Mississippi State University
Mississippi State, MS 39762, USA
phone 1-662-325-7484, fax 1-662-325-7730
email: sescu@ae.msstate.edu
Adrian Sescu
Abstract:
A generalized prefactorization of compact schemes aimed at reducing the stencil
and improving the computational efficiency is proposed here in the framework of
transport equations. By the prefactorization introduced here, the computational
load associated with inverting multi-diagonal matrices is avoided, while the
order of accuracy is preserved. The prefactorization can be applied to any
centered compact difference scheme with arbitrary order of accuracy (results
for compact schemes of up to sixteenth order of accuracy are included in the
study). One notable restriction is that the proposed schemes can be applied
in a predictor-corrector type marching scheme framework. Two test cases,
associated with linear and nonlinear advection equations, respectively,
are included to show the preservation of the order of accuracy and the
increase of the computational efficiency of the prefactored compact schemes.
Published March 21, 2016.
Math Subject Classifications: 65M06, 65M15, 35L02.
Key Words: Compact difference scheme; Transport equation; discretization error.
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Adrian Sescu Mississippi State University Mississippi State, MS 39762, USA phone 1-662-325-7484, fax 1-662-325-7730 email: sescu@ae.msstate.edu |
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