The immersed interface method for the Navier-Stokes equations with singular forces

By Zhilin Li, Ming-Chih Lai. 2001

424 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/6254976f8aa5098d22eef2a7459c81413397b252

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In Computational Mechanics

Citations in the corpus

A hybrid Cartesian/immersed boundary method for simulating flows with 3D, geometrically complex, moving bodies (2005, methodology): “This method was initially applied to solve 2D elliptic equations [30] and Stokes flow problems with flexible boundaries [31] and more recently it was extended to solve the 2D, incompressible Navier–Stokes equations [32].”
An immersed boundary technique for simulating complex flows with rigid boundary (2007, methodology): “Lai and Peskin [18] proposed a new formally second-order accurate immersed boundary method to simulate flows past a rigid cylinder.”
A mass‐conserving Level‐Set method for modelling of multi‐phase flows (2005, neutral): “If s is parallel to the interface, un= n · u and us= s · u, it can be shown [23, 24] that in general [ @un @n ] =0; [ @un @s ] =0 [ @us @n ] =−[ ] @un @s ; [ @us @s ] =0 (9)”
A Fast Finite Differenc Method For Solving Navier-Stokes Equations on Irregular Domains (2003, methodology): “Among them are, just to name a few, Peskin’s immersed boundary method with numerous applications [7, 8, 11, 24, 28]; the ghost fluid method [15]; the immersed interface method [16]; the finite volume method [2, 26, 29, 32], etc.”
A Cartesian Grid Method for Solving the Two-Dimensional Streamfunction-Vorticity Equations in Irregular Regions (2002, methodology): “For one example of how the immersed interface method can be applied to a primitive variable formulation of the Navier–Stokes equations, see [29].”
A discontinuous‐Galerkin‐based immersed boundary method (2008, background): “The precise way to do it varies among authors, and not all of them are equivalent in terms of accuracy [38, 72, 71, 19, 45, 62].”
Simulating flows with moving rigid boundary using immersed-boundary method (2010, methodology): “Based on work of Li and Lai [8] for the Navier–Stokes equations with singular forcing, the IIM has also been explored by Le et al.”
An Immersed Interface Method for Incompressible Navier-Stokes Equations (2003, methodology): “This is the approach used by Li and Lai [16], but it is considerably more complicated and the jumps in derivatives of the velocity (the last jump conditions in (2.4)) must also be explicitly incorporated in a different manner with this approach.”
Numerical Methods for Fluid-Structure Interaction — A Review (2012, methodology): “Various applications of this method have been studied (e.g., Jayathilake, Khoo and Tan 2010; Layton 2009, Li and Lai 2001; Tan, Lim and Khoo 2009); careful mathematical analysis of its accuracy has also been conducted (e.g., Beale and Layton 2006, 2009; Tornberg and Engquist 2004).”
The immersed boundary method (2002, methodology): “As mentioned above, the ‘immersed interface method’ (LeVeque and Li 1994, LeVeque and Li 1997, Li and Lai 2001 ) avoids this smearing and maintains second-order accuracy by modifying the dierence equations near the interface.”
An immersed interface method for simulating the interaction of a fluid with moving boundaries (2006, methodology): “In this test, we compute the moving boundary problem considered by Li and Lai [19], where a 2D distorted pressurized balloon immersed in an incompressible fluid relaxes to its circular equilibrium shape.”