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By Kang M., Fedkiw R. P., Liu X.

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Matrix Computations, The Johns Hopkins University Press, Baltimore. 9. Harlow, F. , and Welch, J. E. (1965). Numerical calculation of time-dependent viscous incompressible flow of fluid with a free surface. Phys. Fluids 8, 2182 2189. 10. Landau, L. , and Lifshitz, E. M. (1978). Fluid Mechanics, Pergamon Press, NY. 11. , and Kang, M. (2000), A boundary condition capturing method for Poisson's equation on irregular domains. J. Comput. Phys. 160, 151 178. 12. , and Sethian, J. A. (1988). Fronts propagating with curvature dependent speed: Algorithms based on Hamilton Jacobi formulations.

File: 854J 706030 . By:XX . Date:18:01:01 . Time:12:58 LOP8M. B. Page 01:01 Codes: 437 Signs: 70 . 3. Example 3 Figures 3, 4, 7 and 8 might require some further explanation for the novice reader unfamiliar with the behavior of numerical methods on unstable problems. Note that Fig. 4 contains a higher degree of instability than Fig. 3 and that Fig. 8 contains a higher degree of instability than Fig. 7 indicating that the GFM contains a higher degree of instability than the delta function method.

05 seconds on a 40_40 mesh. These two solutions lie directly on top of each other. The interface is not visibly distorted by parasitic flows in part because our scheme is able to sharply resolve the pressure jump as shown in Fig. 10. Figure 11 shows the initial data plotted on top of the exact solution for the delta function method. Note that the Fig. 10. Steady state air bubble Ghost Fluid Method. File: 854J 706032 . By:XX . Date:18:01:01 . Time:12:59 LOP8M. B. Page 01:01 Codes: 1395 Signs: 1019 .

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