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The mathematical proof of mass conservation for CG with non-conforming meshes is presented in Appendix B.
The scheme guarantees the exact mass conservation for each component and the exact conservation of total momentum and energy in the whole particle system.
The mass conservation for diffusion-driven evaporation is resolved by considering the effect of interface cooling on the change in density of saturated vapour along the liquid-vapour interface of sessile droplets.
In this work, analysis is used to identify two sources of kinetic energy conservation error in the collocated-mesh scheme: (1) errors arising from the interpolations used to estimate the velocity on the cell faces, and (2) errors associated with the slightly inconsistent pressure field used to ensure mass conservation for the cell face volume fluxes.
For each system estimates of either sediment volumes (mass) or sediment fluxes of continental and marine subsystems have been compiled in order to receive a complete routing in terms of mass conservation for specific time periods since the Late Glacial Maximum as well as the Cenozoic.
Eq. (1) represents the mass conservation for the landslide.
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The outflowing air is then carried by the winds at high altitude and must eventually subside for mass conservation of air to be satisfied.
In this study, a separate PDE for the mass conservation of the liquid water is solved to calculate the saturation levels.
Most of the present formulations for the mass conservation of species do not correctly represent changes in the time scale of diffusion as a function of porosity in a system of porous media.
Considering a hyperbolic system including the Euler equations for the mixture and a mass conservation equation for each species, we propose a new approximation scheme for the convective term of the species equations.
The solution of governing differential equations, which consist of the conservation of mass and momentum for the hydrodynamics, the transport equation for the suspended sediment fluxes and the sediment mass conservation equation for the bed level changes are carried out by the use of Alternating Direction Implicit (ADI) Finite Difference Method (FDM).
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