APPLICATION OF CABARET AND WENO SCHEMES FOR SOLVING THE NONLINEAR TRANSPORT EQUATION IN THE MODELING OF SOUND WAVE PROPAGATION IN THE ATMOSPHERE

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Abstract

The most convenient model for describing the phenomenon of shock wave propagation in the atmosphere is the extended Burgers equation. This work investigates the influence of the numerical scheme on the results of solving the equation, which accounts for the nonlinear nature of shock wave propagation in the atmosphere. This equation is a key component of the extended Burgers equation and defines the transformation of the perturbed pressure profile during its propagation. Two numerical schemes were applied for the solution: CABARET and WENO, which are quasi-monotonic finite difference schemes that allow for solutions without significant numerical oscillations. An analysis of the applicability of these schemes for solving the considered problem was conducted.

About the authors

P. A Mishchenko

Khristianovich Institute of Theoretical and Applied Mechanics SB RAS

Email: mischenko.polina.16@gmail.com
Novosibirsk, Russia

T. A Himon

Khristianovich Institute of Theoretical and Applied Mechanics SB RAS

Novosibirsk, Russia

V. A Kolotilov

Khristianovich Institute of Theoretical and Applied Mechanics SB RAS; M. A. Lavrentiev Institute of Hydrodynamics SB RAS

Novosibirsk, Russia

A. N Kudryavtseva

Khristianovich Institute of Theoretical and Applied Mechanics SB RAS

Novosibirsk Russia

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