Analysis of a Fractional-Step Method on Overset Grids

Burton, Tristan; Eaton, John K.

doi:10.1006/jcph.2002.7012

Cited by 38 publications

(26 citation statements)

References 16 publications

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“…The numerical method used to simulate the flow around the spherical particles is a second-order staggered overset grid method, inspired by and similar to the method used by Burton & Eaton (2002, 2005 to simulate turbulent flow around a single spherical particle. However, the details are not the same.…”

Section: Particle-resolved Simulation Methodsmentioning

confidence: 99%

“…This means that 3 × 27 Cartesian grid points and as many weight coefficients are used for each velocity component in a virtual cell. Burton & Eaton (2002) also used third-order interpolations, but they interpolated the pressure gradient instead of the pressure. Interpolation of the pressure was used by Chesshire & Henshaw (1990) and Henshaw (1994), who developed discretization methods for collocated overlapping grids.…”

Section: Appendix a Further Specification Of The Numerical Methodsmentioning

confidence: 99%

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Particle-resolved direct numerical simulation of homogeneous isotropic turbulence modified by small fixed spheres

Vreman

2016

J. Fluid Mech.

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A statistically stationary homogeneous isotropic turbulent flow modified by 64 small fixed non-Stokesian spherical particles is considered. The particle diameter is approximately twice the Kolmogorov length scale, while the particle volume fraction is 0.001. The Taylor Reynolds number of the corresponding unladen flow is 32. The particle-laden flow has been obtained by a direct numerical simulation based on a discretization of the incompressible Navier-Stokes equations on 64 spherical grids overset on a Cartesian grid. The global (space-and time-averaged) turbulence kinetic energy is attenuated by approximately 9 %, which is less than expected. The turbulence dissipation rate on the surfaces of the particles is enhanced by two orders of magnitude. More than 5 % of the total dissipation occurs in only 0.1 % of the flow domain. The budget of the turbulence kinetic energy has been computed, as a function of the distance to the nearest particle centre. The budget illustrates how energy relatively far away from particles is transported towards the surfaces of the particles, where it is dissipated by the (locally enhanced) turbulence dissipation rate. The energy flux towards the particles is dominated by turbulent transport relatively far away from particles, by viscous diffusion very close to the particles, and by pressure diffusion in a significant region in between. The skewness and flatness factors of the pressure, velocity and velocity gradient have also been computed. The global flatness factor of the longitudinal velocity gradient, which characterizes the intermittency of small scales, is enhanced by a factor of six. In addition, several point-particle simulations based on the Schiller-Naumann drag correlation have been performed. A posteriori tests of the point-particle simulations, comparisons in which the particle-resolved results are regarded as the standard, show that, in this case, the point-particle model captures both the turbulence attenuation and the fraction of the turbulence dissipation rate due to particles reasonably well, provided the (arbitrary) size of the fluid volume over which each particle force is distributed is suitably chosen.

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Section: Particle-resolved Simulation Methodsmentioning

confidence: 99%

Section: Appendix a Further Specification Of The Numerical Methodsmentioning

confidence: 99%

Particle-resolved direct numerical simulation of homogeneous isotropic turbulence modified by small fixed spheres

Vreman

2016

J. Fluid Mech.

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“…Zang and Street [57] have suggested a global mass imbalance correction proportional to the flux to satisfy the global mass conservation for their fractional step method. Burton and Eaton [58] also use an explicit correction but proportional to the local area for their fractional step method. Such local flux correction has been shown to be second order accurate by Zang and Street [57].…”

Section: Methodsmentioning

confidence: 99%

“…Consequently, an explicit mass-imbalance correction needs to be added to the interpolated velocity field to ensure global mass conservation on each overlapping grid. Zang and Street [57] add such an explicit correction, which is proportional to the local flux at each cell, and Burton and Eaton [58] add an explicit correction, which is proportional to the local area of each cell. As shown by Zang and Street such corrections retain the second order accuracy of the solution [57].…”

Section: Introductionmentioning

confidence: 99%

A parallel overset-curvilinear-immersed boundary framework for simulating complex 3D incompressible flows

Borazjani

et al. 2013

Computers & Fluids

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We develop an overset-curvilinear immersed boundary (overset-CURVIB) method in a general non-inertial frame of reference to simulate a wide range of challenging biological flow problems. The method incorporates overset-curvilinear grids to efficiently handle multi-connected geometries and increase the resolution locally near immersed boundaries. Complex bodies undergoing arbitrarily large deformations may be embedded within the overset-curvilinear background grid and treated as sharp interfaces using the curvilinear immersed boundary (CURVIB) method (Ge and Sotiropoulos, Journal of Computational Physics, 2007). The incompressible flow equations are formulated in a general non-inertial frame of reference to enhance the overall versatility and efficiency of the numerical approach. Efficient search algorithms to identify areas requiring blanking, donor cells, and interpolation coefficients for constructing the boundary conditions at grid interfaces of the overset grid are developed and implemented using efficient parallel computing communication strategies to transfer information among sub-domains. The governing equations are discretized using a second-order accurate finite-volume approach and integrated in time via an efficient fractional-step method. Various strategies for ensuring globally conservative interpolation at grid interfaces suitable for incompressible flow fractional step methods are implemented and evaluated. The method is verified and validated against experimental data, and its capabilities are demonstrated by simulating the flow past multiple aquatic swimmers and the systolic flow in an anatomic left ventricle with a mechanical heart valve implanted in the aortic position.

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“…This is a widely discussed topic in the literature with application to the quasi-implicit form of the CBS or similar splitting methods (often referred to as the semi-implicit fractional step method) [93,[99][100][101][102]. However, due to the three-step procedure introduced within the CBS procedure it is prone to a "so-called" splitting error.…”

Section: Splitting Errormentioning

confidence: 99%

The Characteristic-Based Split (CBS) Algorithm: A General Procedure for Compressible and Incompressible Flow

Zienkiewicz¹,

Taylor²,

Nithiarasu³

2014

The Finite Element Method for Fluid Dynamics

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Analysis of a Fractional-Step Method on Overset Grids

Cited by 38 publications

References 16 publications

Particle-resolved direct numerical simulation of homogeneous isotropic turbulence modified by small fixed spheres

Particle-resolved direct numerical simulation of homogeneous isotropic turbulence modified by small fixed spheres

A parallel overset-curvilinear-immersed boundary framework for simulating complex 3D incompressible flows

The Characteristic-Based Split (CBS) Algorithm: A General Procedure for Compressible and Incompressible Flow

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