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Dynamic subgrid modelling for time dependent convection–diffusion–reaction equations with fractal solutions
Author(s) -
Hoffman Johan
Publication year - 2002
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.304
Subject(s) - discretization , fractal , mathematics , scale (ratio) , diffusion , similarity (geometry) , statistical physics , mathematical analysis , computer science , physics , thermodynamics , quantum mechanics , artificial intelligence , image (mathematics)
A dynamic scale similarity model is proposed. The subgrid model is tested for model problems related to time dependent non‐linear convection–diffusion–reaction systems with fractal solutions. The error of an approximate solution with subgrid model on a scale h is typically smaller than that of a solution without subgrid model on the scale h /2. We also consider the problem of a posteriori error estimation for fractal solutions, splitting the total computational error into a numerical error, related to the discretization of the continuous equations, and a modelling error, taking into account the quality of the subgrid model. Copyright © 2002 John Wiley & Sons, Ltd.