An Immersed Boundary Method with Formal Second-Order Accuracy and Reduced Numerical Viscosity

By Ming-Chih Lai, Charles S. Peskin. 2000

956 citations recorded by the source corpus.

Subfields: Computational Mechanics, Fluid Flow and Transfer Processes

View Paper: https://www.semanticscholar.org/paper/95bf4d6b2234d866240908d2c45b19c4314c57de

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In Computational Mechanics

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Citations in the corpus

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].”
A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries (2008, methodology): “First, unlike some past immersed boundary methods [16,23], there are no ad-hoc constants introduced in this procedure and neither is any momentum forcing term [41,23] employed in any of the fluid cells.”
High‐order stable interpolations for immersed boundary methods (2006, methodology): “It is originally rst-order accurate and has been refurbished by Lai and Peskin [5] to be second-order accurate.”
Simulation of a Flapping Flexible Filament in a Flowing Soap Film by the Immersed Boundary Method (2002, methodology): “) is that the skew-symmetric scheme has the desirable property that d dt ‖u‖(2)L2 = 0 (see [27]), which guarantees conservation of kinetic energy of the soap film.”
On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficiently smooth problems (2005, methodology): “In [1,2], Lai and Peskin introduced a formally second order accurate immersed boundary method, but the convergence properties of their algorithm have only been examined computationally for problems with non-smooth solutions.”
A finite element approach to the immersed boundary method (2003, methodology): “The temporal discretization that is currently used by Peskin and his coauthors is a second-order accurate Runge-Kutta method, based on the midpoint rule (see, e.g., [ 21 , 25]).”
A ghost-cell immersed boundary method for flow in complex geometry (2002, methodology): “St is tabulated in Table 1 and matches well with the experiments of Williamson as reported in [25].”
The immersed interface method for the Navier-Stokes equations with singular forces (2001, methodology): “Nevertheless, both approaches described in [5] and [18] use the discrete delta function which usually smears out the solution across the interface.”
A cartesian grid method for modeling multiple moving objects in 2D incompressible viscous flow (2003, methodology): “This result can be generalized to discontinuities in w and any of its derivatives, resulting in a Taylor-like expansion x j ¼ ~ x x j þ ½w þ d ow ox Â Ã þ 1 2 d 2 o 2 w ox 2 h i þ Á Á Á Dx 2 : ð26Þ It is worth noting that an alternative method for handling the discontinuity is expressing it terms o”
A mass‐conserving Level‐Set method for modelling of multi‐phase flows (2005, methodology): “The front-tracking method [3, 4] and the closely related immersed boundary method [5] are combinations of xed and moving mesh methods.”
The immersed boundary method (2002, methodology): “Flow past a cylinder has been studied by the IB method (Lai and Peskin 2000).”
Implicit second-order immersed boundary methods with boundary mass (2008, methodology): “We take the average of the above expressions to obtain the following discretization of the convection term [ 31 ,19]:”