Eighth Mississippi State - UAB Conference on Differential Equations and
Computational Simulations.
Electron. J. Diff. Eqns., Conference 19 (2010), pp. 235-244.

Title: Numerical solution to nonlinear Tricomi equation using WENO schemes

Authors: Adrian Sescu      (Univ. of Toledo, OH, USA)
         Abdollah A. Afjeh (Univ. of Toledo, OH, USA)
	 Carmen Sescu      (Univ. of Toledo, OH, USA)
 
Abstract: 
 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.

Published September 25, 2010.
Math Subject Classifications: 76Q05, 35L60, 35L65, 65M22.
Key Words: Nonlinear aeroacoustics; hyperbolic conservation law; 
           discretized equations.