Dorin Marinescu

Tests of a simulation method for a system of Boltzmann equations

Abstract We report on numerical tests of a convergent simulation scheme for the solutions of a class of nonlinear kinetic equations for rarefied gas mixtures.

Mathematical modeling of the erosion processes in hydrographic basins

The erosion is a complex process determined by many physical, chemical, biological factors, affects the environment in a number of ways, and has a significant impact on the conservation and exploitation of natural resources, as well as on the quality of life. Due to its complexity, it is crucial to build a good erosion model in accordance with the envisaged main effects. The most determinant factors in the soil erosion - the process we focus in this article - are water dynamics, soil particle cohesion, and the cover plant presence. Our study focuses on the topography influence on water dynamics, the interactions plant cover - water flow, soil particle detachment - plant cover. We also analyze the model sensitivity to the variation of some soil parameters.

Water ow on vegetated hill. 1D shallow water equation type model

Abstract A mathematical model for the water ow on a hill covered by variable distributed vegetation is proposed in this article. The model takes into account the variation of the geometrical properties of the terrain surface, but it assumes that the surface exhibits large curvature radius. After describing some theoretical properties for this model, we introduce a simplified model and a well-balanced numerical approximation scheme for it. Some mathematical properties with physical relevance are discussed and finally, some numerical results are presented.

Modeling the water and sediment dynamics in vegetative filter strips

The primary goal of our study is to model the plant cover influence on water and soil erosion dynamics. The mathematical model consists in Saint-Venant equations coupled with the multiple particle class Hairsine-Rose soil erosion model. The numerical solutions are obtained from a finite volume scheme used to discretize the continuum model, where a second order fractional time step is applied for time integration. The numerical scheme is well-balanced and preserves the positivity of water depth and sediment density functions. The presence of the soil erosion equations do not imposes any restriction on the magnitude of the time step. Secondarily, we apply the general model to study the sediment transport in a vegetative buffer.

On a time and space discretized approximation of the Boltzmann equation in the whole space

Abstract In this paper, convergence results on the solutions of a time and space discrete model approximation of the Boltzmann equation for a gas of Maxwellian particles in a bounded domain, obtained by Babovsky and Illner (1989), are extended to approximate the solutions of the Boltzmann equation in the whole physical space. This is done for a class of particle interactions including Maxwell and soft cut-off potentials in the sense of Grad. The main result shows that the solutions of the discrete model converge in L 1 to the solutions of the Boltzmann equation, when the discretization parameters go simultaneously to zero. The convergence is uniform with respect to the discretization parameters. In addition, a sufficient condition for the implementation of the main result is provided. The techniques detailed in this paper may be also applied in other contexts.