conservation of mass

This paper was written to investigate the order of discoveries made in chemistry leading up to the discovery of the periodic table. New experimental techniques, such as the pneumatic trough, voltaic pile, spectroscopy, and potassium analysis led to the discovery of many new elements and their properties which enabled the discovery of the periodic table. The discoveries led to the demise of the classical theory of the elements, to the end of the phlogiston theory and to the creation of the modern ideas of the elements and of the atomic theory. The paper shows the discoveries were made in a necessary and inevitable order with new experimental techniques leading to the discovery of new elements which eventually led to the discovery of the periodic table.

Diffusive transport in porous media is a complex process in multi-scaled fractured media modeling. This paper presents a diffusive transport model for non-Dacian flow in a naturally fractured reservoir with triple porosity and permeability. To address the non-Darcian flow behavior associated with fluid transport in fractured porous media, the Darcy/Forcheimer equation was used. A point-diffusive equation was obtained from mass conservation and the Darcy–Forcheimer momentum equation; this is used together with interface conditions to incorporate the microscopic properties of the domain. Subsequently, the resulting equation was spatially smoothed to obtain an effective macroscopic average model. The macroscopic model obtained, unlike the existing models, has a cross-diffusive term for mass transport by induced fluxes and a mass transfer term accounting for mass transfer between the matrix and the surrounding fractures via the interface. The numerical simulation displayed a horizontal-...

Element Method. The Finite Volume Method guarantees local and global mass conservation. A property not satisfied by the Finite Volume Method. On the down side, the Finite Volume Method requires non trivial modifications to attain high order approximations unlike the Finite Volume Method. It has been contended that the Discontinuous Galerkin Method, locally conservative and high order, is a natural progression for Coastal Ocean Modeling. Consequently, as a primer we consider the vertical ocean-slice model with the inclusion of density effects. To solve these non steady Partial Differential Equations, we develop a pressure projection method for solution. We propose a Hybridized Discontinuous Galerkin solution for the required Poisson Problem in each time step. The purpose, is to reduce the computational cost of classical applications of the Discontinuous Galerkin method. The Hybridized Discontinuous Galerkin method is first presented as a general elliptic problem solver. It is shown t...

This paper considers stratified and shallow water non-Hamiltonian potential-vorticity-based balanced models (PBMs). These are constructed using the exact (Rossby or Rossby–Ertel) potential vorticity (PV). The most accurate known PBMs are those studied by McIntyre and Norton and by Mohebalhojeh and Dritschel. It is proved that, despite their astonishing accuracy, these PBMs all fail to conserve mass locally. Specifically, they exhibit velocity splitting in the sense of having two velocity fields, v and vm, the first to advect PV and the second to advect mass. The difference v − vm is nonzero in general, even if tiny. Unlike the different velocity splitting found in all Hamiltonian balanced models, the present splitting can be healed. The result is a previously unknown class of balanced models, here called “hyperbalance equations,” whose formal orders of accuracy can be made as high as those of any other PBM. The hyperbalance equations use a single velocity field v to advect mass as w...