This thesis centers on the development and analysis of numerical multiscale methods for multiscale problems arising in steady heat conduction, heat transfer and wave propagation in heterogeneous media. In a multiscale problem several scales interact with each other to form a system which has variations over a wide range of scales. A direct numerical simulation of such problems requires resolvin...

Second order elliptic problems in divergence form with a highly varying leading order coefficient on the scale can be approximated on coarse meshes of spacing H only if one uses special techniques. The mixed variational multiscale method, also called subgrid upscaling, can be used, and this method is extended to allow oversampling of the local subgrid problems. The method is shown to be equival...

The eddy viscosity is the tensor in the equation that governs the transport of the large-scale (modulational) perturbations of small-scale stationary flows. As an approximation to eddy viscosity the effective tensor, that arises in the limit as the ratio between the scales ε → 0, can be considered. We are interested here in the accuracy of this approximation. We present results of computational...

Towards global empirical upscaling of FLUXNET eddy covariance observations: validation of a model tree ensemble approach using a biosphere model M. Jung, M. Reichstein, and A. Bondeau Max Planck Institute for Biogeochemistry, Jena, Germany Potsdam Institute for Climate Impact Research (PIK), Potsdam, Germany Received: 7 April 2009 – Accepted: 20 May 2009 – Published: 26 May 2009 Correspondence ...

Multicomponent contaminant transport models in groundwater are typically based on assumptions of local geochemical equilibrium on the grid scale. In heterogenous systems there may be significant coupling between transport processes and geochemical equilibrium at smaller than grid block scale. When these processes are upscaled to grid scale, geochemical evolution may take on a kinetic character....