Continuous Upscaling in Multiscale Modeling

Explore the innovative concept of continuous upscaling in this 49-minute lecture by Associate Professor Alexander Shapiro from the Center for Energy Resources Engineering at the Technical University of Denmark. Delve into the challenges of modeling processes across multiple scales and learn about the mathematical procedure of upscaling or averaging. Discover the various applications and terminologies associated with this technique, including homogenization, spatial filtering, and coarse-graining. Examine the limitations of existing averaging methods and understand the novel approach of continuous averaging developed by Shapiro and his team. Investigate the introduction of an "axis of scales" and the gradual smoothing transformation of fine-scale problems. Learn about the upscaling of densities, fluxes, and transport coefficients, and explore the application of this method to steady-state diffusion. Gain insights into the critical question of whether different upscaling procedures yield consistent coarse-scale models and accurate representations of fine-scale phenomena.