Physical Math Seminar

Tuesday, February 27, 2024 at 2:30pm to 3:30pm

Building 2, 449
182 MEMORIAL DR, Cambridge, MA 02139

Speaker:  Neelesh A. Patankar  (Northwestern University)

Title:  A unified constraint formulation of immersed body techniques for coupled fluid-solid motion


Numerical simulation of moving immersed solid (rigid or deforming) bodies in
fluids is now practiced routinely following techniques based on the immersed
boundary method, the fictitious domain method, and other related methods. These
methods rely on using a background mesh for the fluid equations and tracking the
solid body using Lagrangian points. The key idea is to assume that the entire fluid-
solid domain is a fluid and then to constrain the fluid within the solid domain to
move in accordance with the solid governing equations. However, what is the strong
form of the governing equations that these methods are solving wherein the fluid is
extended into the solid domain? In this talk an extended domain strong form of the
governing equations will be presented. The resulting constrained fluid-solid
governing equations provide a unified framework for various immersed techniques
and are independent of the nature of temporal or spatial discretization schemes. It
will be shown that specific choices of time stepping and spatial discretization lead
to different techniques reported in literature ranging from specified velocities to
freely moving rigid bodies to elastic self-propelling bodies. An extension to simulate
Brownian systems by adding thermal fluctuations in the fluid equations via random
stress terms (fluctuating hydrodynamics) will be presented. Resolution of long-
standing challenges in immersed techniques pertaining to high solid-to-fluid density
ratio, leakage through the interface, and internal boundary conditions will be
discussed. These techniques have been used in wide ranging applications including
aquatic locomotion, underwater vehicles, car aerodynamics, organ physiology (e.g.
cardiac flow, esophageal transport, respiratory flows), wave energy convertors,
among others.




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