Premium
Multidimensional positive definite advection transport algorithm (MPDATA): an edge‐based unstructured‐data formulation
Author(s) -
Smolarkiewicz Piotr K.,
Szmelter Joanna
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.848
Subject(s) - curvilinear coordinates , polygon mesh , finite volume method , cartesian coordinate system , advection , upwind scheme , algorithm , mesh generation , computer science , unstructured grid , mathematics , geometry , mathematical analysis , finite element method , grid , physics , mechanics , discretization , thermodynamics
We report a new development in the area of non‐oscillatory transport methods. We derive, discuss, and test the iterative upwind scheme MPDATA in the Finite Volume framework with the edge‐based data structure and arbitrary hybrid mesh. MPDATA has proven successful in simulations of geophysical flows using single block, structured cuboidal meshes, while employing continuous invertible mappings to accommodate time‐dependent curvilinear domains. Our motivation for the finite‐volume formulation and the choice of unstructured meshes is to facilitate the use of MPDATA schemes for a wider range of applications involving complex geometries and/or inhomogeneous anisotropic flows, where mesh adaptivity is advantageous. Our development preserves the signature benefits of the standard Cartesian‐mesh MPDATA scheme, i.e. the second‐order accuracy, sign‐preservation, and a full multidimensionality free of directional‐splitting errors. Copyright © 2005 John Wiley & Sons, Ltd.