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 atmospheric models. During the last d...

MPDATA is a exible and computationally e cient methodology that has been applied to advection, remapping, and full uid solvers. In this paper, we extend the fundamental concept, iterated upwind compensation of error, to incorporate a new degree of freedom—that of gauge transformations—with the goal of constructing a monotonicity preserving option for MPDATA. We further augment this scheme by ad...

An advancement of the unstructured-mesh finite-volume MPDATA (Multidimensional Positive Definite Advection Transport Algorithm) is presented that formulates the error-compensative pseudo-velocity of the scheme to rely only on face-normal advective fluxes to the dual cells, in contrast to the full vector employed in previous implementations. This is essentially achieved by expressing the tempora...

The multidimensional positive definite advection transport algorithm (MPDATA) belongs to the group of nonoscillatory forward-in-time algorithms, and performs a sequence of stencil computations. MPDATA is one of the major parts of the dynamic core of the EULAG geophysical model. The Intel Xeon Phi coprocessor is the first product based on the Intel Many Integrated Core (Intel MIC) architecture. ...

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 preserve the fundamental conservation l...

in this paper high order multidimensional positive definite advection transport algorithm (mpdata) and compact finite difference methods are applied to one (1-d) and two-dimensional (2-d) advection equation. mpdata methods are designed based on upwind scheme using anti-diffusive velocity that compensates diffusivity of upwind method. in high order compact method one implicit relation between a ...

The paper advances the limited-area anelastic model [Smolarkiewicz et al., J. Comput. Phys., 254 (2013) 184] for investigation of nonhydrostatic dynamics in mesoscale atmospheric flows. New developments include the extension to a tetrahedral-based median-dual option for unstructured meshes and a static mesh adaptivity technique using an error indicator based on inherent properties of the Multid...

Bartman et al., (2022). PyMPDATA v1: Numba-accelerated implementation of MPDATA with examples in Python, Julia and Matlab. Journal Open Source Software, 7(77), 3896, https://doi.org/10.21105/joss.03896