A meshless approach to capturing moving interfaces in passive transport problems

CMES - Computer Modeling in Engineering and Sciences

Volumn 31, Issue 3, 2008, Pages 157-188

  Mai Cao, L ^a   Tran Cong, T ^b  

^a Ho Chi Minh City University of Technology   (Viet Nam)

^b UNIVERSITY OF SOUTHERN QUEENSLAND   (Australia)

Author keywords

IRBFN; Level set method; Meshless method; Moving interfaces; Passive transport; Radial basis functions; Semi lagrangian approach; Taylor IRBFN

Indexed keywords

IRBFN; LEVEL SET METHOD; MESHLESS METHOD; MOVING INTERFACES; PASSIVE TRANSPORT; RADIAL BASIS FUNCTIONS; SEMI-LAGRANGIAN APPROACH; TAYLOR-IRBFN;

CONVERGENCE OF NUMERICAL METHODS; DROP BREAKUP; LAGRANGE MULTIPLIERS; LEVEL MEASUREMENT; MEDICAL IMAGING; RADIAL BASIS FUNCTION NETWORKS;

SET THEORY;

EID: 58149525782     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (37)

1. Allievi, A.; Bermejo, R. (2000): Finite element modified method of characteristics for the Navier-Stokes equations. InternationalJournal for Numerical Methods in Fluids, vol. 32, pp. 439-464.
2. Atluri, S. (2004): The Meshless Local Petrov-Galerkin (MLPG) Method for Domain & BIE Discretizations . Tech Science Press, Encino, CA, USA.
3. Bardi, M.; Osher, S. (1991): The non-convex multidimensional Riemann problem for Hamilton-Jacobi equations. SIAM Journal on Mathematical Analysis, vol. 22, pp. 344-351.
4. Behrens, J.; Iske, A. (2002): Grid-free adaptive semi-Lagrangian advection using radial basis functions. Computers and Mathematics with ap plications, vol. 43, pp. 319-327.
5. Chang, Y.; Hou, T.; Merriman, B.; Osher, S. (1996): A level set formulation of Eulerian interface capturing method for incompressible fluid flows. Journal of Computational Physics,vol. 124, pp. 449-464.
6. Crandall, M.; Lions, P. (1984): Two approximations of solutions of Hamilton-Jacobi equations. Math. Comput., vol. 43, pp. 1-19.
7. Cuvelier, C.; Schulkes, R. (1990): Some numerical methods for the computation of capillary free boundaries governed by the Navier-Stokes equations. SIAM Review, vol. 32, no. 3, pp. 355-423.
8. Donea, J. (1984): A Taylor-Galerkin method for convective transport problems. International Journal for Numerical Methods in Engineering, vol. 20, pp. 101-119.
9. Donea, J.; Huerta, A. (2003): Finite Element Methods for Flow Problems. John Wiley & Sons Ltd., England.
10. Floryan, J.; Rasmussen, H. (1989): Numerical methods for viscous flows with moving boundary. Applied Mechanics Reviews, vol. 42, no. 12, pp. 323-341.
11. Hirt, C.; Nichols, B. (1981): Volume of fluid (VOF) method for the dynamics of free boundaries. Journal ofComputational Physics, vol. 39, no. 1, pp. 201 -225.
12. Iafrati, A.; Mascio, A.; Campana, E. (2001): A level set technique applied to unsteady free surface flows. International Journal for Numerical Methods in Fluids, vol. 35, pp. 281-297.
13. Jacqmin, D. (1999): Calculation of two-phase Navier-Stokes flows using phase-field modelling. Journal ofComputational Physics, vol. 155, pp. 96-127.
14. Kansa, E. (1990): Multiquadrics - A scattered data approximation scheme with applications to computational fluid-dynamics-II. Solutions to parabolic, hyperbolic and elliptic partial differential equations. Computers and Mathematics with Applications, vol. 19, no. 8/9, pp. 147-161.
15. Mai-Cao, L.; Tran-Cong, T. (2005): A mesh-less IRBFN-based method for transient problems. CMES:ComputerModeling in Engineering & Sciences, vol. 18, no. 1, pp. 59-77.
16. Mai-Duy, N. (2004): Indirect rbfn method with scattered points for numerical solution of pdes. CMES:ComputerModeling in Engineering & Sci ences, vol. 6, pp. 209-226.
17. Mai-Duy, N.; Mai-Cao, L.; Tran-Cong, T. (2007): Computation of transient viscous flows using indirect radial basis function net works. CMES:Computer Modeling in Engineering & Sciences, vol. 7, no. 2, pp. 149-171.
18. Mai-Duy, N.; Tran-Cong, T. (2001): Numerical solution of differential equations using mul-tiquadric radial basis function networks. Neural Networks, vol. 14, pp. 185-199.
19. Mai-Duy, N.; Tran-Cong, T. (2001): Numerical solution of navier-stokes equations using mul-tiquadric radial basis function networks. International Journal for Numerical Methods in Fluids, vol. 37, pp. 65-86.
20. Mai-Duy, N.; Tran-Cong, T. (2003): Approximation of function and its derivatives using radial basis function networks. Applied Mathematical Modelling, vol. 27, pp. 197-220.
21. Moody, J.; Darken, C. (1989): Fast learning in networks of locally-tuned processing units. Neural Computations, vol. 1, pp. 281-294.
22. Oliveira, A.; Baptista, A. (1995): A comparison of integration and interpolation Eulerian Lagrangian methods. International Journal for Numerical Methods in Fluids, vol. 21, pp. 183-204.
23. Osher, S.; Fedkiw, R. (2003): Level Set Methods and Dynamic Implicit Surfaces, volume 153 of Applied Mathematical Sciences. Springer, New York.
24. Osher, S.; Sethian, J. (1988): Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. Journal ofComputational Physics, vol. 79, pp. 12-49.
25. Peng, D.; Merriman, B.; Osher, S.; Zhao, H.; Kang, M. (1999): A PDE-based fast local level set method. Journal ofComputational Physics, vol. 155, pp. 410-438.
26. Sarler, B. (2005): A radial basis function col location approach in computational fluid dynamics. CMES:Computer Modeling in Engineering & Sciences, vol. 7, no. 2, pp. 185-193.
27. Sethian, J. (1999): Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science. Cambridge University Press, New York.
28. Shu, C.; Ding, H.; Yeo, K. (2005): Computation of incompressible navier-stokes equations by local rbf-based differential quadrature method. CMES:ComputerModeling in Engineering & Sciences, vol. 7, no. 2, pp. 195-205.
29. Shu, C.; Osher, S. (1989): Efficient implementation of essentially non-oscillatory shock capturing schemes II. Journal of Computational Physics, vol. 83, pp. 32-78.
30. Staniforth, A.; Cote, J. (1991): Semi-lagrangian integration schemes for atmospheric models - A review. Monthly Weather Review,vol. 119,pp. 2206-2223.
31. Sussman,M.; Fatemi,E. (1999): An efficient, interface-preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow. SIAM Journal on Scientific Computing, vol. 20, no. 4, pp. 1165-1191.
32. Sussman, M.; Smereka, P. (1997): Axisym-metric free boundary problems. Journal ofFluid Mechanics, vol. 341, pp. 269-294.
33. Sussman, M.; Smereka, P.; Osher, S. (1994): A level set approach for computing solutions to incompressible two-phase flow. Journal of Computational Physics, vol. 114, pp. 146-159.
34. Temperton, C.; Staniforth, A. (1987): An efficient two-time level semi-Lagrangian semi-implicit integration scheme. Quart. J. Roy. Meteor. Soc., vol. 113, pp. 1025-1039.
35. Tornberg, A. (2000): Interface Tracking Meth ods with Application to Multiphase Flows.PhD thesis, Royal Institute of Technology, Stockholm, 2000.
36. Unverdi, S.; Tryggvason, G. (1992): A front-tracking method for viscous, incompressible, multi-fluid flows. Journal of computational physics, vol. 100, pp. 25-37.
37. Wang, S.; Lim, K.; Khoo, B.; Wang, M. (2007): A geometric deformation constrained level set method for structural shape and topology optimization. CMES:Computer Modeling in Engineering & Sciences, vol. 18, no. 3, pp. 155-181.