Mass Conservation Equation (mass + conservation_equation)

Distribution by Scientific Domains


Selected Abstracts


A finite volume method for large strain analysis of incompressible hyperelastic materials

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2005
I. Bijelonja
Abstract This paper describes development of a displacement,pressure based finite volume formulation for modelling of large strain problems involving incompressible hyperelastic materials. The method is based on the solution of the integral conservation equations governing momentum balance in total Lagrangian description. The incompressibility constraint is enforced by employing the integral form of the mass conservation equation in deformed configurations of the body. A Mooney,Rivlin incompressible material model is used for material description. A collocated variable arrangement is used and the spatial domain is discretized using finite volumes of an arbitrary polyhedral shape. A segregated approach is employed to solve resulting set of coupled non-linear algebraic equations, utilizing a SIMPLE based algorithm for displacement,pressure coupling. Comparisons of numerical and analytical results show a very good agreement. For the limited range of cell topologies tested the developed method appears to be locking free. Copyright © 2005 John Wiley & Sons, Ltd. [source]


Darcy's law-based model for wicking in paper-like swelling porous media

AICHE JOURNAL, Issue 9 2010
Reza Masoodi
Abstract The wicking of liquid into a paper-like swelling porous medium made from cellulose and superabsorbent fibers was modeled using Darcy's law. The work is built on a previous study in which the Washburn equation, modified to account for swelling, was used to predict wicking in a composite of cellulose and superabsorbent fibers. In a new wicking model proposed here, Darcy's law for flow in porous media is coupled with the mass conservation equation containing an added sink or source term to account for matrix swelling and liquid absorption. The wicking-rate predicted by the new model compares well with the previous experimental data, as well as the modified Washburn equation predictions. The effectiveness of various permeability models used with the new wicking model is also investigated. © 2010 American Institute of Chemical Engineers AIChE J, 2010 [source]


Algorithms for vector field generation in mass consistent models

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2010
Ciro Flores
Abstract Diagnostic models in meteorology are based on the fulfillment of some time independent physical constraints as, for instance, mass conservation. A successful method to generate an adjusted wind field, based on mass conservation equation, was proposed by Sasaki and leads to the solution of an elliptic problem for the multiplier. Here we study the problem of generating an adjusted wind field from given horizontal initial velocity data, by two ways. The first one is based on orthogonal projection in Hilbert spaces and leads to the same elliptic problem but with natural boundary conditions for the multiplier. We derive from this approach the so called E,algorithm. An innovative alternative proposal is obtained from a second approach where we consider the saddle,point formulation of the problem,avoiding boundary conditions for the multiplier, and solving this problem by iterative conjugate gradient methods. This leads to an algorithm that we call the CG,algorithm, which is inspired from Glowinsk's approach to solve Stokes,like problems in computational fluid dynamics. Finally, the introduction of new boundary conditions for the multiplier in the elliptic problem generates better adjusted fields than those obtained with the original boundary conditions. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 [source]


Numerical and experimental investigation of heat and mass transfer in unsaturated porous media with low convective drying intensity

HEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 5 2008
Tao Lu
Abstract The heat and mass transfer in an unsaturated wet cylindrical bed packed with quartz particles was investigated theoretically and experimentally for relatively low convective drying rates. The medium was dried by blowing dry air over the top of the porous bed which was insulated by impermeable, adiabatic material on the bottom and sides. Local thermodynamic equilibrium was assumed in the mathematical model describing the multi-phase flow in the unsaturated porous medium using the energy and mass conservation equations for heat and mass transfer during the drying. The drying model included convection and capillary transport of the moisture, and convection and diffusion of the gas. The wet and dry regions were coupled with a dynamic boundary condition at the evaporation front. The numerical results indicated that the drying process could be divided into three periods: the initial temperature rise period, the constant drying rate period, and the reduced drying rate period. The numerical results agreed well with the experimental data, verifying that the mathematical model can evaluate the drying performance of porous media for low drying rates. ©2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(5): 290,312, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20205 [source]


Non-hydrostatic 3D free surface layer-structured finite volume model for short wave propagation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2009
L. Cea
Abstract In this paper a layer-structured finite volume model for non-hydrostatic 3D environmental free surface flow is presented and applied to several test cases, which involve the computation of gravity waves. The 3D unsteady momentum and mass conservation equations are solved in a collocated grid made of polyhedrons, which are built from a 2D horizontal unstructured mesh, by just adding several horizontal layers. The mesh built in such a way is unstructured in the horizontal plane, but structured in the vertical direction. This procedure simplifies the mesh generation and at the same time it produces a well-oriented mesh for stratified flows, which are common in environmental problems. The model reduces to a 2D depth-averaged shallow water model when one single layer is defined in the mesh. Pressure,velocity coupling is achieved by the Semi-Implicit Method for Pressure-Linked Equations algorithm, using Rhie,Chow interpolation to stabilize the pressure field. An attractive property of the model proposed is the ability to compute the propagation of short waves with a rather coarse vertical discretization. Several test cases are solved in order to show the capabilities and numerical stability of the model, including a rectangular free oscillating basin, a radially symmetric wave, short wave propagation over a 1D bar, solitary wave runup on a vertical wall, and short wave refraction over a 2D shoal. In all the cases the numerical results are compared either with analytical or with experimental data. Copyright © 2008 John Wiley & Sons, Ltd. [source]