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...or the regular part both extend naturally to 3D. The motion of the interface would have to be represented differently in three dimensions. The level set method can be used in 2D or 3D ([19],[15]). In =-=[3]-=- 2D periodic Stokes flow with an interface was computed using Strain’s semi-Lagrangian contouring method for the interface motion and Ewald summation for velocity integrals, an approach which extends ...

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...re translated into the jump conditions across the interface. These jump conditions are then taken care by changing the discretization of the differential operators at stencils acrossing the interface =-=[19, 3]-=-. To our point of view, there are still some aspects left to be improved for the methods initiated by Peskin, LeVeque and Li: Immersed boundary method in general is only first order in space [25, p.50...

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...essible flow, the surface stretching is recorded in the function φ, which allows us to rephrase our fluid-structure problem with this function. There is several ways to prove this intuitive fact, see =-=[8, 7, 2]-=-. We could start from the stretching written in Lagrangian and prove that |∇φ| verifies the same equation, as in [19] that is to say ∂t|∇φ|+u∇|∇φ| = −|∇φ| ∇φT ∇u∇φ |∇φ| 2 = −|∇φ| ∇φ ∇φ ⊗ : ∇u |∇φ| |∇φ...

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...numerical methods for FSI. One of the earliest and perhaps most influential methods is the immersed boundary method (IBM) of Peskin [59,43]. IBM directly motivates the immersed interface method (IIM) =-=[46,55,48,6,7,44,39]-=- and the immersed finite element method (IFEM) [75,54,74,33,71]. IBM details related to the work of different schools on ods for FSI. The well-posedness of FSI has been studied b for various models. B...

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...e of interest. For the sharp interface analysis of the functional, we refer to [15,39,45]. An even simpler but better known energy functional is given by E[φ] = ∫ ( 2 |∇φ|2 + 1 4 (φ2 − 1)2 ) dx, =-=(3)-=- which has often been used to model the dimensionless interfacial tension (interfacial area) [1]. Given an interfacial energy E = E[φ] (or E = Eb[]) defined for the phase field function φ, the determ...

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...0, 2016http://rspa.royalsocietypublishing.org/Downloaded froms2916 M. Higley et al. Studies of capsules in fluid flow have been conducted with different membrane constitutive laws, including Hookean (=-=Beale & Strain 2008-=-), neo-Hookean or Skalak (Walter et al. 2010), and area-incompressible or inextensible membranes (Veerapaneni et al. 2009). Different numerical methods have also been used, such as boundary integral a...

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...essible flow, the surface stretching is recorded in the function φ, which allows us to rephrase our fluid-structure problem with this function. There is several ways to prove this intuitive fact, see =-=[8, 7, 2]-=-. We could start from the stretching written in Lagrangian and prove that |∇φ| verifies the same equation, as in [19] that is to say ∂t|∇φ|+ u∇|∇φ| = −|∇φ| ∇φT∇u∇φ |∇φ|2 = −|∇φ| ∇φ |∇φ| ⊗ ∇φ |∇φ| : ∇u...