Two new volume-ofuid (VOF) reconstruction algorithms, which are based on a least-square t technique, are presented. Their performance is tested for several standard shapes and is compared to a few other VOF=PLIC reconstruction techniques, showing in general a better convergence rate. The geometric nature of Lagrangian and Eulerian split advection algorithms is investigated in detail and a new m...

In this work, the existence of a global minimizer for the previous Lagrangian formulation of nonpolar solvationmodel proposed in [1] has been proved. One of the proofs involves a construction of a phase field model that converges to the Lagrangian formulation. Moreover, an Eulerian formulation of nonpolar solvationmodel is proposed and implemented under a similar parameterization scheme to that...

We present a general Lagrangian formalism that allows the treatment of vorticity. We give solutions for the rotational perturbations up to the third-order in a flat background universe. We show how the primordial vorticity affects the evolution of the density fluctuation in high-density regions. The study of the galaxy formation based on gravitational instability has not revealed the origin of ...

We develop an Eulerian-Lagrangian iterative solution technique for accurate and efficient numerical simulation of single-phase compositional flow through three-dimensional compressible porous media in the presence of multiple injection and production wells. In the numerical simulator, an Eulerian-Lagrangian method is used to solve the convectiondiffusion transport equations and a mixed finite e...

A closed set of exact equations describing statistical theory of turbulent self-diffusion by multivariate-normal turbulent velocity field is derived. In doing so, we first suggest exact formulas for correlations 〈fi(p)fj(p ′)R[f ]〉, 〈g(p)R[f ]〉 and 〈g(p)fj(p ′)R[f ]〉 when the functional R[f ] is functional of functions fi’s having multivariate-normal distribution, g and fi’s have joint normal d...

[1] In light of the increasing number of drifting buoys in the ocean and recent advances in the realism of ocean general circulation models toward oceanic forecasting, the problem of assimilation of Lagrangian observations data in Eulerian models is investigated. A new and general rigorous approach is developed based on optimal interpolation (OI) methods, which takes into account directly the L...

Correctly predicting transient particle transport in indoor environments is crucial to improving the design of ventilation systems and reducing the risk of acquiring airborne infectious diseases. Recently, a new model was developed on the basis of Markov chain frame for quickly predicting transient particle transport indoors. To evaluate this Markov chain model, this study compared it with the ...

A macroscopic traffic flow model describes the evolution of aggregated traffic characteristics over time and space, which is a basic and critical component for various modern intelligent transportation systems, e.g., a real-time freeway control system. Traditional macroscopic traffic flow models are built in the Eulerian coordinates using Eulerian traffic characteristics, such as density, speed...

We formulate a perturbative approximation to gravitational instability, based on Lagrangian hydrodynamics in Newtonian cosmology. We take account of ‘pressure’ effect of fluid, which is kinematically caused by velocity dispersion, to aim hydrodynamical description beyond shell crossing. Master equations in the Lagrangian description are derived and solved perturbatively up to second order. Then...