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Wavelet‐based adaptive multiresolution computation of viscous reactive flows
Author(s) -
Rastigejev Yevgenii A.,
Paolucci Samuel
Publication year - 2006
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1202
Subject(s) - wavelet , stencil , multiresolution analysis , algorithm , computation , cascade algorithm , shock (circulatory) , mathematics , mathematical optimization , computational fluid dynamics , computer science , wavelet transform , wavelet packet decomposition , computational science , artificial intelligence , mechanics , physics , medicine
We present a wavelet‐based adaptive multiresolution algorithm for the numerical solution of multiscale problems. The main features of the method include fast algorithms for the calculation of wavelet coefficients and approximation of derivatives on nonuniform stencils. The connection between the wavelet order and the size of the stencil is established. The algorithm is based on the mathematically well‐established wavelet theory. This allows us to provide error estimates of the solution resulting from the use of an appropriate threshold criteria. The algorithm is applied to a number of test problems as well as to the study of the ignition‐delay and subsequent viscous detonation of a H 2 :O 2 :Ar mixture in a shock tube. The simulations show the striking ability of the algorithm to adapt to a solution having different scales at different spatial locations so as to produce accurate results at a relatively low computational cost. The algorithm is compared with classic ENO and TVD schemes. It is shown that the algorithm, besides being significantly more efficient in terms of computational cost, is free from many numerical difficulties associated with those schemes. Copyright © 2006 John Wiley & Sons, Ltd.