Transactions of the Korean Society of Mechanical Engineers B (대한기계학회논문집B)

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

Method of Numerical Simulation by Using the Local Harmonic Functions in the Cylindrical Coordinates

국소적 조화함수를 사용한 원통좌표계에서의 유동 해석

  • Published : 2007.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

Many practical flow problems are defined with the circular boundary. Fluid flows within a circular boundary are however susceptible to a singularity problem when the cylindrical coordinates are employed. To remove this singularity a method has been developed in this study which uses the local harmonic functions in discretization of derivatives as well as interpolation. This paper describes the basic reason for introducing the harmonic functions and the overall numerical methods. The numerical methods are evaluated in terms of the accuracy and the stability. The Lamb-dipole flow is selected as a test flow. We will see that the harmonic-function method indeed gives more accurate solutions than the conventional methods in which the polynomial functions are utilized.

Keywords

References

  1. Verzicco, R. and Orlandi, P., 1996, 'A Finite- Difference Scheme for Three-dimensional Incompressible Flows in Cylindrical Coordinates,' J. Comput. Phys. Vol. 123, pp. 402-414 https://doi.org/10.1006/jcph.1996.0033
  2. Fukagata, K. and Kasagi, N., 2002, 'Highly Energy-conservative Finite Difference Method for the Cylindrical Coordinate System,' J. Comput. Phys., Vol. 181, pp. 478-498 https://doi.org/10.1006/jcph.2002.7138
  3. Akselvoll, K. and Moin, P., 1996, 'An Efficient Method for Temporal Integration of the Navier-Stokes Equations in Confined Axisymmetric geometries,' J. Comput. Phys., Vol. 125, pp. 454-463 https://doi.org/10.1006/jcph.1996.0107
  4. Suh, Y.K., 2003, 'Development of Zonal-embedded-grid Method and its Application,' Proc. 2nd KSV Conf., pp. 55-58
  5. Suh, Y.K. and Yeo, C.H., 2004, 'Study on the Spin-up of Fluid in a Semi-circular Container Using a Zonal-embedded-grid Method,' J. KSV, Vol. 2, No. 2, pp. 32-37
  6. Suh, Y.K. and Yeo, C.H., 2006, 'Finite Volume Method with Zonal-embedded Grids for Cylindrical Coordinates,' Int. J. Num. Methods Fluids, Vol. 52, pp. 263-295 https://doi.org/10.1002/fld.1177