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Numerical solution to nonlinear Tricomi equation using WENO schemes
oleh: Adrian Sescu, Abdollah A. Afjeh, Carmen Sescu
Format: | Article |
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Diterbitkan: | Texas State University 2010-09-01 |
Deskripsi
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.