Modeling and Simulation of Simultaneous Transport and Incompressible Flows on all Level Sets in a Bulk Domain

Mechanical models and a finite element approach for the simultaneous solution of transport and incompressible flows on all (curved) level sets over some bulk domain are proposed. A level-set function is used to define a set of (d-1)-dimensional curved manifolds which are bounded by the d-dimensional bulk domain. For the numerical analysis, the bulk domain is discretized using d-dimensional finite elements which do not conform to the level sets implying the domains of interest. The resulting method was coined Bulk Trace FEM before and numerical studies confirm optimal higher-order convergence rates for the proposed method when the bulk models feature sufficiently smooth solutions.