Application of the VOF method based on unstructured quadrilateral mesh

Abstract

To simulate two-dimensional free-surface flows with complex boundaries directly and accurately, a novel VOF (Volume-of-fluid) method based on unstructured quadrilateral mesh is presented. Without introducing any complicated boundary treatment or artificial diffusion, this method treated curved boundaries directly by utilizing the inherent merit of unstructured mesh in fitting curves. The PLIC (Piecewise Linear Interface Calculation) method was adopted to obtain a second-order accurate linearized reconstruction approximation and the MLER (Modified Lagrangian-Eulerian Re-map) method was introduced to advect fluid volumes on unstructured mesh. Moreover, an analytical relation for the interface’s line constant vs. the volume clipped by the interface was developed so as to improve the method’s efficiency. To validate this method, a comprehensive series of large straining advection tests were performed. Numerical results provide convincing evidences for the method’s high volume conservative accuracy and second-order shape error convergence rate. Also, a dramatic improvement on computational accuracy over its unstructured triangular mesh counterpart is checked.

Keywords

VOF / unstructured quadrilateral mesh / PLIC / MLER

References

[1] Rider W. J., Kothe D. B. Reconstructing volume tracking[J]. J Comput Phys, 1998, 141: 112-152

[2] Scardovelli R., Zaleski S. Direct numerical simulation of free-surface and interfacial flow[J]. Ann Rev Fluid Mech, 1999, 31: 567-603

[3] Osher S., Fedkiw R. Level set methods: an overview and some recent results[J]. J Comput Phys, 2001, 169: 463-502

[4] Jacqmin D. Calculation of two-phase Navier-Stokes flows using phase-field modeling[J]. J Comput Phys, 1999, 155: 96-127

[5] Hirt C. W., Nichols B. D. Volume-of-fluid (VOF) method for the dynamics of free boundaries[J]. J Comput Phys, 1981, 39: 201-225

[6] Hirt C. W., Sicilian J. M. A porosity technique for the definition of obstacles in rectangular cell meshes[C]. Proceedings of 4th International Conference on Ship Hydrodynamics, 1985, Washington DC: National Academic of Science, 548-567

[7] Ji C. N., Wang Y. Z., Wang J. F. A novel VOF-type volume-tracking method for free-surface flows based on unstructured triangular mesh[J]. China Ocean Engineering, 2005, 19(4): 529-538

[8] Youngs D. L. Morton K. W., Baincs M. J. Time-dependent multi-material flow with large fluid distortion[C]. Numerical Methods for Fluid Dynamics, 1982, New York: Academic Press, 273-285

[9] Press W. H., Teukolsky S. A., Vetterling W. T., et al. Numerical recipes in Fortran[M]. 1986, Cambridge: Cambridge University Press

[10] Yang X. F., James A. J. Analytic relations for reconstructing piecewise linear interfaces in triangular and tetrahedral grids[J]. J Comput Phys, 2006, 214: 41-54

[11] Mosso S. J., Swam B. K., Kothe D. B., et al. et al. Schiano P., Ecer A., Periaux J., et al. et al. A parallel volume-tracking algorithm for unstructured meshes[C]. Parallel Computational Fluid Dynamics: Algorithm and Results Using Advanced Computers, 1997, Capri: Academic Press, 323-341

[12] Rourke J. O. Computational geometry in C[M]. 1993, Cambridge: Cambridge University Press