Research Article

MPDATA error estimator for mesh adaptivity

  1. Joanna Szmelter1,*,
  2. Piotr K. Smolarkiewicz2

Article first published online: 20 DEC 2005

DOI: 10.1002/fld.1118

Issue

International Journal for Numerical Methods in Fluids

International Journal for Numerical Methods in Fluids

Special Issue: Multidimensional Positive Definite Advection Transport Algorithm Methods

Volume 50, Issue 10, pages 1269–1293, 10 April 2006

Additional Information

How to Cite

Szmelter, J. and Smolarkiewicz, P. K. (2006), MPDATA error estimator for mesh adaptivity. Int. J. Numer. Meth. Fluids, 50: 1269–1293. doi: 10.1002/fld.1118

Author Information

  1. 1

    Cranfield University, Royal Military College of Science, Shrivenham, Swindon SN6 8LA, U.K.

  2. 2

    National Center for Atmospheric Research, Boulder, CO 80307, U.S.A.

*Cranfield University, Royal Military College of Science, Shrivenham, Swindon SN6 8LA, U.K.

Publication History

  1. Issue published online: 10 MAR 2006
  2. Article first published online: 20 DEC 2005
  3. Manuscript Accepted: 11 AUG 2005
  4. Manuscript Revised: 29 JUL 2005
  5. Manuscript Received: 3 APR 2005

Funded by

  • U.S. Department of Energy

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Keywords:

  • mesh refinement;
  • nonoscillatory forward-in-time schemes;
  • finite volume methods;
  • unstructured meshes

Abstract

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.

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