In this paper we propose to revisit the notion of simple Riemann solver both in Lagrangian and Eulerian coordinates following seminal work Gallice ”Positive entropy stable Godunov-type schemes for gas dynamics MHD equations or coordinates” Numer. Math., 94, 2003. We provide relation between forms systems conservation laws 1D. Then an approximate (simple) is derived based on notions positivity p...

Dilute liquid sprays can be modeled at the mesoscale using a kinetic equation, namely the Williams-Boltzmann equation, containing terms for spatial transport, evaporation and fluid drag. The most common method for simulating the Williams-Boltzmann equation uses Lagrangian particle tracking wherein a finite ensemble of numerical “parcels” provides a statistical estimate of the joint surface area...

In the revised version, we emphasized new results from EOF analysis and Lagrangian approach. Following sentence is added in the abstract: “The EOF analysis indicated that these diurnal variations over the African continent seem to be closely related to continental-scale daytime solar heating and topography. On the other hand, advection effect on the diurnal variation appeared to be minor becaus...

The one-dimensional shallow water equations in Eulerian coordinates are considered. Relations between symmetries and conservation laws for the potential form of equations, shown. An invariant difference scheme with arbitrary bottom topography is constructed. It possesses all finite-difference analogues laws. Some topographies require moving meshes coordinates, which stationary mass Lagrangian c...

This paper contributes to a recently proposed Arbitrary Lagrangian–Eulerian Modal (ALEM) approach that makes it possible develop finite elements with variable volume suitable for modeling wire-ropes in reeving systems. Reeving systems often include motors continuously modify the total mechanical energy. If energy dissipation is omitted or underestimated computations, numerical solution may expe...

Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation models. The Lagrangian represe...

A model, based on ozone-concentration tendency equation, is developed to study synoptic ozone-column variations. The application is referred to a middle-latitude site and to an atmospheric layer extending from the surface up to about 35-km altitude. Photochemical effects at the considered location for synoptic time scales are considered negligible. The data input consists of umkehr ozone profil...

By adding a proper term to the Lagrangian density of a real non-linear KG system with a proposed non-topological unstable solitary wave solution, its stability guaranteed appreciably. This additional term in the new modified Lagrangian density behaves like a strong internal force which stands against any arbitrary small deformation in the proposed non-topological solitary wave solution.