Rami Masri:
Coupled 3D-1D solute transport models: Derivation, model error analysis, and numerical approximation
Zeit und Ort
Dienstag, 17.10.23, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Zusammenfassung
Starting from full-dimensional models of solute transport, we derive and analyze multi-dimensional (3D-1D) coupled models of time-dependent convection, diffusion, and exchange in and around pulsating vascular and perivascular networks. These models are widely applicable for modelling transport in vascularized tissue, brain perivascular spaces, vascular plants and similar environments. The well-posedness of the full and the multi-dimensional equations is established. In the derivation of the 3D-1D model, a 3D inclusion is reduced to its centerline. Thus, we establish a-priori estimates on the associated modelling errors in evolving Bochner spaces in terms of the inclusion's diameter. We consider both continuous and discontinuous Galerkin approximations to the coupled 3D-1D problems, and we discuss the convergence properties of the numerical schemes. Finally, we present numerical simulations in idealized geometries and in a brain mesh with a large network of vessels on its surface and inside the parenchyma. \n