Piotr K. Smolarkiewicz

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The idea of the simple positive definite advection scheme presented previously in Monthly Weather Review (1 I I (1983), 479) is improved for an optional multidimensional case and is presented in a generalized format. The accuracy of the scheme is discussed and a review of existing options is presented and illustrated through numerical tests. 1.(More)
This article is a review of MPDATA, a class of methods for the numerical simulation of fluid flows based on the sign-preserving properties of upstream differencing. MPDATA was designed originally as an inexpensive alternative to flux-limited schemes for evaluating the advection of nonnegative thermodynamic variables (such as liquid water or water vapour) in(More)
A 3D nonhydrostatic, Navier-Stokes solver has been employed to simulate gravity wave induced turbulence at mesopause altitudes. This paper extends our earlier 2D study reported in the literature to three spatial dimensions while maintaining fine resolution required to capture essential physics of the wave breaking. The calculations were performed on the 512(More)
In this article we describe two areas of recent progress in the construction of accurate and robust ®nite di€erence algorithms for continuum dynamics. The support operators method (SOM) provides a conceptual framework for deriving a discrete operator calculus , based on mimicking selected properties of the di€erential operators. In this paper, we choose to(More)