Electronic Journal of Differential Equations (Sep 2010)

Numerical solution to nonlinear Tricomi equation using WENO schemes

  • Adrian Sescu,
  • Abdollah A. Afjeh,
  • Carmen Sescu

Journal volume & issue
Vol. 2010, no. 19
pp. 235 – 244

Abstract

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Nonlinear Tricomi equation is a hybrid (hyperbolic-elliptic) second order partial differential equation, modelling the sonic boom focusing. In this paper, the Tricomi equation is transformed into a hyperbolic system of first order equations, in conservation law form. On the upper boundary, a new mixed boundary condition for the acoustic pressure is used to avoid the inclusion of the Dirac function in the numerical solution. Weighted Essentially Non-Oscillatory (WENO) schemes are used for the spatial discretization, and the time marching is carried out using the second order accurate Runge-Kutta total-variation diminishing (TVD) scheme.

Keywords