Centered numerical fluxes can be constructed for compressible Euler equations which preserve kinetic energy in the semi-discrete finite volume scheme. The essential feature is that the momentum flux should be of the form f m j+ 1 2 = p̃j+ 1 2 +uj+ 1 2 f ρ j+ 2 where uj+ 2 = (uj+uj+1)/2 and p̃j+ 1 2 , f ρ j+ 1 2 are any consistent approximations to the pressure and the mass flux. This scheme thus ...

The prediction of ionic currents in protein channels of biological membranes is one of the central problems of computational molecular biophysics. Existing continuum descriptions of ionic permeation fail to capture the rich phenomenology of the permeation process, so it is therefore necessary to resort to particle simulations. Brownian dynamics (BD) simulations require the connection of a small...

We consider nonlinear hyperbolic conservation laws, posed on a differential (n + 1)-manifold with boundary referred to as a spacetime, and in which the “flux” is defined as a flux field of n-forms depending on a parameter (the unknown variable). We introduce a formulation of the initial and boundary value problem which is geometric in nature and is more natural than the vector field approach re...

the forced convection heat transfer of turbulent al2o3-water nanofluid flow inside the grooved tubeswith the different aspect ratio of the rectangular grooves is numerically investigated. the governingequations have been solved using finite volume method (fvm) coupled with simple algorithm. it isassumed the heat flux is constant on the grooved walls. the single-phase approach is applied for the...

"Diffuse interface" theories for single-component fluids—dating back to van der Waals, Korteweg, Cahn-Hilliard, and many others—are currently based upon an ad hoc combination of thermodynamic principles (built largely upon Helmholtz's free-energy potential) and so-called “nonclassical” continuum-thermomechanical principles (built largely upon Newtonian mechanics), with the latter originating wi...