The immersed boundary method: A projection approach

By Kunihiko Taira, Tim Colonius. 2007

695 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Methods & Scientific Computing

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Steven L. Brunton
2. J. Nathan Kutz
3. Maizar Raissi
4. G. Em Karniadakis
5. Joshua L. Proctor
6. Paris Perdikaris
7. Clarence W. Rowley
8. Bingni W. Brunton

In Numerical Methods & Scientific Computing

1. Maizar Raissi
2. G. Em Karniadakis
3. Paris Perdikaris
4. Steven L. Brunton
5. J. Nathan Kutz
6. Clarence W. Rowley
7. Bingni W. Brunton
8. Scott T. M. Dawson

Citations in the corpus

• Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations (2018, methodology): “Specifically, we simulate the Navier-Stokes equations describing the two-dimensional fluid flow past a circular cylinder at Reynolds number 100 using the Immersed Boundary Projection Method [46, 47].”
• Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems (2018, methodology): “In particular, following the problem setup presented in [23] and [24], we simulate the Navier-Stokes equations describing the two-dimensional fluid flow past a circular cylinder at Reynolds number 100 using the Immersed Boundary Projection Method [25, 26].”
• Discovering governing equations from data by sparse identification of nonlinear dynamical systems (2015, methodology): “Data are collected for the fluid flow past a cylinder at Reynolds number 100 using direct numerical simulations of the 2D Navier–Stokes equations (44, 45).”
• Hidden physics models: Machine learning of nonlinear partial differential equations (2017, methodology): “As for the data, following the exact same instructions as the ones provided in [34] and [2], we simulate the Navier-Stokes equations describing the two-dimensional fluid flow past a circular cylinder at Reynolds number 100 using the Immersed Boundary Projection Method [35, 36].”
• A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations (2009, methodology): “In [12], the force at the boundary is determined explicitly while in [13,14] the force is computed implicitly by solving a linear system.”
• Model Reduction for Flow Analysis and Control (2017, methodology): “The data were generated using an immersed boundary projection method (Taira & Colonius 2007, Colonius & Taira 2008), with the unstable equilibrium solution computed by employing selective frequency damping (Åkervik et al. 2006).”
• Machine-learning-based spatio-temporal super resolution reconstruction of turbulent flows (2020, methodology): “With both coarse input data, the reconstructed flow fields are in reasonable agreement with the reference DNS data in terms of the contour plots and the L 2 error norms listed below the reconstructed flow field.”
• Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition (2014, methodology): “We use an immersed boundary projection method (Taira and Colonius, 2007; Colonius and Taira, 2008), with a domain consisting of a series of nested grids, with the finest grid enclosing the body, and each successive grid twice as large as the previous.”
• On dynamic mode decomposition: Theory and applications (2013, methodology): “We simulate the dynamics using the fast immersed boundary projection method detailed in [34,35].”
• Physics-informed learning of governing equations from scarce data (2020, neutral): “, SINDy [5, 6]) to produce a reasonable discovery.”