Journal of the Korea Computer Graphics Society (한국컴퓨터그래픽스학회논문지)

Korea Computer Graphics Society (한국컴퓨터그래픽스학회)
권호 표지

CIP method on Triangular Meshes

비격자메쉬에서의 고차오더 대류 방정식 해결방법

  • Heo, Nam-Bin (Graphics and Media Lab, Seoul National University) ;
  • Ko, Hyeong-Seok (Graphics and Media Lab, Seoul National University)
  • 허남빈 (그래픽스 및 미디어 연구실, 서울대학교) ;
  • 고형석 (그래픽스 및 미디어 연구실, 서울대학교)
  • Published : 2009.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper presents a new CIP method for unstructured mesh to reduce the numerical dissipation. To reflect precise physical characteristics, CIP method updates both the physical quantity and the derivative information. The proposed method uses the Finite Volume Method(FVM) to solve the non-advection term of CIP equation. And we performed several experiments to improve the accuracy of third-order interpolation. Our result shows that our algorithm has less numerical dissipation than that of linear advection solver.

이 논문은 비격자메쉬에서의 비물리적 감쇄현상을 감소시키는 새로운 CIP 대류방법을 제안한다. 제시되는 방법은 물리량과 물리량의 미분정보를 함께 사용하여 기존의 선형방법보다 더 정확한 물리현상을 반영할 수 있다. 비격자메쉬에서 해결하기 힘든 CIP의 비대류항을 풀기 위해 기존의 격자 메쉬에서 사용되었던 유한차분법 방법과는 다른 유한체적법을 사용하였다. 그리고 대류항의 보다 나은 정확도를 위해 여러가지 보간법에 대해 정확도 실험을 수행하였으며, 선형방법과의 비교 실험을 통해 보다 적은 비물리적 감쇄현상을 보임을 확인할 수 있었다.

Keywords

References

  1. J. Stam, “Stable fluids,” ACM SIGGRAPH ’99, pp. 121–128, 1999.
  2. D. Kim and H. Choi, “A second-order time-accurate finite volume method for unsteady incompressible flow on hybrid unstructured grids,” Journal of Computational Physics 162, pp. 411–428, 2000.
  3. Y.-T. Zhang and C.-W. Shu, “High-order weno schemes for hamilton-jacobi equations on triangular meshes,” SIAM Journal of Scientific Computing, pp. 1005–1030, 2003.
  4. S. Ii, M. Shimuta, and F.Xiao, “A 4th-order and single-cellbased advection scheme on unstructured grids using multimoments,” Computer Physics Communications 173, pp. 17–33, 2005.
  5. B. E. Feldman, J. F. O'Brien, and B. Klingner, “Animating gases with hybrid meshes,” ACM Transactions on Graphics 24, 3, pp. 904–909, 2005.
  6. B. M. Klingner, B. E. Feldman, N. Chentanez, and J. F. O'Brien, “Fluid animation with dynamic meshes,” ACM Transactions on Graphics 25, 3, pp. 820–825, 2006.
  7. B. Kim., Y. Liu, I. Llamas, and J. Rossignac, “Advections with significantly reduced dissipation and diffusion,” IEEE Trans. Vis. Comput. Graph 13, 1, pp. 135–144, 2007.
  8. A. Selle, R. Fedkiw, B. Kim, Y. Liu, and J. Rossignac, “An unconditionally stable maccormack method,” SIAM Journal of Scientific Computing, p. (in press), 2008.
  9. O.-Y. Song, H. Shin, and H.-S. Ko, “Stable but nondissipative water,” ACM Transactions on Graphics 24, 1, pp. 81–97, 2005.
  10. O.-Y. Song, D. Kim, and H.-S. Ko, “Derivative particles for simulating detailed movements of fluids,” IEEE Transactions on Visualization and Computer Graphics 13,4, pp. 711–719, 2007.
  11. D. Kim, O.-Y. Song, and H.-S. Ko, “A semi-lagrangian cip fluid solver without dimensional splitting,” Computer Graphics Forum 27, pp. 467–475, 2008.
  12. N. Chentanez, B. Feldman, F. Labelle, J. O’Brien, and J. Shewchuk, “Liquid simulation on lattice-based tetrahedral meshes,” In Proceedings of ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 219–228, 2007.
  13. A.W. Bargteil, T. G. Goktekin, J. F. O'Brien, and J. A. Strain, “A semi-lagrangian contouring method for fluid simulation,” ACM Transactions on Graphics 25, 1, pp. 19–38, 2006.
  14. J. Warren, S. Schaefer, A. N. Hirani, , and M. Desbrun, “Barycentric coordinates for convex sets,” Advances in Computational and Applied Mathematics, pp. 319–338, 2007.
  15. F. Losasso, F. Gibou, and R. Fedkiw, “Simulating water and smoke with an octree data structure,” In the Proceedings of ACM SIGGRAPH 2004, pp. 457–462, 2004.
  16. F. Gibou, R. Fedkiw, L.-T. Cheng, and M. Kang, “A second order accurate symmetric discretization of the poisson equation on irregular domains,” Journal of Computational Physics 176, pp. 205–227, 2002.
  17. C. W. Shu and S. Osher, “Efficient implementation of essentially non-oscillatory shock-capturing schemes,” Journal of Computational Physics 77, pp. 439–471, 1988.
  18. A. Staniforth and J. Cote, “Semi-lagrangian integration scheme for atmospheric model - a review,” Mon.Weather Rev. 199, 12, pp. 2206–2223, 1991.
  19. T. Yabe and T. Aoki, “A universal solver for hyperbolic equations by cubic-polynomial interpolation i. one-dimensional solver,” Computer Physics Communications 66, pp. 219–232, 1991.
  20. T. Yabe and T. Aoki, “A universal solver for hyperbolic equations by cubic-polynomial interpolation ii. two and three-dimensional solver,” Computer Physics Communications 66, pp. 232–242, 1991.
  21. T. Yabe, F. Xiao, and T. Utsumi, “The constrained interpolation profile method for multiphase analysis,” Journal of Computational Physics 169, pp. 556–593, 2001.
  22. P. Alliez, D. Cohen-Steiner, M. Yvinec, , and M. Desbrun, “Variational tetrahedral meshing,” In the Proceedings of ACM SIGGRAPH 2005, pp. 617–625, 2005.
  23. S. Ii and F. Xiao, “Cip/multi-moment finite volume method for euler equations : A semi-lagrangian characteristic formulation,” Journal of Computational Physics 222, pp. 849–871, 2007.