Momentum/continuity coupling with large non-isotropic momentum source terms. (English) Zbl 1252.76063

Summary: Pressure-based methods such as the SIMPLE algorithm are frequently used to determine a coupled solution between the component momentum equations and the continuity equation. This paper presents a colocated variable pressure correction algorithm for control volumes of polyhedral/polygonal cell topologies. The correction method is presented independent of spatial approximation. The presence of non-isotropic momentum source terms is included in the proposed algorithm to ensure its applicability to multi-physics applications such as gas and particulate flows. Two classic validation test cases are included along with a newly proposed test case specific to multiphase flows. The classic validation test cases demonstrate the application of the proposed algorithm on truly arbitrary polygonal/polyhedral cell meshes. A comparison between the current algorithm and commercially available software is made to demonstrate that the proposed algorithm is competitively efficient. The newly proposed test case demonstrates the benefits of the current algorithm when applied to a multiphase flow situation. The numerical results from this case show that the proposed algorithm is more robust than other methods previously proposed.


76M25 Other numerical methods (fluid mechanics) (MSC2010)
Full Text: DOI


[1] Patankar, Numerical Heat Transfer and Fluid Flow (1980)
[2] Patankar, A calculation procedure for heat mass and momentum transfer in three dimensional parabolic flows, International Journal of Heat and Mass Transfer 15 pp 1787– (1972) · Zbl 0246.76080
[3] Chow WL, Rhie CM. A numerical study of the turbulent flow past an isolated airfoil with trailing edge separation. Technical Report AIAA-82-0998, Center for Turbulence Research, 1982.
[4] Mathur, A pressure-based method for unstructured meshes, Numerical Heat Transfer, Part B 31 pp 195– (1997)
[5] Ferziger, Computational Methods for Fluid Dynamics (1997)
[6] Date, Fluid dynamical view of pressure checkerboarding problem and smoothing pressure correction on meshes with colocated variables, International Journal of Heat and Mass Transfer 46 pp 4885– (2003) · Zbl 1050.76036
[7] Snider, An incompressible three-dimensional multiphase particle-in-cell model for dense particulate flows, International Journal of Computational Physics 170 pp 523– (2001) · Zbl 1051.76054
[8] Leonard, A stable and accurate convective modelling procedure based on quadratic upstream interpolation, Computer Methods in Applied Mechanics and Engineering 19 pp 59– (1979) · Zbl 0423.76070
[9] Jasak, High resolution nvd differencing scheme for arbitrarily unstructured meshes, International Journal for Numerical Methods in Fluids 31 (2) pp 431– (1999) · Zbl 0952.76057
[10] Darwish, TVD schemes for unstructured grids, International Journal of Heat and Mass Transfer 46 pp 599– (2003) · Zbl 1121.76357
[11] AIAA. A multi-dimensional linear reconstruction scheme for arbitrary unstructured Grids. Sixteen AIAA Computational Fluid Dynamics Conference, Orlando, FL, 23-26 June 2003.
[12] Jasak H. Error analysis and estimation for the finite volume method with applications to fluid flow. Ph.D. Thesis, Department of Mechanical Engineering, Imperial College of Science, Technology and Medicine, June 1996.
[13] Oosterlee, Benchmark solutions for the incompressible Navier-Stokes equations in general coordinates on staggered grids, International Journal for Numerical Methods in Fluids 17 pp 301– (1993) · Zbl 0800.76334
[14] Enayet, Laser-doppler measurements of laminar and turbulent flow in a pipe bend, International Journal of Heat and Fluid Flow 3 pp 213– (1982)
[15] He, A numerical method for 3D viscous incompressible flows using non-orthogonal grids, International Journal for Numerical Methods in Fluids 18 pp 449– (1994)
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