Convective difference schemes

TL;DR: A class of explicit, Eulerian finite-difference algorithms for solving the continuity equation which are built around a technique called “flux correction,” which yield realistic, accurate results.

TL;DR: In this article, the authors studied the instability of a boundary layer for a range of physical parameters (Rayleigh number, amounts of thickening, and boundary conditions) and derived expressions that related the growth of the instability and the time needed to remove the boundary layer as a function of the amount of horizontal shortening (f), the Rayleigh number (R), and the ratio (a/d) of the thicknesses of the rigid and fluid layers.

TL;DR: In this article, a review of the geophysical information and the fluid dynamics of convection in a Boussinesq fluid of infinite Prandtl number is presented and analyzed in terms of simple physical models.

TL;DR: In this paper, the authors investigate more accurate difference methods and show that fourth order methods are optimal in some sense, and compare these methods with a variant of the Fourier technique.

TL;DR: In this article, a wide class of difference equations is described for approximating discontinuous time dependent solutions, with prescribed initial data, of hyperbolic systems of nonlinear conservation laws, and the best ones are determined, i.e., those which have the smallest truncation error and in which the discontinuities are confined to a narrow band of 2-3 meshpoints.