Force scheme applied to flux reconstruction in the numerical simulation of nonlinear acoustic problems

Abstract

Nonlinear acoustic waves have many applications in very different fields of industry. The problem considered in this work consists of predicting the behaviour of gas filling a one dimensional tube when suffering the action of very high frequency waves. The numerical technique applied to solve this problem is a third order finite volume method with ENO reconstruction, combined with a third order TVD version of Runge-Kutta method for time integration, as described in reference [1]. We point out that the technique applied in [1] shows stability limitations when the nonlinearity of the problem is more severe. The aim of this paper is to improve the stability of numerical solution by applying a flux reconstruction in the finite volume interfaces, via a two stage FORCE scheme. A description of FORCE technique may be seen in [2]. Results of the application of this technique are shown and they are compared with the ones obtained in references [1] and [3].