On the positivity of mass in commonly used numerical transport schemes

Maximum and Minimum Principles for Radionuclide Transport Calculations in Geological Radioactive Waste Repository: Comparison Between a Mixed Hybrid Finite Element Method and Finite Volume Element discretizations

“…2 (Ostiguy and Laprise 1990;Herrera and Valocchi 2006). Those oscillations (calculation of negative concentrations as well as of concentrations higher than the maximal initial one) stem both from the advective and diffusive terms of the transport equation.…”

Regional climate modelling

“…In addition to its computational efficiency, the semi-Lagrangian transport scheme has little numerical dispersion, which results in a reduction of spurious ripples in the distribution of transported substances, compared to conventional unconstrained Eulerian transport schemes (e.g. [75,76]). The interpolations required in the semi-Lagrangian scheme result in some damping of the small scales, which could be problematic for quasi-inviscid applications such as orographic internal gravity waves.…”

“…[75,76,79,52,8]), and several scientists were sceptics about its suitability for climate models. Experience has shown, however, that this marching scheme is competitive in its performance and that it can afford substantial computational savings.…”

Retrieval of the microphysical properties in a CASP storm by integration of a numerical kinematic model

“…A "hole filling" procedure, combined with global prorated borrowing (e.g. Ostiguy and Laprise, 1990) is applied between steps (16a) and (16b) to remove these aberrations. To complete the forecast cycle, a weak running time filter of Robert (see Asselin, 1972) is applied f0 prevent the separation of solutions that might develop in time with such a three time-level scheme.…”