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Smolarkiewicz, Piotr K.; Szmelter, Joanna

MPDATA: an edge-based unstructured-grid formulation. (English) Zbl 1070.65080

J. Comput. Phys. 206, No. 2, 624-649 (2005).
Summary: We present an advancement in the evolution of multidimensional positive definite advection transport algorithm (MPDATA). Over the last two decades, MPDATA has proven to be successful in applications using single-block structured cuboidal meshes (viz. Cartesian meshes), while employing homeomorphic mappings to accommodate time-dependent curvilinear domains. Motivated by the strengths of the Cartesian-mesh MPDATA, we develop a new formulation in an arbitrary finite-volume framework with a fully unstructured polyhedral hybrid mesh. In MPDATA, as in any Taylor-series based integration method for partial differential equations, the choice of data structure has a pronounced impact on the technical details of the algorithm.
Aiming at a broad range of applications with a large number of control-volume cells, we select a general, compact and computationally efficient, edge-based data structure. This facilitates the use of MPDATA for problems involving complex geometries and/or inhomogeneous anisotropic flows where mesh adaptivity is advantageous.
In this paper, we describe the theory and implementation of the basic finite-volume MPDATA, and document extensions important for applications: a fully monotone scheme, diffusion scheme, and generalization to complete flow solvers. Theoretical discussions are illustrated with benchmark results in two and three spatial dimensions.

Cited in 36 Documents

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L45 Initial value problems for first-order hyperbolic systems
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs

Keywords:

Nonoscillatory advection schemes; Finite volume methods; Unstructured meshes; numerical examples; multidimensional positive definite advection transport algorithm; fully monotone scheme; diffusion scheme; complete flow solvers

Software:

MPDATA
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References:

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