Godunov,
S. K., 1959, “A Difference Method for Numerical Calculation of Discontinuous Solutions of Hydrodynamics,” Mat. Sb., 47(3), pp. 271–306.

LeVeque, R. J., 1992, *Numerical Methods for Conservation Laws, Lectures in Mathematics, ETH Zürich*, Birkhäuser Verlag, Basel-Boston-Berlin.

Karni,
S., 1996, “Multicomponent Flow Calculations by a Consistent Primitive Algorithm,” J. Comput. Phys., 112, pp. 31–43.

Abgrall,
R., 1996, “How to Prevent Pressure Oscillations in Multicomponent Flow Calculations: A Quasi Conservative Approach,” J. Comput. Phys., 125, pp. 150–160.

Karni,
S., 1996, “Hybrid Multifluid Algorithms,” SIAM J. Sci. Comput. (USA), 17(5), pp. 1019–1039.

Fedkiw,
R. P., Aslam,
T., Merriman,
B., and Osher,
S., 1999, “A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method),” J. Comput. Phys., 152, 457–492.

Chern,
I.-L., Glimm,
J., McBryan,
O., Plohr,
B., and Yaniv,
S., 1986, “Front Tracking for Gas Dynamics,” J. Comput. Phys., 62, pp. 83–110.

Osher,
S., and Sethian,
J. A., 1988, “Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations,” J. Comput. Phys., 79, 12–49.

Peskin,
C. S., 1977, “Numerical Analysis of Blood Flow in the Heart,” J. Comput. Phys., 25, pp. 220–252.

Hirt,
C. W., and Nichols,
B. D., 1981, “Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries,” J. Comput. Phys., 39, pp. 201–225.

Rider,
W. J., and Kothe,
D. B., 1998, “Reconstructing Volume Tracking,” J. Comput. Phys., 141(2), pp. 112–152.

Unverdi,
S. O., and Tryggvason,
G., 1992, “A Front-Tracking Method for Viscous, Incompressible, Multi-Fluid Flows,” J. Comput. Phys., 100, pp. 25–37.

Harlow,
F. H., and Welch,
J. E., 1965, “Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid With Free Surface,” Phys. Fluids, 8, pp. 2182–2189.

Fedkiw,
R. P., Marquina,
A., and Merriman,
B., 1999, “An Isobaric Fix for the Overheating Problem in Multimaterial Compressible Flows,” J. Comput. Phys., 148, 545–578.

Fedkiw,
R. P., 2002, “Coupling an Eulerian Fluid Calculation to a Lagrangian Solid Calculation With the Ghost Fluid Method,” J. Comput. Phys., 175, 200–224.

Thompson,
K. W., 1990, “Time-Dependent Boundary Conditions for Hyperbolic Systems, II,” J. Comput. Phys., 89, pp. 439–461.

Nourgaliev, R. R., Dinh, T. N., Suschikh, S. Yu., Yuen, W. W., and Theofanous, T. G., 2003, “The Characteristics-Based Matching Method for Compressible Flow in Complex Geometries,” *AIAA 2003-0247, 41st AIAA Aerospace Sciences Meeting and Exhibit*, January 6–9, 2003, Reno, NV, USA.

Sethian, J. A., 1999, *Level Set Methods and Fast Marching Methods*, Cambridge University Press.

Nourgaliev, R. R., Dinh, T. N., and Theofanous, T. G., 2004, “A Pseudocompressibility Method for the Simulation of Single- and Multiphase Incompressible Flows,” Int. J. Multiphase Flow, (in press).

Nourgaliev, R. R., Dinh, T. N., and Theofanous, T. G., 2003, “On Capturing of Interfaces in Multimaterial Compressible Flows Using a Level-Set-Based Cartesian Grid Method. Multiphase Compressible Fluid-Solid (Particulate) Flows,” *CRSS Research Report 05/03-1*, 53p., May 23, 2003.

Fedkiw, R., Merriman, B., Donat, R., and Osher, S., 1998, “The Penultimate Scheme for Systems of Conservation Laws: Finite Difference ENO with Marquina’s Flux Splitting,” *Progress in Numerical Solutions of Partial Differential Equations*, Arcachon, France, edited by M. Hafez, July 1998.

Shu,
C.-W., and Osher,
S., 1989, “Efficient Implementation of Essentially Non-Oscillatory Shock-Capturing Schemes II (Two),” J. Comput. Phys., 83, 32–78.

Shu, C.-W., 1997, “Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws,” *NASA/CR-97-206253, ICASE Report No. 97-65*.

Anderson, J. D., 1995, *Computational Fluid Dynamics, The Basics With Applications*, McGraw-Hill, Inc.

Poinsot,
T. J., and Lele,
S. K., 1992, “Boundary Conditions for Direct Simulations of Compressible Viscous Flows,” J. Comput. Phys., 101, pp. 104–129.

Peng,
D. P., Merriman,
B., Osher,
S., Zhao,
H., and Kang,
M., 1999, “A PDE-Based Fast Local Level Set Method,” J. Comput. Phys., 155, pp. 410–438.

Sod,
G. A., 1978, “A Survey of Several Finite Difference Methods for Systems of Nonlinear Hyperbolic Conservation Laws,” J. Comput. Phys., 27, 1–31.

Menikoff,
R., 1994, “Errors When Shocks Waves Interact due to Numerical Shock Width,” SIAM J. Sci. Comput. (USA), 15(5), p. 1227.

Noh,
W., 1978, “Errors for Calculations of Strong Shocks Using an Artificial Viscosity and an Artificial Heat Flux,” J. Comput. Phys., 72, p. 78.

Donat,
R., and Marquina,
A., 1996, “Capturing Shock Reflections: An Improved Flux Formula,” J. Comput. Phys., 125, 42–58.

Fursenko,
A. A., Sharov,
D. M., Timofeev,
E. V., and Voinovich,
P. A., 1992, “Numerical Simulation of Shock Wave Interaction With Channel Beds and Gas Nonuniformities,” Comput. Fluids, 21(3), pp. 377–396.

Goloviznin, V. P., Zhmakin, A. I., Komissaruk, B. A., Mende, H. P., and Fursenko, A. A., 1981, “On Propagation of Shock Waves in Planar and Axisymetric Channels,” *Preprint of FTI—709*, Leningrad, 49 p. (In Russian).

Dukhovski,
I. A., Komissaruk,
B. A., Kovalev,
P. I., and Mende,
H. P., 1985, “High-Speed Photography of the Interaction of a Water Drop With a Supersonic Sphere,” Opt. Laser Technol., 17(3), pp. 148–150.