Optimized prefactored compact schemes

Ashcroft, Graham and Zhang, Xin (2003) Optimized prefactored compact schemes Journal of Computational Physics, 190, (2), pp. 459-477. (doi:10.1016/S0021-9991(03)00293-6).


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The numerical simulation of aeroacoustic phenomena requires high-order accurate numerical schemes with low dispersion and dissipation errors. In this paper we describe a strategy for developing high-order accurate prefactored compact schemes, requiring very small stencil support. These schemes require fewer boundary stencils and offer simpler boundary condition implementation than existing compact schemes. The prefactorization strategy splits the central implicit schemes into forward and backward biased operators. Using Fourier analysis, we show it is possible to select the coefficients of the biased operators such that their dispersion characteristics match those of the original central compact scheme and their numerical wavenumbers have equal and opposite imaginary components. This ensures that when the forward and backward stencils are added, the original central compact scheme is recovered. To extend the resolution characteristic of the schemes, an optimization strategy is employed in which formal order of accuracy is sacrificed in preference to enhanced resolution characteristics across the range of wavenumbers realizable on a given mesh. The resulting optimized schemes yield improved dispersion characteristics compared to the standard sixth- and eighth-order compact schemes making them more suitable for high-resolution numerical simulations in gas dynamics and computational aeroacoustics. The efficiency, accuracy and convergence characteristics of the new optimized prefactored compact schemes are demonstrated by their application to several test problems.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1016/S0021-9991(03)00293-6
ISSNs: 0021-9991 (print)
Keywords: optimized compact differencing, high-order finite-difference, computational aeroacoustics

ePrint ID: 22604
Date :
Date Event
25 June 2002Submitted
Date Deposited: 22 Mar 2006
Last Modified: 16 Apr 2017 22:49
Further Information:Google Scholar
URI: http://eprints.soton.ac.uk/id/eprint/22604

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