A representation of curved boundaries for the solution of the Navier-Stokes equations on a staggered three-dimensional Cartesian grid

By M. Kirkpatrick, Steven William Armfield, J. Kent. 2003

227 citations recorded by the source corpus.

A method is presented for representing curved boundaries for the solution of the Navier-Stokes equations on a non-uniform, staggered, three-dimensional Cartesian grid. The approach involves truncating the Cartesian cells at the boundary surface to create new cells which conform to the shape of the surface. We discuss in some detail the problems unique to the development of a cut cell method on a staggered grid. Methods for calculating the fluxes through the boundary cell faces, for representing pressure forces and for calculating the wall shear stress are derived and it is verified that the new scheme retains second-order accuracy in space. In addition, a novel "cell-linking" method is developed which overcomes problems associated with the creation of small cells while avoiding the complexities involved with other cell-merging approaches. Techniques are presented for generating the geometric information required for the scheme based on the representation of the boundaries as quadric surfaces. The new method is tested for flow through a channel placed oblique to the grid and flow past a cylinder at Re = 40 and is shown to give significant improvement over a staircase boundary formulation. Finally, it is used to calculate unsteady flow past a hemispheric protuberance on a plate at a Reynolds number of 800. Good agreement is obtained with experimental results for this flow.

Subfields: Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/19e9ce8c8ec5bfba051c6dc5e8a18868817828f5

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In Computational Mechanics

Citations in the corpus

A Sharp-Interface Immersed Boundary Method with Improved Mass Conservation and Reduced Spurious Pressure Oscillations (2011, unknown): “[18] used ‘cell-linking’ technique instead of ‘merging’, and Meyer et al.”
A general reconstruction algorithm for simulating flows with complex 3D immersed boundaries on Cartesian grids (2003, methodology): “The latter class of methods is particularly attractive because boundary conditions can be accurately applied on a sharp solid interface – thus, alleviating an important limitation of the immersed boundary approach – without requiring tedious cell-merging procedures typically employed in cut-cell for”
A ghost-cell immersed boundary method for flow in complex geometry (2002, methodology): “[24] present a second-order accurate IBM on a non-uniform, staggered three-dimensional Cartesian grid.”
A hybrid Cartesian/immersed boundary method for simulating flows with 3D, geometrically complex, moving bodies (2005, methodology): “Implementing a pure staggered grid discretization in a Cartesian grid approach, however, would be cumbersome due to need for special treatment of grid nodes near the body – see [19] for a recent extensive discussion on the difficulties encountered in the implementation of a staggered grid approach i”
A cartesian grid embedded boundary method for the heat equation and poisson's equation in three dimensions (2004, result): “There have been a number of other investigators using similar approaches working in two dimensions [17] or in the context of specific applications problems in three dimensions [9,14].”