Stable Numerics for Incompressible and Compressible Flows

In this talk, we present different approaches for the numerical solutions of PDEs for applications arising mainly in Computational Fluid Dynamics (CFD) at different scales. Starting from problems emerging in the context of incompressible flows of thin viscoelastic films (long waves), we are going to end with examples on a global scale, non-hydrostatic, atmospheric modeling for numerical weather and climate predictions.

First, we show a numerical investigation of the nonlinear interfacial dynamics of dewetting/wetting thin layers/droplets of non-Newtonian (viscoelastic) fluids of Jeffreys type in different settings. The effects of viscoelasticity and substrate slippage on the dynamics of thin viscoelastic films and the coalescence of droplets are investigated.

Finally, we present some recent work in the Climate Modeling Alliance (CliMA), a consortium project developing a new Earth System Model (ESM), with a focus on ClimaCore.jl, the new open-source dynamical core (dycore) library for the land and atmosphere components of the ESM. We will include explorations and developments in the integration of stabilization methods, such as flux-limiters and flux-corrected transport, as a means of improving stability and positivity preservation, enabling the model to achieve a given numerical accuracy even in the presence of moist processes and to conserve energy, mass, and water without resorting to the ad hoc fixers common in some atmosphere models.

Bio
https://valeriabarra.org/