Multigrid and related multilevel methods are the approaches of choice for solving the linear systems that result from discretization of a wide class of PDEs. A large gap, however, exists between the theoretical analysis of these algorithms and their actual performance. This paper focuses on the extension of the wellknown local mode (often local Fourier) analysis approach to a wider class of pro...

The transport of explosives from buried mines in a three-dimensional (3D) array has been numerically modeled using the finite-volume technique. Compounds such as trinitrotoluene, dinitrotoluene, and their degradation products, are semi volatile and somewhat soluble in water. Furthermore, they can strongly adsorb to the soil and undergo chemical and biological degradation. Consequently, the spat...

A new simple Lagrangian method with favorable stability and efficiency properties for computing general plane curve evolutions is presented. The method is based on the flowing finite volume discretization of the intrinsic partial differential equation for updating the position vector of evolving family of plane curves. A curve can be evolved in the normal direction by a combination of fourth or...

We investigate a periodic, one-dimensional, linear, and degenerate advection-diffusion equation. The problem is hyperbolic in a subinterval and parabolic in the complement, and the boundary conditions only impose the periodicity of the advective-diffusive flux to ensure mass conservation. Following Gastaldi and Quarteroni (1989), a condition is added to select the “physically acceptable” soluti...

Porous media with low/moderate regional velocities can exhibit a complex dynamic of contamination plumes, in which advection and molecular diffusion are comparable. In this work, we present two-dimensional scenario constant concentration source impermeable upper lower boundaries. order to characterise the plume patterns, detailed discriminated dimensionless technique is used obtain groups that ...

Based on reanalysis data for the years 1980–2001 from the European Centre for Medium-Range Weather Forecasts (ERA-40 data), a climatology of tropospheric zonal-mean water vapor fields and fluxes in isentropic coordinates is presented. In the extratropical free troposphere, eddy fluxes dominate the meridional flux of specific humidity along isentropes. At all levels, isentropic eddy fluxes trans...

In this note we consider proper ways to combine numerical schemes for advective transport and nonlinear chemistry. Obvious combinations are obtained with splitting in a so-called fractional step approach. We shall discuss for this approach correct implementations of source terms and innow boundary conditions. Further we consider the use of multistep methods with explicit treatment of the advect...