A high quality interpolation method for colocated polyhedral/polygonal control volume methods. (English) Zbl 1242.76234
Summary: A high quality and efficient interpolation method for polyhedral/polygonal control volume simulation data is presented. The proposed method utilizes a non-ambiguous and efficient mesh decomposition technique. A pseudo-Laplacian is used to solve an optimization problem to approximate the variation between discrete data points in a linear fashion. The interpolation method guarantees continuous interpolation data throughout the control volume mesh topology and faithfully reproduces the input control volume data. The interpolation connectivity is structured to mimic the interpolation methods utilized by the control volume discretization. The method only requires the geometry of the input data to perform interpolations. This allows key interpolation data to be calculated once and stored for efficient interpolations. The benefits of the proposed algorithm are highlighted by an interpolation test case which demonstrates the benefits of the current method compared to a popular interpolation method currently used in industry. Since the proposed method is designed to augment an existing mesh data structure it can be used to update existing control volume software.
MSC:
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
References:
| [1] | Gerald, Curtis F.; Wheatley, Patrick O., Applied numerical analysis (1994), Addison-Wesley Publishing Company · Zbl 0877.65003 |
| [2] | Vetterling, William T.; Press, William H.; Teukolsky, Saul A.; Flannery, Brian P., Numerical recipes in C (1988), Cambridge University Press: Cambridge University Press New York (NY, USA) · Zbl 0661.65001 |
| [3] | Zienkiewicz, O. C.; Taylor, R. L., The finite element method, vols. 1 and 2 (1989), McGraw Hill Book Company: McGraw Hill Book Company England · Zbl 0991.74002 |
| [4] | Anderson, Dale A.; Tannehill, John C.; Pletcher, Richard H., Computational fluid mechanics and heat transfer (1997), Taylor and Francis: Taylor and Francis Washington (DC) · Zbl 1285.76003 |
| [5] | Ferziger, Joel H.; Perić, Milovan, Computational methods for fluid dynamics (1997), Springer: Springer Germany, [corrected second printing] · Zbl 0943.76001 |
| [6] | Patankar, Suhas V., Numerical heat transfer and fluid flow (1980), Hemisphere Publishing Corporation: Hemisphere Publishing Corporation New York · Zbl 0521.76003 |
| [7] | Wendt, John F., Computational fluid dynamics: an introduction (1992), Springer-Verlag: Springer-Verlag New York · Zbl 0754.76002 |
| [8] | Taylor Roger Peyret, Thomas D., Computational methods for fluid flow (1983), Springer-Verlag: Springer-Verlag New York · Zbl 0514.76001 |
| [9] | Hirsch, Charles, Numerical computation of internal and external flows, vol. 1 (1988), John Wiley and Sons: John Wiley and Sons New York · Zbl 0662.76001 |
| [10] | Franklin, J. D.; Lee, Joon Sang, Momentum/continuity coupling with large non-isotropic momentum source terms, Int J Numer Methods Fluids, 61, 9, 946-969 (2009) · Zbl 1252.76063 |
| [11] | Chow WL, Rhie CM. A numerical study of the turbulent flow past an isolated airfoil with trailing edge separation. In: Joint thermophysics, fluids, plasma and heat transfer conference, St. Louis, MO, June 1982. American Institute of Aeronautics and Astronautics and American Society of Mechanical Engineers; 1982 [Technical Report AIAA-82-0998].; Chow WL, Rhie CM. A numerical study of the turbulent flow past an isolated airfoil with trailing edge separation. In: Joint thermophysics, fluids, plasma and heat transfer conference, St. Louis, MO, June 1982. American Institute of Aeronautics and Astronautics and American Society of Mechanical Engineers; 1982 [Technical Report AIAA-82-0998]. |
| [12] | Miettinen, A.; Rahman, M. M.; Siikonen, T., A pressure-correction method for solving fluid flow problems on a collocated grid, Numer Heat Transfer Part B, 32, 63-84 (1997) |
| [13] | Biagioli, Fernando, Calculation of laminar flows with second-order schemes and collocated variable arrangement, Int J Numer Methods Fluids, 26, 887-905 (1998) · Zbl 0928.76067 |
| [14] | Zhu, J.; Rodi, W., A low dispersion and bounded convection scheme, Comput Methods Appl Mech Eng, 92, 87-96 (1991) · Zbl 0825.76518 |
| [15] | Knupp, Patrick; Steinberg, Stanly, Fundamentals of grid generation (1993), CRC Press: CRC Press Boca Raton (FL, USA), p. 33431 · Zbl 0855.65123 |
| [16] | Schroeder, Will; Martin, Ken; Larensen, Bill, The visualization toolkit an object-oriented approach to 3D graphics (1996), Prentice Hall PTR: Prentice Hall PTR Upper Saddle River (NJ, USA) |
| [17] | Mühlhaus Chongin Zhao, H. B.; Hobbs, B. E.; Ord, A., A consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements, Int J Numer Methods Eng, 45, 1509-1526 (1999) · Zbl 0943.74075 |
| [18] | Rausch RD, Batina JT, Yang NTY. Spatial adaption procedures on unstructured meshes for accurate unsteady aerodynamic flow computations. Technical report AIAA-91-1106. AIAA; March 1991.; Rausch RD, Batina JT, Yang NTY. Spatial adaption procedures on unstructured meshes for accurate unsteady aerodynamic flow computations. Technical report AIAA-91-1106. AIAA; March 1991. |
| [19] | AIAA. A multi-dimensional linear reconstruction scheme for arbitrary unstructured grids. In: 16th AIAA computational fluid dynamics conference, Orlando, (FL); June 2003.; AIAA. A multi-dimensional linear reconstruction scheme for arbitrary unstructured grids. In: 16th AIAA computational fluid dynamics conference, Orlando, (FL); June 2003. |
| [20] | Shewchuk, Jonathan Richard, Triangle: engineering a 2D quality mesh generator and Delaunay triangulator, (Lin, Ming C.; Manocha, Dinesh, First ACM workshop on applied computational geometry. Applied computational geometry: towards geometric engineering. First ACM workshop on applied computational geometry. Applied computational geometry: towards geometric engineering, Lecture notes in computer science, vol. 1148 (1996), Springer-Verlag), 203-222 |
| [21] | Cardoze, David E.; Blandford, Daniel K.; Blelloch, Guy E.; Kadow, Clemens, Compact representations of simplical meshes in two three dimensions, Int J Comput Geometry Appl, 15, 1, 3-24 (2005) · Zbl 1060.65555 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
