Pressure-based finite-volume techniques have emerged as the methods of choice for a wide variety of industrial applications involving incompressible fluid flow. In this paper, we trace the evolution of this class of solution techniques. We review the basics of the finite-volume method, and trace its extension to unstructured meshes through the use of cell-based and control-volume finite-element schemes. A critical component of the solution of incompressible flows is the issue of pressure-velocity storage and coupling. The development of staggered-mesh schemes and segregated solution techniques such as the SIMPLE algorithm are reviewed. Co-located storage schemes, which seek to replace staggered-mesh approaches, are presented. Coupled multigrid schemes, which promise to replace segregated-solution approaches, are discussed. Extensions of pressure-based techniques to compressible flows are presented. Finally, the shortcomings of existing techniques and directions for future research are discussed.
Pressure-Based Finite-Volume Methods in Computational Fluid Dynamics
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Acharya, S., Baliga, B. R., Karki, K., Murthy, J. Y., Prakash, C., and Vanka, S. P. (January 7, 2007). "Pressure-Based Finite-Volume Methods in Computational Fluid Dynamics." ASME. J. Heat Transfer. April 2007; 129(4): 407–424. https://doi.org/10.1115/1.2716419
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