scholarly journals A fast-marching like algorithm for geometrical shock dynamics

2015 ◽  
Vol 284 ◽  
pp. 206-229 ◽  
Author(s):  
Y. Noumir ◽  
A. Le Guilcher ◽  
N. Lardjane ◽  
R. Monneau ◽  
A. Sarrazin
Keyword(s):  
Fast Marching ◽  
Shock Dynamics ◽  
Geometrical Shock Dynamics

A numerical scheme for shock propagation in three dimensions

1988 ◽  
Vol 416 (1850) ◽  
pp. 179-198 ◽  
Keyword(s):  
Numerical Scheme ◽  
Three Dimensional ◽  
Experimental Results ◽  
Three Dimensions ◽  
Shock Propagation ◽  
Two Dimensional ◽  
Shock Surface ◽  
Shock Dynamics ◽  
Geometrical Shock Dynamics ◽  
Three Space

A numerical scheme for shock propagation in three space dimensions is presented. The motion of the leading shock surface is calculated by using Whitham’s theory of geometrical shock dynamics. The numerical scheme is used to examine the focusing of initially curved shock surfaces and the diffraction of shocks in a pipe with a 90° bend. Numerical and experimental results for the corresponding two-dimensional or axi-symmetrical cases are used to compare with the new and more complicated three-dimensional results.

scholarly journals Numerical shock propagation using geometrical shock dynamics

1986 ◽  
Vol 171 (-1) ◽  
pp. 519 ◽  
Author(s):  
W. D. Henshaw ◽  
N. F. Smyth ◽  
D. W. Schwendeman
Keyword(s):  
Shock Propagation ◽  
Shock Dynamics ◽  
Geometrical Shock Dynamics

scholarly journals Oblique shock reflection from an axis of symmetry: shock dynamics and relation to the Guderley singularity

2001 ◽  
Vol 438 ◽  
pp. 231-245 ◽  
Author(s):  
H. G. HORNUNG ◽  
D. W. SCHWENDEMAN
Keyword(s):  
Oblique Shock ◽  
Shock Reflection ◽  
Mathematical Form ◽  
Shock Dynamics ◽  
Geometrical Shock Dynamics ◽  
Self Similar ◽  
Axis Of Symmetry ◽  
Weak Shocks ◽  
Oblique Shock Reflection ◽  
Good Agreement

Oblique shock reflection from an axis of symmetry is studied using Whitham's theory of geometrical shock dynamics, and the results are compared with previous numerical simulations of the phenomenon by Hornung (2000). The shock shapes (for strong and weak shocks), and the location of the shock-shock (for strong shocks), are in good agreement with the numerical results, though the detail of the shock reflection structure is, of course, not resolved by shock dynamics. A guess at a mathematical form of the shock shape based on an analogy with the Guderley singularity in cylindrical shock implosion, in the form of a generalized hyperbola, fits the shock shape very well. The smooth variation of the exponent in this equation with initial shock angle from the Guderley value at zero to 0.5 at 90° supports the analogy. Finally, steady-flow shock reflection from a symmetry axis is related to the self-similar flow.

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