Operator splitting methods for systems of convection-diffusion equations: nonlinear error mechanisms and correction strategies

Authors final draft post-refereeing.Many numerical methods for systems of convection-diffusion equations are based upon an operator splitting formulation, where convective and diffusive forces are accounted for in separate substeps. We describe the nonlinear mechanism of the splitting error in such numerical methods in the onedimensional case, a mechanism that is intimately linked to the local linearizations introduced implicitly in the (hyperbolic) convection steps by the use of an entropy condition. For convection-dominated flows, we demonstrate that operator splitting methods typically generate a numerical widening of viscous fronts, unless the splitting step is of the same magnitude as the diffusion scale. To compensate for the potentially damaging splitting error, we propose a corrected operator splitting (COS) method for general systems of convection-diffusion equations with the ability of correctly resolving the nonlinear balance between the convective and diffusive forces. In particular, COS produces viscous shocks with correct structure also when the splitting step is large. A front tracking method for systems of conservation laws, which in turn relies heavily on a Riemann solver, constitutes an important part of our COS strategy. The proposed COS method is successfully applied to a system modelling two-phase, multicomponent flow in porous media and a triangular system modelling three-phase flow

Human Resources and the Resource Based View of the Firm

The resource-based view (RBV) of the firm has influenced the field of strategic human resource management (SHRM) in a number of ways. This paper explores the impact of the RBV on the theoretical and empirical development of SHRM. It explores how the fields of strategy and SHRM are beginning to converge around a number of issues, and proposes a number of implications of this convergence

Cytokine Combination Therapy with Erythropoietin and Granulocyte Colony Stimulating Factor in a Porcine Model of Acute Myocardial Infarction

PurposeErythropoietin (EPO) and granulocyte colony stimulating factor (GCSF) have generated interest as novel therapies after myocardial infarction (MI), but the effect of combination therapy has not been studied in the large animal model. We investigated the impact of prolonged combination therapy with EPO and GCSF on cardiac function, infarct size, and vascular density after MI in a porcine model.MethodsMI was induced in pigs by a 90 min balloon occlusion of the left anterior descending coronary artery. 16 animals were treated with EPO+GCSF, or saline (control group). Cardiac function was assessed by echocardiography and pressure-volume measurements at baseline, 1 and 6 weeks post-MI. Histopathology was performed 6 weeks post-MI.ResultsAt week 6, EPO+GCSF therapy stabilized left ventricular ejection fraction, (41 ± 1% vs. 33 ± 1%, p < 0.01) and improved diastolic function compared to the control group. Histopathology revealed increased areas of viable myocardium and vascular density in the EPO+GCSF therapy, compared to the control. Despite these encouraging results, in a historical analysis comparing combination therapy with monotherapy with EPO or GCSF, there were no significant additive benefits in the LVEF and volumes overtime using the combination therapy.ConclusionOur findings indicate that EPO+GCSF combination therapy promotes stabilization of cardiac function after acute MI. However, combination therapy does not seem to be superior to monotherapy with either EPO or GCSF

A pore network model for calculation of interfacial velocities

Two-phase flow in porous media is characterized by fluid-fluid interfaces that separate the fluid phases at the pore scale. These interfaces support pressure differences between phases, and their dynamics allow for saturation changes within the porous medium. Dynamic porescale network models allow interface dynamics to be modeled explicitly, such that each fluid-fluid interface within a network of pores is tracked explicitly in space and time. Because these models produce a detailed description of both phase and interface dynamics, results from these models can be averaged to provide values for many upscaled variables. These include nontraditional variables such as amounts of interfacial area, and volumeaveraged interfacial velocities. While these upscaled variables provide insights into the underlying dynamics of two-phase flow systems, they also allow new theories involving interfacial area to be tested directly. Results from a test of one such theory reveals that proposed constitutive equations involving interfacial velocities fail to match results from the network model for most cases considered. Therefore the macroscopic equations require additional development before they can be used for macro-scale simulations

Decentralization in a post-conflict context : an analysis of the performance of the community empowerment and local governance project in East Timor

The overarching aim of this thesis is to draw lessons from the Community Empowerment and Local Government Project (hereinafter CEP) in East Timor which can be used when designing future projects in East Timor and post-conflict contexts elsewhere. On August 30th 1999 an overwhelming majority of the East Timorese voted for independence from Indonesia, and the referendum was preceded and followed by a near total destruction of the country. A Joint Assessment Mission led by the World Bank and several other donors concluded that 75 percent of the country s infrastructure had been destroyed and that the entire administrative apparatus had been dismantled. CEP was initiated based on the recommendations by the assessment mission. This project aimed to decentralize development politics by institutionalizing democratically elected village councils which received funding for projects based on proposals. This thesis first describes the performance of CEP as a decentralization program, using Crook and Manor s (1998) three heuristic sub-categories; efficiency, responsiveness and process as a framework, and thereafter explains shortcomings in performance through Crook and Sverrisson s (2002) five variables; central-local relations, the configuration of local structures, participation, allocation of resources and length of time. As part of the analysis it is determined whether the post-conflict impact can be captured through the five explanatory variables mentioned earlier, or if it should be included through an independent variable reflecting the post-conflict context. At the end of the thesis lessons learned and suggestions for future projects are discussed

A Local Streamline Eulerian-Lagrangian Method for Two-Phase Flow

A method for solving the saturation equation for two-phase now is presented. The method may be viewed as an operator splitting method or as an Eulerian-Lagrangian backtracking procedure or as a modi£ed method of characteristics. For each time step, the method consists of an advection step and a diffusion step. The advection step requires the tracking of streamlines locally around certain integration points. On each streamline we have to solve a nonlinear hyperbolic equation. This is done using a front tracking method. The solution from the tracking step is projected back onto a fixed grid, and we finally have to solve a parabolic heat-type equation

A Streamline Front Tracking Method for Two- and Three-Phase Flow Including Capillary Forces

In: Contemporary Mathematics: Fluid flow and transport in porous media: mathematical and numerical treatment 295, Zhangxin Chen and Richard E. Ewing (Eds.), pp. 49-61.Preprin

Two phase flow including interfacial area as a variable

Based on the procedure of (Gray & Hassanizadeh 1998) we state macroscale conservation equations for multi phase flow in porous media including interfacial area as a variable. The phases we consider are a solid phase, a wetting phase and a non-wetting phase. Some modeling work is done to decide the functionality of the coefficients in the equations. In particular we construct constitutive relationships for the interfacial area as a function of saturation and capillary pressure, and the resistance terms. The final set of equations is reduced to a 2 x 2 system with the saturation and the interfacial area as independent variables. Some preliminary numerical experiments are reported