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The thesis at hand deals with the numerical solution of multiscale problems arising in the modeling of processes in fluid and thermo dynamics. Many of these processes, governed by partial differential equations, are relevant in engineering, geoscience, and environmental studies. More precisely, this thesis discusses the efficient numerical computation of effective macroscopic thermal conductivity tensors of high-contrast composite materials. The term "high-contrast" refers to large variations in the conductivities of the constituents of the composite. Additionally, this thesis deals with the numerical solution of Brinkman's equations. This system of equations adequately models viscous flows in (highly) permeable media. It was introduced by Brinkman in 1947 to reduce the deviations between the measurements for flows in such media and the predictions according to Darcy's model.
Internal waves are oscillating disturbances within a stable density-stratified fluid. In stratified water basins, these waves have been detected and pointed out as one of the most important processes of water movement and vertical mixing. A fraction of the wind momentum and energy that cross the water surface are responsible for generating large standing internal waves, also called basin-scale internal seiches, in stratified basins. Despite the huge number of publications describing different mechanisms that can influence the dissipation rates and accelerate the wave damping of internal seiche in thermally stratified lakes and reservoirs, many details of their application to field observations are site specific and do not evaluate the effects in a combined way. This research paid particular attention to some mechanisms that may contribute in inhibiting the generation of internal seiche through field measurements and numerical simulations. Our results underline the importance of bathymetry on energy dissipation, indicating that the gentle sloping bottom may act as a primary mechanism to inhibit the formation of internal seiches. The basin shapes (reservoir bends) and self-induced mixing near the wave crest act as secondary mechanisms to extract energy from upwelling events, which is responsible for triggering internal seiches in thermally stratified lakes. Numerical simulations indicate that a higher amount of energy is transferred from the wind to the internal seiche for an increasing deviation of the stratification from a two-layer structure, suggesting that the stratification profile is not responsible for inhibiting the occurrence of basin-scale internal waves, but only for modifying its structure, favoring the formation of internal waves with higher vertical modes. The outcome of this study may be of great relevance in describing the biogeochemical cycle in lakes and reservoirs, since each mechanism may have different trigger effects on the cycle of nutrients and other elements in thermally stratified lakes.