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 …

Multidimensional positive definite advection transport algorithm (MPDATA) was proposed in
the early eighties as a simple positive‐definite advection scheme with small implicit …

A class of high-resolution algorithms is developed for advection of a scalar quantity in a
given incompressible flow field in one, two, or three space dimensions. Multidimensional …

A class of high resolution multidimensional wave-propagation algorithms is described for
general time-dependent hyperbolic systems. The methods are based on solving Riemann …

We study the flow of a density-stratified fluid past a three-dimensional obstacle, using a
numerical model. Our special concern is the response of the fluid when the Froude number …

A new method is developed to obtain a conservative and positive definite advection scheme
that produces only small numerical diffusion. Advective fluxes are computed utilizing the …

An isopycnic-coordinate oceanic circulation model formulated with the aim of simulating
thermodynamically and mechanically driven flow in realistic basins is presented. Special …

Meteorological fields are required inputs for air-quality models, but they can contain
significant errors which contribute to uncertainties in simulations of airborne chemical …

One-dimensional advection of sharp and smooth passive scalar profiles.(Left) Top pattern
labeled t= 0 shows three different initial conditions. Only approximately one-third of the …

This paper presents a nonoscillatory option (ie, free of dispersive ripples) of the advection
algorithm described previously in J. Comput. Phys.(54 (1984), 325; 67 (1986), 396). The …