Lab Home | Phone | Search
Center for Nonlinear Studies  Center for Nonlinear Studies
 Home 
 People 
 Current 
 Affiliates 
 Visitors 
 Students 
 Research 
 ICAM-LANL 
 Publications 
 Conferences 
 Workshops 
 Sponsorship 
 Talks 
 Colloquia 
 Colloquia Archive 
 Seminars 
 Postdoc Seminars Archive 
 Quantum Lunch 
 Quantum Lunch Archive 
 CMS Colloquia 
 Q-Mat Seminars 
 Q-Mat Seminars Archive 
 P/T Colloquia 
 Archive 
 Kac Lectures 
 Kac Fellows 
 Dist. Quant. Lecture 
 Ulam Scholar 
 Colloquia 
 
 Jobs 
 Postdocs 
 CNLS Fellowship Application 
 Students 
 Student Program 
 Visitors 
 Description 
 Past Visitors 
 Services 
 General 
 
 History of CNLS 
 
 Maps, Directions 
 CNLS Office 
 T-Division 
 LANL 
 
Tuesday, October 31, 2006
10:00 AM - 11:00 AM
CNLS Conference Room (TA-3, Bldg 1690)

Seminar

A compact MPFA method with improved monotonicity

Ivar Aavatsmark
Centre for Integrated Petroleum Research, Department of Mathematics, Bergen, Norway

MPFA methods were introduced to solve control-volume formulations on general grids. While these methods are general in the sense that they may be applied to any grid, their convergence properties vary. An important property for multiphase flow is the monotonicity of the numerical elliptic operator. In a recent paper, conditions for monotonicity on quadrilateral grids have been developed. These conditions indicate that MPFA formulations which lead to smaller flux stencils are desirable for grids with high aspect ratio or severe skewness and for media with strong anisotropy or strong heterogeneity. We introduce a new MPFA method for quadrilateral grids termed the L-method. The methodology is valid for general media. For homogeneous media and uniform grids, this method has four-point flux stencils and seven-point cell stencils in two dimensions. The reduced stencil appears as a consequence of adapting the method to the closest neighboring cells. We have tested the convergence and monotonicity properties for this method and compared it with the O-method. For moderate grids the convergence rates are the same, but for rough grids with large aspect ratios, the convergence of the O-methods is lost, while the L-method converges with a reduced convergence rate. The L-method has a somewhat larger monotonicity range than the O-methods, but the dominant difference is that when monotonicity is lost, the O-methods may give large oscillations, while the oscillations with the L-method are small or absent.

Host: Mikhail Shashkov