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Pengtao Sun, University of Nevada, Las Vegas, Numerical Studies for Unsteady Moving Interface Problems and Applications to Fluid-Structure Interactions (FSI)
October 12, 2021 | 3:00 pm - 4:00 pm EDT
In this talk, I will present our recent numerical methodology studies for unsteady moving
interface problems and applications to dynamic fluid-structure interaction (FSI) problems. Our
numerical methodologies include the body-fitted mesh method (arbitrary Lagrangian−Eulerian (ALE)
method), the body-unfitted mesh method (fictitious domain (FD) method), combining with the mixed
finite element approximation, as well as the mesh-free/deep neural network (DNN) method.
A fully coupled (monolithic) mixed finite element method is developed for the proposed monolithic
ALE and FD methods to unconditionally stabilize numerical computations for moving−interface and
FSI problems. Numerical analyses on the well-posedness, stability and convergence are carried out
for ALE and FD methods when they are applied to various moving−interface problems. Convergence
theorems conclude those numerical analyses with an optimal convergence in regard to the regularity
assumption of real solutions. All theoretical results are validated by numerical experiments as well.
In particular, I will also present a new type of monolithic ALE-FEM for the parabolic/mixed
parabolic interface problem, towards a dynamic fluid-poroelastic-structure interaction (FPSI)
problem―a type of important hemodynamic problem. Corresponding stability and optimal
convergence analyses are carried out for this method in semi- and fully discrete scheme. Both ALE
(affine) mapping and Piola mapping play crucial roles in the development of this method for a
unsteady interface problem in which a H(div)-type mixed problem is involved. All theoretical results
are validated by numerical experiments as well.
Our well developed ALE method has been successfully applied to several realistic dynamic FSI
problems in the fields of hydrodynamics and hemodynamics. Some numerical animations will be
shown in this talk to illustrate that the proposed and well analyzed numerical methods can produce
high fidelity numerical results for realistic FSI problems in an efficient and accurate fashion.
interface problems and applications to dynamic fluid-structure interaction (FSI) problems. Our
numerical methodologies include the body-fitted mesh method (arbitrary Lagrangian−Eulerian (ALE)
method), the body-unfitted mesh method (fictitious domain (FD) method), combining with the mixed
finite element approximation, as well as the mesh-free/deep neural network (DNN) method.
A fully coupled (monolithic) mixed finite element method is developed for the proposed monolithic
ALE and FD methods to unconditionally stabilize numerical computations for moving−interface and
FSI problems. Numerical analyses on the well-posedness, stability and convergence are carried out
for ALE and FD methods when they are applied to various moving−interface problems. Convergence
theorems conclude those numerical analyses with an optimal convergence in regard to the regularity
assumption of real solutions. All theoretical results are validated by numerical experiments as well.
In particular, I will also present a new type of monolithic ALE-FEM for the parabolic/mixed
parabolic interface problem, towards a dynamic fluid-poroelastic-structure interaction (FPSI)
problem―a type of important hemodynamic problem. Corresponding stability and optimal
convergence analyses are carried out for this method in semi- and fully discrete scheme. Both ALE
(affine) mapping and Piola mapping play crucial roles in the development of this method for a
unsteady interface problem in which a H(div)-type mixed problem is involved. All theoretical results
are validated by numerical experiments as well.
Our well developed ALE method has been successfully applied to several realistic dynamic FSI
problems in the fields of hydrodynamics and hemodynamics. Some numerical animations will be
shown in this talk to illustrate that the proposed and well analyzed numerical methods can produce
high fidelity numerical results for realistic FSI problems in an efficient and accurate fashion.
Zoom link: https://ncsu.zoom.us/j/
passcode: NAseminar
passcode: NAseminar