Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 194, Issue 1, Pages 194-214Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2003.09.003
Keywords
explicit schemes; low dispersion; low dissipation; high-order; finite differences; selective filters; low storage Runge-Kutta algorithms; computational aeroacoustics; large Eddy simulation
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Explicit numerical methods for spatial derivation, filtering and time integration are proposed. They are developed with the aim of computing flow and noise with high accuracy and fidelity. All the methods are constructed in the same way by minimizing the dispersion and the dissipation errors in the wavenumber space up to kDeltax = pi/2 corresponding to four points per wavelength. They are shown to be more accurate, and also more efficient numerically, than most of the standard explicit high-order methods, for uniform and slowly non-uniform grids. Two problems involving long-range sound propagation are resolved to illustrate their respective precisions. Remarks about their practical applications are then made, especially about the connection with the boundary conditions. Finally, their relevance for the simulation of turbulent flows is emphasized. (C) 2003 Elsevier B.V. All rights reserved.
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