A Taylor series‐based finite volume method for the Navier–Stokes equations

Wu, G.X.; Hu, Zheng

doi:10.1002/fld.1767

Cited by 7 publications

(3 citation statements)

References 16 publications

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“…These distances are comparable to those in previous publications, for example in Wu & Hu (2008) [29] and are sufficient to neglect the effects of the boundary truncation far upstream and downstream of the cylinder. For the cases with the wall and symmetry boundaries, the top boundary is located at a height of 10D from the centre of the cylinder.…”

Section: Problem Setupsupporting

confidence: 85%

Boundary shear flow past a cylinder near a wall

Chen

2019

Applied Ocean Research

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An investigation on boundary shear flow past a circular cylinder near a wall is numerically performed via a stabilized finite element method. The main focus is to uncover its major difference with the flows corresponding to the symmetry boundary, and to two identical circular cylinders in a side-by-side arrangement. In particular at Reynolds number Re = 100, extensive simulations are made for different gaps between the cylinder and wall. It is noted that in the wake of the cylinder the vortex contour lines shift upwards. At Re = 100, the flow behind a cylinder near the wall may be time dependent. With a reduction of the gap spacing to a magnitude in (0.75,1), the vortex shedding nearly vanishes. For the flow behind two identical circular cylinders side and side, the flow may change from periodic flow to totally irregular one. The drag force C D , lift force C L,rms and Strouhal number St of the circular cylinder near the wall vary differently with the gap, compared with those in the other two cases. When the cylinder is located in the boundary layer, the boundary shear flow has strong effect on the hydrodynamic quantities. Extensive simulations are also made for Re = 200, 400, 600 and 800. It is found that the Reynolds number has strong effect on the flow and force on the cylinder, not only through the variation of Re itself but also the boundary layer of the wall. Withe Re increasing, strong vortex shedding from the near-wall cylinder at e = 0.5 starts above a Re in (200, 300).

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Section: Problem Setupsupporting

confidence: 85%

Boundary shear flow past a cylinder near a wall

Chen

2019

Applied Ocean Research

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“…All the variables are defined at the centre of each cell. The values required at each cell face are obtained through interpolation from the centres of the two cells that share this face [20].…”

Section: Governing Equations and Numerical Methods For Fluid Flowmentioning

confidence: 99%

Flow-induced transverse vibration of a circular cylinder close to a plane wall at small gap ratios

Chen

2020

Applied Ocean Research

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Numerical simulations of flow-induced transverse vibration of a near-wall cylinder with small gap to diameter ratios (e/D ≤ 0.5) at Re = 200 are performed based on the Navier-Stokes equations using a finite volume method based OpenFOAM codes. Multi-block mesh is used. As the cylinder is very close the wall, remeshing is regularly applied during the body oscillation to avoid over distortion of the grid. A model to account for the collision of the cylinder with the wall is adopted, in which when the gap between the cylinder and the wall is smaller than a critical value, the direction of its velocity is reversed. Simulations are made for low mass ratio, relevant to the cases in hydrodynamics. The results show that the motion amplitude generally increases with the reduced velocity U * = U/(f n D) first and then decreases after reaching a peak, and there is no obvious hysteretic transition. When e/D decreases, the largest amplitude decreases, and the reduced velocity at which the largest amplitude occurs increases. The results also indicate that the wall has a significant effect on the natural frequency of the cylinder, suggesting that the fluid force has components strongly affected by the body acceleration and displacement. When e/D decreases, the frequency at which the largest amplitude occurs becomes larger than the natural frequency obtained from the ratio of the cylinder stiffness to the summation of mass and the added mass. It is observed that, in all the cases when e/D ≤ 0.5, the anti-clockwise vortices in the wake of the cylinder are suppressed and only one single vortex of 1S type is shed downstream. As e/D decreases, the clockwise vortex shed from the upper part of the cylinder remains strong, and the anti-clockwise vortex from the lower part of the cylinder gradually becomes weaker, and the vortex street is less deflected upwards.

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“…The L 1 and L ∞ norm errors of a channel flow, which is taken from [31], is used to evaluate the calculation accuracy of the present method. The channel flow is driven by a constant pressure gradient d p/dx in a rectangular channel domain with an exact solution of…”

Section: Channel Flowmentioning

confidence: 99%

A novel Cartesian cut cell solver for incompressible viscous flow in irregular domains

Luo

Lei

et al. 2011

Numerical Methods in Fluids

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SUMMARYA Cartesian cut cell solver with solution-based adaptive mesh refinement is developed for simulating viscous, incompressible flows with arbitrary complex geometries. The cut cells are automatically generated using Volume CAD (VCAD), a framework for storing geometric and material attribute data. Unlike earlier cut cell methods, this solver organizes the cutting patterns into only six categories and further subdivides the resulting pentagon into two quadrilaterals, such that mesh data can be stored by uniform data structure and the post-processing of flow data can be handled conveniently. A novel method is proposed to treat minuscule cut cells without the process of cell merging. A collocated finite volume method, which can be used even when multiple cell shapes and orthogonal and non-orthogonal grids exist in the decomposition, is employed to discretize the Navier-Stokes equations. A modified SIMPLE-based smoothing pressure correction scheme is applied in this cut cell method to suppress checkerboard pressure oscillations caused by collocated arrangement. The solver is first used to simulate a channel flow to demonstrate its calculation accuracy expressed with L 1 and L ∞ norm errors and then the method is utilized to solve three benchmark problems of flow and heat transfer within irregular domains to verify its feasibility, efficiency, accuracy and potential in engineering applications.

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A Taylor series‐based finite volume method for the Navier–Stokes equations

Cited by 7 publications

References 16 publications

Boundary shear flow past a cylinder near a wall

Boundary shear flow past a cylinder near a wall

Flow-induced transverse vibration of a circular cylinder close to a plane wall at small gap ratios

A novel Cartesian cut cell solver for incompressible viscous flow in irregular domains

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