A.M.Roma's: Home Page > Research
A.M.Roma's: Home Page > Research
Research
Many problems in biofluid dynamics involve the interaction between a transient, incompressible viscous fluid and an immersed biological tissue, which may have time-dependent shape, time-dependent elastic properties, or both (e.g., the interaction between blood, heart muscles and heart valve leaflets).Although these problems can be handled in a robust manner by the Immersed Boundary Method (Peskin) and qualitatively good results be obtained, this method suffers from a certain "lack of resolution" which is related to limitations of computers such as speed and storage. Finner immersed boundary (biological tissue) geometrical details and certain flow features can be adequately resolved only if the computational mesh is fine. If a uniform mesh is used, this requirement is inevitably extended to the entire computational domain, and the resulting mesh may exceed the storage capacity of the computer.
My main research interest is to develop an efficient computational setting for the Immersed Boundary Method employing an Adaptive Mesh Refinement Technique (Berger), capable of removing the original uniform mesh restriction of the method. This adaptive version for the Immersed Boundary Method can enhance the accuracy by covering locally an immersed boundary vicinity with a sequence of nested, progressively finer rectangular grid patches which dynamically follow the immersed boundary motion. I developed this Adaptive Immersed Boundary Method during my PhD program.
Since January 1999, I am reimplementing all my 14,000 line code to make the adaptive version of the method more generally applicable. So far, the data structures to handle the adaptive grids and the multilevel-multigrid methods to solve parabolic and elliptic equations were implemented. Soon, after preliminary tests are over, these implementations will be employed to solve the Navier-Stokes equations for a model problem with periodic boundary condions.
New features of this code will include the ability to handle variable density incompressible flows (hopefully continuous density variations on the order of one thousand to one), and non-fixed refinement ratios between neighbor levels, that is, in a same discrete problem we will be able to allow mixed refinement ratios (2, 4 or 8).
Looking into the future, I have several applications in sight for this adaptive version of the Immersed Boundary Method. Among them, I intend to revisit few Peskin's models, mainly to study the interaction between blood and natural/artificial heart valves. Also, I have a great interest in the simulation of aquatic animal locomotion and flows in flexible, arbitrarily shaped tubes.
· Publications · Research Group · Students ·