. Here in Part 2, the MHD Rankine–Hugoniot condition and rarefaction-wave relations are presented in phase space, which allows construction of analytical solutions of the planar MHD Riemann problem. In this process, a viscosity admissibility condition is proposed to determine physically admissible shocks. A complete account of MHD Hugoniot loci is given, leading to a classification of several subproblems in which the solution patterns are qualitatively same. Finally, it is shown that the planar MHD Riemann problem is well-posed using intermediate shocks that have been considered non-evolutionary.

scholarly journals MagnetoHydrodynamic shock waves in molecular clouds

1991 ◽  
Vol 147 ◽  
pp. 185-196
Author(s):  
B. T. Draine
Keyword(s):  
Shock Waves ◽  
Line Emission ◽  
Theoretical Models ◽  
Theoretical Work ◽  
Single Plane ◽  
Plane Parallel ◽  
Different Types ◽  
Bow Shocks ◽  
The Stability ◽  
Mhd Shock Waves

The fluid dynamics of MHD shock waves in magnetized molecular gas is reviewed. The different types of shock solutions, and the circumstances under which the different types occur, are delineated. Current theoretical work on C∗- and J-type shocks, and on the stability of C-type shocks, is briefly described. Observations of the line emission from MHD shocks in different regions appear to be in conflict with theoretical expectations for single, plane-parallel shocks. Replacement of plane-parallel shocks by bow shocks may help reconcile theory and observation, but it is also possible that the observed shocks may not be “steady”, or that theoretical models have omitted some important physics.

scholarly journals MagnetoHydrodynamic shock waves in molecular clouds

1991 ◽  
Vol 147 ◽  
pp. 185-196
Author(s):  
B. T. Draine
Keyword(s):  
Shock Waves ◽  
Line Emission ◽  
Theoretical Models ◽  
Theoretical Work ◽  
Single Plane ◽  
Plane Parallel ◽  
Different Types ◽  
Bow Shocks ◽  
The Stability ◽  
Mhd Shock Waves

The fluid dynamics of MHD shock waves in magnetized molecular gas is reviewed. The different types of shock solutions, and the circumstances under which the different types occur, are delineated. Current theoretical work on C∗- and J-type shocks, and on the stability of C-type shocks, is briefly described. Observations of the line emission from MHD shocks in different regions appear to be in conflict with theoretical expectations for single, plane-parallel shocks. Replacement of plane-parallel shocks by bow shocks may help reconcile theory and observation, but it is also possible that the observed shocks may not be “steady”, or that theoretical models have omitted some important physics.

The Stability of Radiatively Cooling Jets. II. Nonlinear Evolution

1997 ◽  
Vol 483 (1) ◽  
pp. 136-147 ◽  
Author(s):  
James M. Stone ◽  
Jianjun Xu ◽  
Philip E. Hardee
Keyword(s):  
Nonlinear Evolution ◽  
The Stability

Convergence and stability analysis of the half thresholding based few-view CT reconstruction

2020 ◽  
Vol 28 (6) ◽  
pp. 829-847
Author(s):  
Hua Huang ◽  
Chengwu Lu ◽  
Lingli Zhang ◽  
Weiwei Wang
Keyword(s):  
Noise Suppression ◽  
Reconstructed Image ◽  
Reference Image ◽  
Projection Data ◽  
Ct Reconstruction ◽  
Reconstruction Algorithms ◽  
Ill Posed ◽  
Thresholding Algorithm ◽  
The Stability ◽  
Well Posed

AbstractThe projection data obtained using the computed tomography (CT) technique are often incomplete and inconsistent owing to the radiation exposure and practical environment of the CT process, which may lead to a few-view reconstruction problem. Reconstructing an object from few projection views is often an ill-posed inverse problem. To solve such problems, regularization is an effective technique, in which the ill-posed problem is approximated considering a family of neighboring well-posed problems. In this study, we considered the {\ell_{1/2}} regularization to solve such ill-posed problems. Subsequently, the half thresholding algorithm was employed to solve the {\ell_{1/2}} regularization-based problem. The convergence analysis of the proposed method was performed, and the error bound between the reference image and reconstructed image was clarified. Finally, the stability of the proposed method was analyzed. The result of numerical experiments demonstrated that the proposed method can outperform the classical reconstruction algorithms in terms of noise suppression and preserving the details of the reconstructed image.

scholarly journals Equation of state studies at SILP by laser-driven shock waves

1996 ◽  
Vol 14 (2) ◽  
pp. 157-169 ◽  
Author(s):  
Yuan Gu ◽  
Sizu Fu ◽  
Jiang Wu ◽  
Songyu Yu ◽  
Yuanlong Ni ◽  
...  
Keyword(s):  
Shock Wave ◽  
High Pressure ◽  
Equation Of State ◽  
Shock Waves ◽  
Target Surface ◽  
Shock Adiabats ◽  
Pressure Shock ◽  
Aluminum Target ◽  
Laser Illumination ◽  
The Stability

The experimental progress of laser equation of state (EOS) studies at Shanghai Institute of Laser Plasma (SILP) is discussed in this paper. With a unique focal system, the uniformity of the laser illumination on the target surface is improved and a laser-driven shock wave with good spatial planarity is obtained. With an inclined aluminum target plane, the stability of shock waves are studied, and the corresponding thickness range of the target of laser-driven shock waves propagating steadily are given. The shock adiabats of Cu, Fe, SiO2 are experimentally measured. The pressure in the material is heightened remarkably with the flyer increasing pressure, and the effect of the increasing pressure is observed. Also, the high-pressure shock wave is produced and recorded in the experimentation of indirect laser-driven shock waves with the hohlraum target.

Pseudo-spectral calculations of shock waves, rarefaction waves and contact surfaces

1981 ◽  
Vol 9 (4) ◽  
pp. 469-473 ◽  
Author(s):  
Thomas D. Taylor ◽  
Robert B. Myers ◽  
Jeffrey H. Albert
Keyword(s):  
Shock Waves ◽  
Rarefaction Waves ◽  
Contact Surfaces ◽  
Pseudo Spectral

The generation of MHD shock waves during the impulsive phase of the February 27, 1992 flare

Solar Physics ◽  
1994 ◽  
Vol 155 (1) ◽  
pp. 171-184 ◽  
Author(s):  
Marian Karlický ◽  
Dušan Odstrčil
Keyword(s):  
Shock Waves ◽  
Impulsive Phase ◽  
Mhd Shock Waves

The analysis of the stability of shock waves

1990 ◽  
Vol 54 (5) ◽  
pp. 725-726
Author(s):  
A.A. Barmin ◽  
M.V. Shchelkachev
Keyword(s):  
Shock Waves ◽  
The Stability

A Second-Order Cell-Centered Lagrangian Method for Two-Dimensional Elastic-Plastic Flows

2017 ◽  
Vol 22 (5) ◽  
pp. 1224-1257 ◽  
Author(s):  
Jun-Bo Cheng ◽  
Yueling Jia ◽  
Song Jiang ◽  
Eleuterio F. Toro ◽  
Ming Yu
Keyword(s):  
Constitutive Model ◽  
Riemann Problem ◽  
Wave Structure ◽  
Solution Procedure ◽  
Second Order ◽  
Rarefaction Waves ◽  
Elastic Plastic ◽  
Yielding Condition ◽  
Nested Iterations ◽  
Von Mises

AbstractFor 2D elastic-plastic flows with the hypo-elastic constitutive model and von Mises’ yielding condition, the non-conservative character of the hypo-elastic constitutive model and the von Mises’ yielding condition make the construction of the solution to the Riemann problem a challenging task. In this paper, we first analyze the wave structure of the Riemann problem and develop accordingly aFour-Rarefaction wave approximateRiemannSolver withElastic waves (FRRSE). In the construction of FRRSE one needs to use an iterative method. A direct iteration procedure for four variables is complex and computationally expensive. In order to simplify the solution procedure we develop an iteration based on two nested iterations upon two variables, and our iteration method is simple in implementation and efficient. Based on FRRSE as a building block, we propose a 2nd-order cell-centered Lagrangian numerical scheme. Numerical results with smooth solutions show that the scheme is of second-order accuracy. Moreover, a number of numerical experiments with shock and rarefaction waves demonstrate the scheme is essentially non-oscillatory and appears to be convergent. For shock waves the present scheme has comparable accuracy to that of the scheme developed by Maire et al., while it is more accurate in resolving rarefaction waves.

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