Relevance to WCCM–ECCOMAS

The Immersed Boundary (IB) method has emerged as a powerful and versatile class of computational techniques for solving problems involving fluid-structure interaction (FSI). Unlike traditional body-conforming mesh approaches, IB methods handle complex, moving, or deforming geometries by representing the structure as a force exerted on a simpler, fixed background fluid grid. This course is designed to provide a comprehensive introduction to the theory, implementation, and application of immersed boundary methods for FSI.

Course description

The Immersed Boundary (IB) method has emerged as a powerful and versatile class of computational techniques for solving problems involving fluid-structure interaction (FSI). Unlike traditional body-conforming mesh approaches, IB methods handle complex, moving, or deforming geometries by representing the structure as a force exerted on a simpler, fixed background fluid grid.

This course is designed to provide a comprehensive introduction to the theory, implementation, and application of immersed boundary methods for FSI.

The primary objectives are: Provide a clear, intuitive, and mathematically grounded understanding of the fundamental principles behind the IB method. Survey the major families of IB methods, including the original IB method, penalty method, direct-forcing approach, ghost-cell and cut-cell methods, highlighting their respective strengths and weaknesses. Equip participants with the knowledge to implement a basic 2D IB solver and to critically evaluate and select the appropriate numerical parameters for their own problems. Demonstrate the application of IB methods to a range of real-world problems, from biological flows to industrial applications. Introduce participants to open-source frameworks and libraries where IB methods are implemented, enabling them to apply these techniques immediately in their own research or development work.

Objectives and target groups

This course is intended for a multidisciplinary audience of researchers, engineers, and students who wish to incorporate fluid-structure interaction capabilities into their computational toolkit, including

• PhD Students and Postdoctoral Researchers in Mechanical, Aerospace, Civil, and Biomedical Engineering, as well as Applied Mathematics and Computational Physics, who are new to the field or have recently started working on FSI problems.
• Research Scientists and Engineers in industry (e.g., automotive, aerospace, biomedical devices, energy) who need to simulate problems involving flow and moving/flexible structures but find traditional moving-mesh methods too cumbersome or computationally expensive.
• Master's Students in computational science and engineering programs seeking advanced knowledge in CFD.
• Computational Fluid Dynamics (CFD) Software Developers interested in implementing or enhancing FSI capabilities in their codes.

Scientific and technical areas covered

• Fundamentals of Fluid-Structure Interaction (FSI): Introduction to FSI problems, classification (strong vs. weak coupling), challenges of moving meshes and mesh deformation, and the monolithic vs. partitioned solution approaches. The added-mass effect and its impact on numerical stability for light structures.
• The Mathematical Framework of the Immersed Boundary Method: Discretization of the Navier-Stokes equations on a Cartesian grid (finite difference/finite volume) and implementation of various immersed boundary method:
• The Classical Penalty/Feedback Forcing IB Method: How to model elastic boundaries by treating them as a collection of springs.
• The Direct-Forcing Approach: A more robust and stable method for imposing boundary conditions on immersed bodies, particularly rigid bodies.
• Introduction to Ghost-Cell Methods: How to precisely defines the fluid-solid interface to maintain sharp resolution.
• Applications and Case Studies:
• Bio-Fluid Dynamics: Simulation of heart valves deformation.
• Industrial FSI: Analysis of vortex-induced vibrations (VIV) in heat exchanger tubes.
• Hands-on Software and Implementation: A practical session guiding participants through a simple MATLAB implementation of a 2D IB solver for an elastic membrane. An overview of advanced open-source frameworks (e.g., OpenFOAM with IB libraries) will also be provided.