Immersed boundary methods

Numerical methods model boundaries or structures inside a fluid grid and couple their effects to the flow without conforming the grid to them.

Lagrangian–Eulerian coupling: A computational framework coupling moving material points with fields defined on a fixed spatial grid. Immersed boundary methods use this division to represent structures and fluid on different computational descriptions.
Charles Peskin: An applied mathematician who developed the immersed boundary method for modeling blood flow through heart valves. His work established the method's Lagrangian structure and Eulerian fluid-grid formulation.
Fluid–structure interaction: The coupled dynamics of a fluid and a deformable or moving solid. Immersed boundary methods are a major way to compute this two-way interaction on nonconforming grids.
Body-fitted grid: A computational mesh whose cells conform to the boundaries of the modeled domain. It resolves boundaries geometrically, unlike immersed methods that leave the background grid unaligned.
Regularized delta function: A smoothed approximation to the Dirac delta function used to distribute point quantities over nearby grid cells. It transfers forces from structural points to the fluid grid and interpolates velocities back.
Heart valve simulation: Computational modeling of blood flow interacting with deforming heart valves. This was the motivating problem for Peskin's original immersed boundary formulation.
Blood flow simulation: Computational modeling of blood motion through vessels and heart chambers. Immersed boundaries can represent moving valves and vessel structures within a fluid domain.
Cut-cell method: A Cartesian-grid technique that clips cells intersected by boundaries and computes fluxes through the resulting fragments. It represents sharp geometry through modified cells rather than spread forces or boundary corrections.
Penalty method: A numerical technique that enforces constraints approximately by adding restoring forces proportional to constraint violations. It can keep fluid motion close to a moving boundary without fitting grid cells to it.
IBM marker-and-cell method: A computational method developed by Peskin for simulating fluid flow interacting with elastic structures. It introduced the marker-force coupling that became the classical immersed boundary method.

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Lattice Boltzmann methodRelated: It can couple deformable boundaries to lattice Boltzmann fluid solvers.