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.