An Immersed Interface Method for Incompressible Navier-Stokes Equations

By Long Lee, Randall J. LeVeque. SIAM Journal on Scientific Computing, 2003

385 citations recorded by the source corpus.

Subfields: Computational Mechanics, Surfaces, Coatings and Films

View Paper: https://www.semanticscholar.org/paper/d91e1fa4dc998c80033b38f3bce11bef39e91d7e

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Citations in the corpus

An unfitted finite element method using discontinuous Galerkin (2009, methodology): “The Immersed Boundary Method [6] and Immersed Interface Method [7] are based on the same idea as the Fictitious domain method, but the constraints are introduced using virtual forces.”
A surfactant-conserving volume-of-fluid method for interfacial flows with insoluble surfactant (2004, background): “[34– 42,55,56]), coupled level-set and volume of fluid [43–45], immersed interface (e.g. see [48,49,26, 27 ]) and ghost-fluid (e.g.”
On the numerical oscillation of the direct-forcing immersed-boundary method for moving boundaries (2012, methodology): “In the method presented by Li and coworkers [6, 7], the solution experiences discontinuities across the physical interface immersed in the domain, and the finite-difference formulae involving the nodes across the interface are corrected by taking into consideration of the discontinuities.”
High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources (2006, background): “Various extensions and further improvements of the IIM have been considered in the literature [4– 6,10,16–19,21,23,24,30,31,36,42,43,46,47,51].”
A discontinuous‐Galerkin‐based immersed boundary method (2008, neutral): “Locally, a boundary–fitting interpolation is built by means of a specific treatment of the grid points adjacent to the boundary [41, 40, 36].”
Drag law for monodisperse gas–solid systems using particle-resolved direct numerical simulation of flow past fixed assemblies of spheres (2011, methodology): “ch as the immersed interface method (Lee and Leveque, 2003; Xu and Wang, 2006).”
An immersed interface method for simulating the interaction of a fluid with moving boundaries (2006, methodology): “Examples include the virtual/immersed boundary method Motivated by the goal to eventually obtain second-order accuracy in Peskin's immersed boundary method, LeVeque and Li [17] [18] developed the immersed interface method.”
An eXtended Finite Element Method/Lagrange multiplier based approach for fluid-structure interaction (2008, methodology): “Prominent fixed grid methods for incompressible flow include the Immersed Boundary (IB) method [35,36] and its many derivations [24,26,28].”
Modelling and simulation of porous immersed boundaries (2009, methodology): “Lee and LeVeque [19] developed a hybrid approach for simulating immersed boundaries, based on a combination of the immersed interface method and the IB method, which uses a higher order correction to the difference stencils for the jump in normal stress across the membrane (i.e., correcting for the ”
An adaptive, formally second order accurate version of the immersed boundary method (2007, methodology): “(An alternative approach is taken by the immersed interface method [44,45], where such discontinuities are explicitly accounted for by the method in a manner that yields higher order accuracy.”
On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficiently smooth problems (2005, methodology): “These oscillations, sometimes considered to be a characteristic of the immersed boundary method [13], are virtually eliminated by making use of our hybrid method.”
Direct numerical simulations of gas/liquid multiphase flows (2011, methodology): “These include the method of Glimm and collaborators (Glimm and McBryan, 1985), where the fixed grid is modified near the front to 15 make a grid line follow the interface, as well as more recent “sharp-interface methods” (such as Fedkiw et al., 1999; Ye et al., 1999; Lee and LeVeque, 2003).”
The immersed boundary method: A projection approach (2007, methodology): “In the IIM, the boundary force is decomposed into tangential and normal components (fs and fn, respectively).”