42,640 research outputs found
A two-pressure model for slightly compressible single phase flow in bi-structured porous media
Problems involving flow in porous media are ubiquitous in many natural and engineered systems. Mathematical modeling of such systems often relies on homogenization of pore-scale equations and macroscale continuum descriptions. For single phase flow, Stokes equations at the pore-scale are generally approximated by Darcy’s law at a larger scale. In this work, we develop an alternative model to Darcy’s law that can be used to describe slightly compressible single phase flow within bi-structured porous media. We use the method of volume averaging to upscale mass and momentum balance equations with the fluid phase split into two fictitious domains. The resulting macroscale model combines two coupled equations for average pressures with regional Darcy’s laws for velocities. In these equations, effective parameters are expressed via integrals of mapping variables that solve boundary value problems over a representative unit cell. Finally, we illustrate the behaviour of these equations in a two-dimensional model porous medium and validate our approach by comparing solutions of the homogenized equations with computations of the exact microscale problem
Fluid Solver Independent Hybrid Methods for Multiscale Kinetic equations
In some recent works [G. Dimarco, L. Pareschi, Hybrid multiscale methods I.
Hyperbolic Relaxation Problems, Comm. Math. Sci., 1, (2006), pp. 155-177], [G.
Dimarco, L. Pareschi, Hybrid multiscale methods II. Kinetic equations, SIAM
Multiscale Modeling and Simulation Vol 6., No 4,pp. 1169-1197, (2008)] we
developed a general framework for the construction of hybrid algorithms which
are able to face efficiently the multiscale nature of some hyperbolic and
kinetic problems. Here, at variance with respect to the previous methods, we
construct a method form-fitting to any type of finite volume or finite
difference scheme for the reduced equilibrium system. Thanks to the coupling of
Monte Carlo techniques for the solution of the kinetic equations with
macroscopic methods for the limiting fluid equations, we show how it is
possible to solve multiscale fluid dynamic phenomena faster with respect to
traditional deterministic/stochastic methods for the full kinetic equations. In
addition, due to the hybrid nature of the schemes, the numerical solution is
affected by less fluctuations when compared to standard Monte Carlo schemes.
Applications to the Boltzmann-BGK equation are presented to show the
performance of the new methods in comparison with classical approaches used in
the simulation of kinetic equations.Comment: 31 page
A review of wildland fire spread modelling, 1990-present, 1: Physical and quasi-physical models
In recent years, advances in computational power and spatial data analysis
(GIS, remote sensing, etc) have led to an increase in attempts to model the
spread and behaviour of wildland fires across the landscape. This series of
review papers endeavours to critically and comprehensively review all types of
surface fire spread models developed since 1990. This paper reviews models of a
physical or quasi-physical nature. These models are based on the fundamental
chemistry and/or physics of combustion and fire spread. Other papers in the
series review models of an empirical or quasi-empirical nature, and
mathematical analogues and simulation models. Many models are extensions or
refinements of models developed before 1990. Where this is the case, these
models are also discussed but much less comprehensively.Comment: 31 pages + 8 pages references + 2 figures + 5 tables. Submitted to
International Journal of Wildland Fir
Spatially averaged flows over mobile rough beds : definitions, averaging theorems, and conservation equations
Peer reviewedPostprin
- …