After a short discussion of recent discretization techniques for the lattice-Boltzmann equations we motivate and discuss some alternative approaches using implicit, nonuniform FD discretization and mesh refinement techniques. After presenting results of a stability analysis we use an implicit approach to simulate a boundary layer test problem. The numerical results compare well to the reference solution when using strongly refined meshes. Some basic ideas for a nonuniform mesh refinement (with non-cartesian mesh topology) are introduced using the standard discretization procedure of alternating collision and propagation.
The behaviour of the blood flow passing through artificial heart values in aortic position is numerically simulated by discretizing the Navier-Stokes equations for viscous incompressible flow through the finite element method. Three different artificial valves, Starr-Edwards, St Jude and disc valves, are modelled by using the finite element method as well as the Navier-Stokes equations for viscous incompressible flow. The blood flow behaviour is characterized by discretizing both planar and axisymmetric domains of the value devices. The streamlines as well as the velocity distributions are studied and compared. Likewise, the pressure patterns are analysed and compared. Some numerical examples of the three valves are presented and discussed herein.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.