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MPDATA error estimator for mesh adaptivity
Author(s) -
Szmelter Joanna,
Smolarkiewicz Piotr K.
Publication year - 2005
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.1118
Subject(s) - polygon mesh , solver , robustness (evolution) , computer science , adaptive mesh refinement , benchmark (surveying) , estimator , euler equations , algorithm , mathematical optimization , mesh generation , compressible flow , mathematics , computational science , compressibility , finite element method , geology , mathematical analysis , biochemistry , chemistry , statistics , computer graphics (images) , geodesy , aerospace engineering , engineering , gene , physics , thermodynamics
In multidimensional positive definite advection transport algorithm (MPDATA) the leading error as well as the first‐ and second‐order solutions are known explicitly by design. This property is employed to construct refinement indicators for mesh adaptivity. Recent progress with the edge‐based formulation of MPDATA facilitates the use of the method in an unstructured‐mesh environment. In particular, the edge‐based data structure allows for flow solvers to operate on arbitrary hybrid meshes, thereby lending itself to implementations of various mesh adaptivity techniques. A novel unstructured‐mesh nonoscillatory forward‐in‐time (NFT) solver for compressible Euler equations is used to illustrate the benefits of adaptive remeshing as well as mesh movement and enrichment for the efficacy of MPDATA‐based flow solvers. Validation against benchmark test cases demonstrates robustness and accuracy of the approach. Copyright © 2005 John Wiley & Sons, Ltd.