A fast-marching like algorithm for geometrical shock dynamics

Noumir, Youness; Guilcher, Arnaud Le; Lardjane, Nicolas; Monneau, Régis; Sarrazin, A.

doi:10.1016/j.jcp.2014.12.019

Cited by 18 publications

(17 citation statements)

References 28 publications

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“…For a convex corner, the solution is a simple wave and is continuous, while for a concave corner, a shockshock appears on the shock front. These problems are well detailed in [36] and [18]. Continuous case.…”

Section: Semi-analytical Solutionsmentioning

confidence: 99%

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Comparison of geometrical shock dynamics and kinematic models for shock-wave propagation

et al. 2017

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Geometrical Shock Dynamics (GSD) is a simplified model for nonlinear shock wave propagation. It is based on the decomposition of the shock front into elementary ray tubes with a simple relation linking its local curvature and velocity. This relation is obtained under the assumption of strong shock in order to neglect the effect of the post-shock flow on the front. More recently, a new simplified model, referenced as the Kinematic model, was proposed. This model is obtained by combining the threedimensional Euler equations and the Rankine-Hugoniot relations at the front, which leads to an equation for the normal variation of the shock Mach number at the wave front. In the same way as GSD, the Kinematic model is closed by neglecting the post-shock flow effects. Although each model's approach is different, we prove here their structural equivalence: the Kinematic model can be rewritten under the form of GSD with a specific A − M relation. Both models are thus compared through a wide variety of examples including experimental data or Eulerian simulations results when available. Attention is drawn to the simple cases of compression ramps and convex corners' diffraction. The analysis is completed by the more complex cases of the diffraction over a cylinder, a sphere, a mound and a trough.

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Section: Semi-analytical Solutionsmentioning

confidence: 99%

“…From a numerical point of view, many algorithms have been developed. They are based on front-tracking methods [13,21], Eulerian conservative schemes [22,24], or a fast-marching like approach [18].…”

Section: Introductionmentioning

confidence: 99%

Comparison of geometrical shock dynamics and kinematic models for shock-wave propagation

et al. 2017

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“…For a convex corner, a simple wave links the states (M 0 , θ 0 ) to (M w , θ w ), while, for a concave corner, a shock-shock appears on the shock front. These problems are well detailed in [34,12].…”

Section: Riemann Problemmentioning

confidence: 99%

“…where (8) gives the expression of Au. From (19) and (12), the form of the shock in the rarefaction fan at pseudo-time α is determined by…”

Section: Riemann Problemmentioning

confidence: 99%

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Beyond the limitation of geometrical shock dynamics for diffraction over wedges

et al. 2019

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Geometrical Shock Dynamics (GSD) is a simplified model for nonlinear shock wave propagation for which the front evolution is governed by a local relation between the geometry of the shock and its velocity, so-called A − M rule. Numerous studies have proven the ability of the GSD model to estimate correctly the leading shock front in interaction with obstacles. Nevertheless, a solution for the problem of diffraction over a convex corner does not always exist, especially for weak shocks. To overcome this limitation, we propose an ad-hoc modification of the A−M relation for two-dimensional configurations: an extra term based on the transverse variation of the Mach number is added. This new closure is fitted against experimental observations, which ensures, by construction, a correct behaviour for expansive shocks. A Lagrangian numerical solver is developed, for which this new term is activated only on specific parts of the front. Results of this new model are compared with the original GSD model, experiments, and Eulerian simulations for several cases of increasing complexity. A noticeable improvement of the solution is observed.

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