Towards the realistic simulation of complex fluidic systems: Decomposition strategies

Simulations of complex fluidic systems, as chemical-process networks or whole-body hemodynamics, is crucial for understanding the interplay among components and optimizing overall performance. However, the best-suited  model for each part (pumps, pipes, vessels, or heart, arteries, capillaries) is quite specific. The simulation of the whole system thus requires a decomposition strategy so that physically different submodels interact to produce the correct dynamics. In this presentation, we address decomposition strategies especially tailored to perform this task. They allow for each submodel to be solved separately, in black-box mode, implementing the interactions between subdomains by boundary conditions alone. The fundamental unknowns reside at the interfaces between subdomains, and the proposed methodology takes full advantage of the small number of interfaces in the problems of interest.
An implicit (linear or nonlinear) system of equations is built at each time step, which is solved by effective matrix-free iterative algorithms. Previous algorithms from the literature can be viewed as specific cases of the proposed approach, in which the iterative solver is some variant of Richardson’s iterations. Our formulation allows for Krylov-based and quasi-Newton methods to be used, with obvious improvement of performance and robustness. We begin with a simple application in heat conduction, so as to explain the ideas, and then turn to fluid flow in hydraulic and biological networks.

This research is a colloboration with Jorge S. Leiva, and Pablo J. Blanco.

About the Speaker : Dr. Gustavo Carlos Buscaglia Received his Ph. D. in Nuclear Engineering from Instituto Balseiro, Argentina, in 1993. He is currently Professor at the Instituto de Ciencias Matematicas e de Computaçao (ICMC-USP), Sao Carlos, SP, Brasil.  His areas of expertise are: Applied Mathematics, with emphasis on Numerical Analysis, Scientific Computing and Finite Elements; Fluid Mechanics, Heat Transfer, Multiphase Flow and Lubrication Theory.