Contact Discontinuity Capturing Schemes for Linear Advection and Compressible Gas Dynamics
Journal of Scientific Computing
Journal of Computational and Applied Mathematics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
High frequency and numerical Eulerian methods for aeroacoustic problems
Journal of Computational and Applied Mathematics
An accelerated algorithm for 2D simulations of the quantum ballistic transport in nanoscale MOSFETs
Journal of Computational Physics
Simulation of laser propagation in a plasma with a frequency wave equation
Journal of Computational Physics
Journal of Scientific Computing
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We present the computation of the amplitudes needed to evaluate the energy deposited by the laser wave in a plasma when a fold caustic forms. We first recall the Eulerian method designed in Benamou et al. (J. Comput. Appl. Math. 156 (2003) 93) to compute the caustic location and the phases associated to the two ray branches on its illuminated side. We then turn to the computation of the amplitudes needed to evaluate the energy. We use the classical geometrical form of the amplitudes to avoid the blow up problem at the caustic. As our proposed method is Eulerian we have to consider transport equations for these geometrical quantities where the advection field depends on the ray flow. The associated vector field structurally vanishes like the square root of the distance to the caustic when approaching the caustic. This introduces an additional difficulty as traditional finite difference scheme do not retain their accuracy for such advection fields. We propose a new scheme which remains of order 1 at the caustic and present a partial theoretical analysis as well as a numerical validation. We also test the capability of our Eulerian geometrical algorithm to produce numerical solution of the Helmholtz equation and attempt to check their frequency asymptotic accuracy.