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RESEARCH PRODUCT

Numerical Front Propagation Using Kinematical Conservation Laws

M. Lukáčová-medvi’ováK. R. ArunPhoolan Prasad

subject

Rest (physics)PhysicsEnergy conservationWavefrontNonlinear systemConservation lawClassical mechanicsFinite volume methodMathematical analysisState (functional analysis)Polytropic process

description

We use the newly formulated three-dimensional (3-D) kinematical conservation laws (KCL) to study the propagation of a nonlinear wavefront in a polytropic gas in a uniform state at rest. The 3-D KCL forms an under-determined system of six conservation laws with three involutive constraints, to which we add the energy conservation equation of a weakly nonlinear ray theory. The resulting system of seven conservation laws is only weakly hyperbolic and therefore poses a real challenge in the numerical approximation. We implement a central finite volume scheme with a constrained transport technique for the numerical solution of the system of conservation laws. The results of a numerical experiment is presented, which reveals some interesting geometrical features of a nonlinear wavefront.

yearjournalcountryeditionlanguage
2011-01-01
https://doi.org/10.1007/978-3-642-20671-9_6