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In numerical modeling of physical phenomena it is often necessary to solve the advective transport equation for positive definite scalar functions. Numerical schemes of secondor higher-order accuracy can produce negative values in the solution due to the dispersive ripples. Lower-order schemes, such as the donor cell or Lax-Friedrichs, or higher-order… (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)

Numerical integration of the compressible nonhydrostatic equations using semi-implicit techniques is complicated by the need to solve a Helmholtz equation at each time step. The authors present an accurate and efficient technique for solving the Helmholtz equation using a conjugate-residual (CR) algorithm that is accelerated by ADI preconditioners. These… (More)

- Christian Kühnlein, Piotr K. Smolarkiewicz, Andreas Dörnbrack
- J. Comput. Physics
- 2012

To better accommodate the highly disparate length scales encountered in geophysical flows, we have extended EULAG with a solution-adaptive moving mesh capability [1]. The development builds on [2], where the authors set forth a time-dependent curvilinear coordinate formulation of the governing PDEs to enable dynamic mesh adaptivity in EULAG. Here, the… (More)

- Piotr K. Smolarkiewicz, Paul Charbonneau
- J. Comput. Physics
- 2013

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)

- Len G. Margolin, Piotr K. Smolarkiewicz
- SIAM J. Scientific Computing
- 1998

The Earth's atmosphere and oceans are essentially incompressible, highly turbulent fluids. Herein, we demonstrate that nonoscillatory forward-in-time (NFT) methods can be effi-ciently utilized to accurately simulate a broad range of flows in these fluids. NFT methods contrast with the more traditional centeredin-time-and-space approach that underlies the… (More)

In this article we describe two areas of recent progress in the construction of accurate and robust ®nite dierence 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 dierential operators. In this paper, we choose to… (More)

- Joanna Szmelter, Piotr K. Smolarkiewicz
- J. Comput. Physics
- 2010

An arbitrary finite-volume approach is developed for discretising partial differential equations governing fluid flows on the sphere. Unconventionally for unstructured-mesh global models, the governing equations are cast in the anholonomic geospherical framework established in computational meteorology. The resulting discretisation retains proven properties… (More)