Finite Volume Methods for Diiusion Convection Equations on General Meshes
abstract Error estimates for the approximate solution of stationary or evo-lutive convection diiusion equations using a nite volume scheme on a general non structured mesh are presented here. These estimates only require a piece-wise regularity of the exact solution.
Discretization schemes for heterogeneous and anisotropic diffusion problems on general nonconforming meshes
A discretization of heterogeneous and anisotropic diffusion problems on general discretization meshes is developed and studied. The unknowns of this scheme are the values at the center of the control volumes and at some internal interfaces, chosen because of some irregularity of the diffusion tensor. If the tensor is regular enough, the values on the interfaces may be deduced from the values at the center, at the expense of loosing the local conservativity of the fluxes. This scheme is shown to be accurate on several numerical examples. Mathematical convergence to the continuous solution is obtained for homogeneous and heterogeneous tensors. An error estimate may be drawn under sufficient regularity assumptions on the solution.
Control of the homopause level
Abstract This paper reviews the hypothesis that internal gravity wave breaking in the factor responsible for upper atmosphere turbulence generation and control of the number density at the homopause level. Available data from Mars and Earth support the hypothesis, originally introduced by Lindzen, that breaking thermal tides are responsible for the necessary turbulence. The lowest-order, equatorially trapped, westward-propagating diurnal tidal mode is the primary cause on the Earth, and lower-order westward-propagating semidiurnal modes are the primary cause on Mars. The frequencies and vertical wavenumbers of the responsible modes determine the eddy diffusion coefficients; energy density is only indirectly involved by determining which modes can break. A general scale relationship between tidal heating and velocity amplitude can be used to assess the breaking potential of tidal modes, and is used here as the basis for arguing that the number density at the Martian homopause is likely to have been stable over much of geologic time. Difficulties with this approach arise in the cases of Venus and Titan because of their peculiar zonal winds. For Jupiter and Saturn, internal gravity waves generated by nontidal mechanisms probably control the homopause.