The objective of this workshop was to bring together researchers working in multiscale simulations with emphasis on multigrid methods and multiscale finite element methods, aiming at chieving of better understanding and synergy between these methods. The goal of multiscale finite element methods, as upscaling methods, is to compute coarse scale solutions of the underlying equations as accuratel...

This paper unravels the problem of an idealised pile-up of n infinite, equi-spaced walls of edge dislocations at equilibrium. We define a dimensionless parameter that depends on the geometric, constitutive and loading parameters of the problem, and we identify five different scaling regimes corresponding to different values of that parameter for large n. For each of the cases we perform a rigor...

A methodology for incorporating subgrid effects in coarse-scale numerical models of flow in heterogeneous porous media is presented. The method proceeds by upscaling the deterministic fine-grid permeability description and then solving the pressure equation over the coarse grid to obtain coarse-scale velocities. The coarse-grid saturation equation is formed through a volume average of the fine-...

Robust Numerical Upscaling at High Contrast

In this article we present some numerical techniques to increase efficiency and applicability of a flow-based upscaling procedure used to solve single and multi-phase flows in naturally fractured reservoirs. These geological formations may be characterized by hundreds up to hundreds of thousands of fractures, ranging from small to medium scales, spreading all over the reservoir. In these scenar...

The interrelations between weight-function upscaling (measurement) and the definition of various nonlocal operators is explored. Let < f > = f∗g where f∗g is the convolution product which represents the effect of upscaling via an instrument (defined by g) on a field variable f and its localized counterpart. Nonlocal field variables are defined and employed for upscaling. In this talk it will be...

Problems related to brown plant hopper outbreaks management in the Mekong Delta-Vietnam are complex and need aggregating information across administrative scales. Brown plant hoppers density and environmental indicators are main factors that support stakeholders have suitable decision making. Due to detail levels of information are different from field scale to region scale, upscaling informati...

Modeling of wave propagation in a heterogeneous medium requires input data that varies on many different spatial and temporal scales. Operator-based upscaling allows us to capture the effect of the fine scales on a coarser domain without solving the full fine-scale problem. The method applied to the constant density, variable sound velocity acoustic wave equation consists of two stages. First, ...

The role of greenhouse gases (GHGs) in global climate change is now well recognized and there a clear need to measure emissions verify the efficacy mitigation measures. To this end, reliable estimates are needed GHG balance at national scale over long time periods, but these difficult make accurately. Because measurement techniques generally restricted relatively small spatial temporal scales, ...