2016
DOI: 10.1016/j.jcp.2016.04.023
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A fast lattice Green's function method for solving viscous incompressible flows on unbounded domains

Abstract: A computationally efficient method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. The method formally discretizes the incompressible Navier-Stokes equations on an unbounded staggered Cartesian grid. Operations are limited to a finite computational domain through a lattice Green's function technique. This technique obtains solutions to inhomogeneous difference equations through the discrete convolution of source terms with the fundamental solutions of the discret… Show more

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Cited by 29 publications
(83 citation statements)
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“…In order to eliminate the errors associated with artificial boundary conditions and to limit operations to small regions dictating the flow evolution (e.g. regions of significant vorticity), while preserving the efficiency and robustness inherent to Cartesian staggered grid methods, we proposed [26] a fast incompressible Navier-Stokes solver based on the fundamental solution, or lattice Green's function (LGF), of discrete operators. Similar to particle and vortex methods, LGF techniques have efficient nodal distributions, automatically enforce natural free-space boundary conditions, and can be evaluated using fast multipole methods (FMMs), e.g.…”
Section: Introductionmentioning
confidence: 99%
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“…In order to eliminate the errors associated with artificial boundary conditions and to limit operations to small regions dictating the flow evolution (e.g. regions of significant vorticity), while preserving the efficiency and robustness inherent to Cartesian staggered grid methods, we proposed [26] a fast incompressible Navier-Stokes solver based on the fundamental solution, or lattice Green's function (LGF), of discrete operators. Similar to particle and vortex methods, LGF techniques have efficient nodal distributions, automatically enforce natural free-space boundary conditions, and can be evaluated using fast multipole methods (FMMs), e.g.…”
Section: Introductionmentioning
confidence: 99%
“…the 2D serial method [27] and the 3D parallel method [28]. Using the LGF-FMM [28] in combination with an projection technique that is free of splitting errors, the LGF flow solver [26] computes fast, parallel solutions to the viscous integrating factor (IF) half-explicit Runge-Kutta (HERK) time integration scheme used to solve the velocity and pressure of the flow.…”
Section: Introductionmentioning
confidence: 99%
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“…Additionally, the FLGF exploits fast Fourier transforms (FFT) to further reduce the computational costs compared to conventional solvers. It has been successfully applied to solve the incompressible Navier-Stokes equations using a finite volume approach [14]. In addition, accurate simulations of external aerodynamics of complex geometries were enabled by coupling it with the immersed boundary method (IB-LGF) [15].…”
Section: Introductionmentioning
confidence: 99%