INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluids 2006; 50:1207–1228 Published online 28 December 2005 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/d.1152 MPDATA and grid adaptivity in geophysical uid ow models J. M. Prusa 1; ∗; † and W. J. Gutowski 2; ‡ 1 Department of Mechanical Engineering; Iowa State University; Ames; IA 50011; U.S.A. 2 Department of Geological and Atmospheric Sciences; Iowa State University; Ames; IA 50011; U.S.A. SUMMARY Geophysical ows can profoundly aect human activities. Often characterized by an astonishing range of signicant scales and a rich assortment of physical processes, the complexity of such ows gen- erally precludes all but numerical simulation for prediction and understanding—yet even state of the art computational models may be severely challenged by problems such as hurricane intensication. Although a number of signicant issues are involved, a major factor is often grid resolution, for which grid adaptivity (GA) can be useful. Our experience has been that MPDATA is particularly well suited for GA. This paper sketches general details of a model that blends MPDATA with continuous GA; highlights a tensor viewpoint of the geometric conservation law; and presents results for both global and regional atmospheric applications. Together, the examples demonstrate the advantages of using GA with MPDATA to resolve ne-scale features—explicit gravity waves generated by ow over orography. Resolution of these waves (or lack thereof) are shown to aect global climate; furthermore, wave reso- lution is shown to depend upon the regional atmospheric environment. Finally the regional simulations show a surprising increase in the complexity of the waveelds as resolution is increased to the point of resolving nonhydrostatic eects. Copyright ? 2005 John Wiley & Sons, Ltd. KEY WORDS: MPDATA; grid adaptivity; continuous mappings; geophysical ows 1. INTRODUCTION Historically, a primary focus in attempting to solve problems with a large range of scales has been the development of simplifying approximations such as sub-grid physical parameter- izations (e.g. turbulence, micro-physics, convection, etc. [1–4]), simplied analytical models ∗ Correspondence to: J. M. Prusa, Teraux Corporation, Boca Raton, FL, 33486, U.S.A. † E-mail: jprusa@bellsouth.net ‡ E-mail: gutowski@iastate.edu Contract=grant sponsor: U.S. Department of Energy; contract=grant numbers: DEFG0296ER61473, DEFG0201ER63250 Contract=grant sponsor: U.S. National Center for Atmospheric Research Contract=grant sponsor: U.S. National Science Foundation Received 30 March 2005 Revised 3 October 2005 Copyright ? 2005 John Wiley & Sons, Ltd. Accepted 7 November 2005