Current Problems in Numerical Analysis

In the talk, we will go through fundamentals of simulating particle laden-flows via Eulerian-Lagrangian approaches. In particular, we consider (i) the solid bodies projected onto the flow computational mesh via a variant of the immersed boundary method (IBM), and (ii) the particle movement and interactions solved via the discrete element method (DEM). We will discuss our custom approaches to both the IBM and DEM and comment on their shortcomings. With respect to IBM, we shall focus on its implementation in the finite volume method, treatment of domain-decomposition and  turbulence modeling. As for DEM, a few notes will be made on our attempts to produce a computationally efficient code for handling arbitrarily-shaped solids. Altogether, the presented methods are highly computationally demanding. Yet, we are ultimately interested in providing computational methods usable in engineering. Unfortunately, the studied systems are transport-dominated and mathematically inconsistent,... more