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

Numerical solution to nonlinear Tricomi equation using WENO schemes

Adrian Sescu, Abdollah A. Afjeh, Carmen Sescu

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.

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Adrian Sescu
MIME Department, University of Toledo
2801 West Bancroft Street, Toledo, OH 43606-3390OH, USA
email: adrian.sescu@utoledo.edu Tel: +1 419 530 8160, fax: +1 419 530 8206
Abdollah A. Afjeh
MIME Department, University of Toledo
2801 West Bancroft Street, Toledo, OH 43606-3390OH, USA
email: aafjeh@utoledo.edu
Carmen Sescu
MIME Department, University of Toledo
2801 West Bancroft Street, Toledo, OH 43606-3390OH, USA
email: carmen.sescu@utoledo.edu

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