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...e interaction equations, see [27]. 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]-=-). More recently, the finite element method has been applied to the spatial discretization of the IBM in [4, 5, 35, 36]. In particular, in [35, 36] it has been proposed the EIBM, extended immersed bou...

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...oblem at the low Reynolds number of the present application, in which the nonlinear terms are negligible in any case. For improved accuracy and reduced numerical viscosity, the IB method described in =-=[22, 23, 24]-=- is currently recommended. 5. “Measuring” the bending modulus and twist modulus. For comparison with the theory of [1] it is important to know the macroscopic bending modulus A of our elastic filament...

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...ments in the immersed boundary methodology have made it possible to raise the Reynolds numbers of computations such as these from the current value of 2 at least to 200 if not higher, see for example =-=[17, 23, 24]-=-. An important future direction will be to apply this improved methodology to the flow in collapsible tubes. But the collapse of tubes at Reynolds number of order 1 is also interesting, and perhaps be...

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... is made on its suitability in three dimensions. Lai and Peskin recently applied the immersed boundary method to solve the cylinder flow problem, although only uniform Cartesian grids were considered =-=[25]-=-. For the present cylinder flow simulation, we use a simplified form of IMBM suitable for flows where the coupling between moving boundaries and the flow is only one-way (i.e., the boundary is known a...

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...ized by a standard finite difference method in a fixed Cartesian (or nonCartesian) grid. The singular delta function is regularized by an approximate smooth function spanning a few grid cells. The immersed boundary method has been incorporated in the front tracking method [50] and the level set method [45,46,6] in the interface treatment. The immersed boundary method, however, is only first order accurate in computing two-phase flow with discontinuous solutions across the interface, even though higher-order approximation to the delta function can be achieved for problems with smooth solutions [4,22,49,15,9]. Beyer and LeVeque [4] studied the approximation to the delta function by a smooth function for the one-dimensional heat equation. The accuracy was measured by a discrete moment condition. They found that it is possible to achieve second-order accuracy by carefully choosing the discrete representation of the delta function. For some problems, however, it is necessary to add a correction term to the approximation to the delta function in order to maintain second-order accuracy. Griffith and Peskin [15] showed that higher-order convergence rates can only be achieved for sufficiently smooth prob...

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...age of simplicity and efficiency for this type of problem. The immersed boundary method is a robust Cartesian grid method. It was originally proposed by Peskin [23, 24] and later further developed in =-=[29, 26, 27, 16]-=-. In this method, the moving surface of an immersed object is parametrized by a set of Lagrangian points comoving with a fluid. The relative positions of the Lagrangian points determine a singular for...

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... blood clotting [5], the deformation of red blood cells in a shear flow [4], the flow in collapsible thin walled vessels [3], the swimming of eels, sperm and bacteria [6, 2], the flow past a cylinder =-=[12]-=-, two-dimensional [1] and three-dimensional models of the cochlea [8], valveless pumping [11] and flexible filament flapping in a flowing soap film [21]. For a recent review of the research in immerse...