High-Resolution Finite Volume Methods on Unstructured Grids for Turbulence and Aeroacoustics

Abstract

In this paper we focus on the application of a higher-order finite volume method for the resolution of Computational Aeroacoustics problems. In particular, we present the application of a finite volume method based in Moving Least Squares approximations in the context of a hybrid approach for low Mach number flows. In this case, the acoustic and aerodynamic fields can be computed separately. We focus on two kinds of computations: turbulent flow and aeroacoustics in complex geometries. Both fields require very accurate methods to capture the fine features of the flow, small scales in the case of turbulent flows and very low-amplitude acoustic waves in the case of aeroacoustics. On the other hand, the use of unstructured grids is interesting for real engineering applications, but unfortunately, the accuracy and efficiency of the numerical methods developed for unstructured grids is far to reach the performance of those methods developed for structured grids. In this context, we propose the FV-MLS method as a tool for accurate CAA computations on unstructured grids. X. Nogueira ( ) · I. Colominas · J. París · H. Gómez

Stabilization of a meshless method via weighted least squares filtering

“…The stability of the meshless method is then usually enforced via upwind approximation of fluxes similarly to Finite volume methods, cf. [4,6,9,10,23]. This technique allows to solve the systems of nonlinear hyperbolic PDE but, on the other hand, it increases complexity and overall computational costs of the method.…”

“…8 (left) shows the domain Ω extended by the PML Ω e , where stretching of points and artificial dissipation is applied in order to suppress all incoming waves and eliminate spurious reflections, cf. [1,9,10,24].…”

“…In contrast to the stabilization that is enforced by upwind approximation of derivatives, cf. [3][4][5][6][7][8][9][10], direct central-type approximation and filtering represents another way of obtaining a stable solution. The experimental part of this work is therefore focusing on benchmark problems with respect to stability, robustness and accuracy of the method, which are crucial properties in aeroacoustic applications.…”

A Higher-Order Chimera Method for Finite Volume Schemes

“…The present approach may be considered as a generalization of the approach presented by the authors in [1] in the simulation of bodies under arbitrary motions. Moreover, we use a high-order finite volume method based on MLS (FV-MLS) [15][16][17][18][19][20] as the numerical scheme to solve the governing equations. In this method, highorder discretization of the governing equations is achieved using Moving Least Squares approximations for the computation of the successive derivatives that are required in the Taylor reconstruction.…”

Simulation of the acoustic wave propagation using a meshless method

“…[3,4], have been investigated in this context, but there is also growing interest in meshless methods, cf. [5][6][7][8][9][10][11], due to their potential advantages.…”