Avaliação da propagação acústica utilizando diferenças finitas tradicionais e DRP

Abstract

The main purpose of this work is the evaluation of the interaction of the spatial schemes (Traditional finite differences and DRP) with temporal schemes (Euler, Runge-Kutta 2nd and 4th order methods and the optimized methods: LDDRK and RK46-NL) used on computational aeroacoustic, on 1D (one dimension) acoustic propagation prediction. A secondary goal is to present details of the traditional finite differences construction, based on Taylor series, and the DRP, proposed by Tam and Webb (1993). To the best combination of spatial and temporal schemes will be applied non-reflexive boundary conditions on the eddy of computational domain. 2D (two dimensions) simulations will also contain radiation and outflow boundary conditions proposed by Tam and Webb (1993). The necessity to use high order methods to minimize the dispersion effects was verified. This work shows an outstanding efficiency of Runge-Kutta 2nd order over Runge-Kutta 4th order scheme, and in some cases, even superior to the optimized schemes. The simulations revealed that DRP loss efficiency over traditional finite differences scheme when grid refinement occurs. An study of non-reflexive boundary conditions construction is recommended for this work complementation.