The study of fluid-structure interaction problems is of great importance in many applicationsof sciences and engineering, and it usually involves complex structure geometries.The body-fitted approach is a conventional method that is frequently used to simulate flowwith a complex boundary. In that approach, the incompressible Navier-Stokes equations arespatially discretized on a curvilinear or unstructured grid that conforms to the immersedstructure boundaries. Therefore, the internal boundary conditions can be imposed easily.However, the body-fitted discretizations have to re-mesh the spatial domain at every timestep correspondingly when the body deforms or moves in the fluid. Since the grid generationcan become a large computational overhead, it would be desirable to avoid the needof re-meshing at each time step. Thus, one should seek the help of the Cartesian grid basednon-boundary conforming methods, such as the so-called immersed boundary (IB) method,to address the complex fluid-structure interaction problems.The main purpose of this three-year project is to develop efficient numerical methodsfor simulating the dynamics of fluid-structure interaction problems. We will focus on thefollowing three topics:1. The direct-forcing IB projection method for the fluid-solid interaction, where the immersedsolid object is moving in the fluid governed by the equations of motion.2. The direct-forcing IB projection method for the fluid-elastic body interaction, wherethe elastic structure is quasi-static, isotropic and homogeneous which undergoes smalldeformations.In the above two direct-forcing IB projection methods, the solid/elastic body domainis treated like a fluid with an additional virtual force field applied to it so that it wouldact like a solid/elastic body. Actually, this virtual force is added to the momentumequations to accommodate the interaction between the solid/elastic body and fluidsuch that the boundary condition at the immersed boundary is exactly satisfied.3. We will also study the IB method combined with the artificial compressibility methodfor solving fluid-structure interaction problems, in which the incompressibility constraintr? u = 0 is replaced by the artificial compressibility equation, #¶tp +r? u = 0,and # > 0 is a small parameter depending on the time step length. The development ofefficient solvers for the linear systems associated with the fully discrete vector-valuedproblems to be solved will be the focus of this penalty approach.
|Effective start/end date||1/08/17 → 31/07/18|
UN Sustainable Development Goals
In 2015, UN member states agreed to 17 global Sustainable Development Goals (SDGs) to end poverty, protect the planet and ensure prosperity for all. This project contributes towards the following SDG(s):
- incompressible Navier-Stokes equations
- fluid-structure interaction
- immersedboundary method
- penalty method
- artificial compressibility method
- direct-forcing method
- projection scheme
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