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...d the nature of the motion require that the disk change its shape only and not its volume. However, as shown in Fig. 9, from our numerical scheme we obtain an area change of the disk of about 4% (cf. =-=Griffith, 2012-=-). Figure 6: The initial configuration of an immersed disk entrained in a flow in a square cavity whose lid is driven with a velocity U towards the right. 5.2.3 Cylinder Falling in Viscous Fluid In th...

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... the solid moves, resulting in additional computational cost. Moreover, in some cases, the coordinate transformation needed at each time step affects volume conservation during velocity interpolation =-=[12]-=-. Under a fully Eulerian description, one considers both fluid and structure as a single continuum model. This strategy avoids some difficulties related to, for example, mesh distortion; however, addi...

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...listed in Table 6.5.2 and shown in Figure 6.5.2. 6.5.2 Simulation of an elastic membrane As a second test on code reliability we compared the results of our code with the ones reported by Griffith in =-=[48]-=-, where the dynamics of a thin, elastic and mass-less membrane immersed in a viscous incompressible fluid was performed. The fluid is taken initially at rest and the membrane is an ellipse with semi-m...

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...staggered-grid finite difference scheme, an approach that yields superior accuracy when used with the IB method as compared to collocated discretizations (i.e., purely cell- or node-centered schemes) =-=[32]-=-. To simplify the exposition, we assume that Ω is the unit square and is discretized on a regular N ×N Cartesian grid with grid spacings ∆x1 = ∆x2 = h = 1N . Let (i, j) label the individual Cartesian ...

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...ion by thermal velocities to diffusive transport [31]. A staggered spatial discretization is advantageous for incompressible flows because it leads to a robust idempotent discrete projection operator =-=[32, 33]-=-. Staggered schemes have previously been developed for isothermal compressible [26] and incompressible flow [20], without, however, carefully assessing discrete fluctuationdissipation balance. Here we...

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...o the two-dimensional adaptive version of the conventional IB method described by Roma et al. [9], and to the adaptive three-dimensional IB method described by Griffith [13]. As discussed by Griffith =-=[15]-=-, staggered-grid IB methods appear to have clear advantages in terms of volume conservation and resolution of pressure discontinuities when compared to collocated IB discretizations, such as those use...

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...be a challenge due to their strong nonlinearity and multi-physics nature. The development of numerical solvers for fluid-structure interaction problems has become particularly active since the 1980’s =-=[64, 65, 25, 33, 50, 47, 37, 36, 39, 38, 22, 43, 42, 48, 49, 68, 67, 3, 69, 23, 26, 45, 46, 19, 32]-=-. Until recently, only monolithic algorithms seemed applicable to blood flow simulations [32, 34, 63, 72, 10, 11]. These algorithms are based on solving the entire nonlinear coupled problem as one mon...

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...to this problem.We choose to use “thick” structures for our numerical tests because the IB method is known to yield poor volume conservation when applied to problems involving thin elastic structures =-=[9]-=-. This unphysical leakage of fluid across the boundary is exacerbated by high elastic stiffness, making it difficult to reach the extreme stiffnesses considered in this work. (Although not shown here,...