A Cartesian Grid Method for Solving the Two-Dimensional Streamfunction-Vorticity Equations in Irregular Regions

Calhoun, Donna

doi:10.1006/jcph.2001.6970

Cited by 281 publications

(170 citation statements)

References 46 publications

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“…C D Calhoun [2] 1.62 Dennis and Chang [3] 1.52 Fornberg [6] 1.50 Taira and Colonius [19] 1.55 Present 1.50 the gravity and the background fluid flow, the disc moves in both the horizontal and vertical directions. Figure 4 shows the displacement of the center of the disc, relative to its initial position, as time goes from 0 to 1.…”

Section: Re=40mentioning

confidence: 99%

Partitioned Computation for Fluid-structure Interaction with Rigid Body Motion

Timalsina¹,

Hou²,

Wang³

2018

JAAM

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We present a new computational framework for fluid-structure interaction problems that involve rigid body motion. Based on a partitioned strategy, the fluid and structural dynamics are computed separately, and the solutions communicate at the interface. The immersed boundary method is employed to handle the fluid-structure interaction, and the direct-forcing technique is utilized to calculate the interaction force. In particular, the rigid body motion is directly and explicitly incorporated into the formulation and computation of the structural dynamics. We demonstrate our methodology by numerically simulating the motion of single and multiple rigid circular discs interacting with nonlinear viscous flow.

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Section: Re=40mentioning

confidence: 99%

Partitioned Computation for Fluid-structure Interaction with Rigid Body Motion

Timalsina¹,

Hou²,

Wang³

2018

JAAM

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“…Assume the (symmetric) diffusion tensor σ in ℒ has the form (51) Writing out the jump (50c) of the normal flux n · σ∇u gives us (52) Differentiating (50b) in the tangential direction t, we see that (53) The determinant of the two by two system (52)-(53) is equal to (54) which with In addition, denote by ρ the jump of the extended source f̃ in (50a), i.e., (57) Writing out (57) explicitly gives us (58) with The determinant of the coefficient matrix in the three by three system (55)- (57) is equal to (59) which is uniformly bounded by a positive constant from below too. So, the jumps ( .…”

Section: Calculation Of Jumps Of the Partial Derivativesmentioning

confidence: 99%

“…This paper presents a class of kernel-free boundary integral (KFBI) methods for solving the elliptic BVPs. It is similar, in spirit, to Li's augmented strategy for constant coefficient problems [25], Wiegmann and Bube's explicit jump II method [26] and Calhoun's Cartesian grid method [52], and is a direct extension of Mayo's original approach [13,41,42]. The most obvious difference of the method from others is that it works with more general elliptic operators with possible anisotropy and inhomogeneity.…”

Section: Introductionmentioning

confidence: 97%

A kernel-free boundary integral method for elliptic boundary value problems

Ying

Henriquez

2007

Journal of Computational Physics

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This paper presents a class of kernel-free boundary integral (KFBI) methods for general elliptic boundary value problems (BVPs). The boundary integral equations reformulated from the BVPs are solved iteratively with the GMRES method. During the iteration, the boundary and volume integrals involving Green's functions are approximated by structured grid-based numerical solutions, which avoids the need to know the analytical expressions of Green's functions. The KFBI method assumes that the larger regular domain, which embeds the original complex domain, can be easily partitioned into a hierarchy of structured grids so that fast elliptic solvers such as the fast Fourier transform (FFT) based Poisson/Helmholtz solvers or those based on geometric multigrid iterations are applicable. The structured grid-based solutions are obtained with standard finite difference method (FDM) or finite element method (FEM), where the right hand side of the resulting linear system is appropriately modified at irregular grid nodes to recover the formal accuracy of the underlying numerical scheme. Numerical results demonstrating the efficiency and accuracy of the KFBI methods are presented. It is observed that the number of GM-RES iterations used by the method for solving isotropic and moderately anisotropic BVPs is independent of the sizes of the grids that are employed to approximate the boundary and volume integrals. With the standard second-order FEMs and FDMs, the KFBI method shows a second-order convergence rate in accuracy for all of the tested Dirichlet/Neumann BVPs when the anisotropy of the diffusion tensor is not too strong.

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“…aeronautics, civil engineering, biological flows, etc.). The number of works in this field is rapidly increasing, which reflects the growing importance of studying the dynamics in the solid-fluid interaction [1][2][3][4]. Most of these simulations are compute-intensive and benefit from high performance computing systems.…”

Section: Introductionmentioning

confidence: 99%

Accelerating fluid–solid simulations (Lattice-Boltzmann & Immersed-Boundary) on heterogeneous architectures

Valero-Lara

Igual

Prieto-Matías

et al. 2015

Journal of Computational Science

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a b s t r a c tWe propose a numerical approach based on the Lattice-Boltzmann (LBM) and Immersed Boundary (IB) methods to tackle the problem of the interaction of solids with an incompressible fluid flow, and its implementation on heterogeneous platforms based on data-parallel accelerators such as NVIDIA GPUs and the Intel Xeon Phi. We explain in detail the parallelization of these methods and describe a number of optimizations, mainly focusing on improving memory management and reducing the cost of hostaccelerator communication. As previous research has consistently shown, pure LBM simulations are able to achieve good performance results on heterogeneous systems thanks to the high parallel efficiency of this method. Unfortunately, when coupling LBM and IB methods, the overheads of IB degrade the overall performance. As an alternative, we have explored different hybrid implementations that effectively hide such overheads and allow us to exploit both the multi-core and the hardware accelerator in a cooperative way, with excellent performance results.

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A Cartesian Grid Method for Solving the Two-Dimensional Streamfunction-Vorticity Equations in Irregular Regions

Cited by 281 publications

References 46 publications

Partitioned Computation for Fluid-structure Interaction with Rigid Body Motion

Partitioned Computation for Fluid-structure Interaction with Rigid Body Motion

A kernel-free boundary integral method for elliptic boundary value problems

Accelerating fluid–solid simulations (Lattice-Boltzmann & Immersed-Boundary) on heterogeneous architectures

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