Benson, D. J., 1992, “Computational Methods in Lagrangian and Eulerian Hydrocodes,” Comput.Methods Appl. Mech. Eng., 99, pp. 235–394.

[CrossRef]Ferziger, J. H. and Peric, M., 2002, *Computational Methods for Fluid Dynamics*, third ed., Springer-Verlag, New York.

Li, B., 2006, “Discontinuous Finite Elements in Fluid Dynamics and Heat Transfer,”*Computational Fluid and Solid Mechanics*, Springer, New York.

Hoffmann, K. A. and Chiang, S. T., 2000, *Computational Fluid Dynamics*, fourth ed., Vol. II, Engineering Education System, Wichita, KS.

Löhner, P., 2008, *Applied CFD Techniques: An Introduction Based on Finite Element Methods*, second ed., John Wiley and Sons, New York.

Peskin, C. S., 2003, “The Immersed Boundary Method,” Acta Numer., 11, pp. 479–517

[CrossRef].

Goldstein, D., Handler, R., and Sirovich, L., 1993, “Modeling a No-Slip Flow Boundary With an External Force Field,” J. Comput. Phys., 105, pp. 354–366.

[CrossRef]Glowinski, R., Pan, T. W., Hesla, T. I., and Joseph, D. D., 1999, “A Distributed Lagrange Multiplier/Fictitious Domain Method for Particulate Flows,” Int. J. Multiphase Flow, 25, pp. 755–794.

[CrossRef]Mohd-Yusof, J., 1997, “Combined Immersed Boundaries/B-Splines Methods for Simulations of Flows in Complex Geometries.” *CTR Annual Research Briefs*, NASA Ames/Stanford University, Stanford, CA.

Fadlun, E., Verzicco, R., Orlandi, P., and Mohd-Yusof, J., 2000, “Combined Immersed-Boundary Finite-Difference Methods for Three-Dimensional Complex Flow Simulations,” J. Comput. Phys., 161(1), pp. 35–60.

[CrossRef]Balaras, E., 2004, “Modeling Complex Boundaries Using an External Force Field on Fixed Cartesian Grids in Large-Eddy Simulations,” Comput. Fluids, 33, pp. 375–404.

[CrossRef]Mittal, R. and Iaccarino, G., 2005, “Immersed Boundary Methods,” Annu. Rev. Fluid Mech., 37(1), pp. 239–261.

[CrossRef]Uhlmann, M., 2005, “An Immersed Boundary Method With Direct Forcing for the Simulation of Particulate Flows,” J. Comput. Phys., 209(2), pp. 448–476.

[CrossRef]Yang, J. and Balaras, E., 2006, “An Embedded-Boundary Formulation for Large-Eddy Simulation of Turbulent Flows Interacting With Moving Boundaries,” J. Comput. Phys., 215, pp. 12–40.

[CrossRef]Roman, F., Napoli, E., Milici, B., and Armenio, V., 2009, “An Improved Immersed Boundary Method for Curvilinear Grids,” Comput. Fluids, 38(8), pp. 1510–1527.

[CrossRef]Min, C. and Gibou, F., 2006, “A Second Order Accurate Projection Method for the Incompressible Navier–Stokes Equations on Non-Graded Adaptive Grids,” J. Comput. Phys., 219(2), pp. 912–929.

[CrossRef]Griffith, B. E., Hornung, R. D., McQueen, D. M., and Peskin, C. S., 2007, “An Adaptive, Formally Second Order Accurate Version of the Immersed Boundary Method,” J. Comput. Phys., 223(1), pp. 10–49.

[CrossRef]Muldoon, F. and Acharya, S., 2008, “A Divergence-Free Interpolation Scheme for the Immersed Boundary Method,” Int. J. Numer. Methods Fluids, 56(10), pp. 1845–1884.

[CrossRef]Vanella, M., Rabenold, P., and Balaras, E., 2010, “A Direct-Forcing Embedded-Boundary Method With Adaptive Mesh Refinement For Fluid–Structure Interaction Problems,” J. Comput. Phys., 229(18), pp. 6427–6449.

[CrossRef]McNally, C. P., 2011, “Divergence-Free Interpolation of Vector Fields From Point Values—Exact ∇ ·

*B* = 0 in Numerical Simulations,” Mon. Not. R. Astron. Soc.: Lett., 413(1), pp. L76–L80.

[CrossRef]Stein, K., Tezduyar, T., and Benney, R., 2003, “Mesh Moving Techniques for Fluid-Structure Interactions With Large Displacements,” ASME J. Appl. Mech., 70(1), pp. 58–63.

[CrossRef]Liu, X., Qin, N., and Xia, H., 2006, “Fast Dynamic Grid Deformation Based on Delaunay Graph Mapping,” J. Comput. Phys., 211(2), pp. 405–423.

[CrossRef]Morrell, J., Sweby, P., and Barlow, A., 2007, “A Cell by Cell Anisotropic Adaptive Mesh ALE Scheme for the Numerical Solution of the Euler Equations,” J. Comput.Phys., 226(1), pp. 1152–1180.

[CrossRef]Banks, J. W., Henshaw, W. D., and Schwendeman, D. W., 2012, “Deforming Composite Grids for Solving Fluid Structure Problems,” J. Comput. Phys., 231(9), pp. 3518–3547.

[CrossRef]Peskin, C., 1972, “Flow Patterns Around Heart Valves—Numerical Method,” J. Comput. Phys., 10(2), pp. 252–271.

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

[CrossRef]Vanella, M. and Balaras, E., 2009, “A Moving-Least-Squares Reconstruction Procedure for Embedded-Boundary Formulations,” J. Comput. Phys., 228, pp. 6617–6628.

[CrossRef]Pinelli, A., Naqavi, I., Piomelli, U., and Favier, J., 2010, “Immersed-Boundary Methods for General Finite-Difference and Finite-Volume Navier–Stokes Solvers,” J. Comput. Phys., 229(24), pp. 9073–9091.

[CrossRef]Kempe, T. and Fröhlich, J., 2012, “An Improved Immersed Boundary Method With Direct Forcing for the Simulation of Particle Laden Flows,” J. Comput. Phys., 231(9), pp. 3663–3684.

[CrossRef]Glowinski, R., Pan, T. W., Hesla, T. I., Joseph, D. D., and Periaux, J., 2000, “A Fictitious Domain Approach to the Direct Numerical Simulation of Incompressible Viscous Flow Past Moving Rigid Bodies: Application to Particulate Flow,” J. Comput. Phys., 169, pp. 363–426.

[CrossRef]Colonius, T. and Taira, K., 2008, “A Fast Immersed Boundary Method Using a Null Space Approach and Multi-Domain Far-Field Boundary Conditions,” Comput. Methods Appl. Mech. Eng., 197(25–28), pp. 2131–2146.

[CrossRef]Griffith, B. E., 2012, “On the Volume Conservation of the Immersed Boundary Method,” Commun. Comput. Phys., 12(2), pp. 401–432.

[CrossRef]Roma, A. M., Peskin, C. S., and Berger, M. J., 1999, “An Adaptative Version of the Immersed Boundary Method,” J. Comput. Phys., 153, pp. 509–534.

[CrossRef]Lai, M. C. and Peskin, C. S., 2000, “An Immersed Boundary Method With Formal Second Order Accuracy and Reduced Numerical Viscosity,” J. Comput. Phys., 160, pp. 705–719.

[CrossRef]Hou, G., Wang, J., and Layton, A., 2012, “Numerical Methods for Fluid-Structure Interaction—A Review,” Commun. Comput. Phys., 12(2), pp. 337–377. Available at:

http://www.global-sci.com/openaccess/v12_337.pdfYang, J., Preidikman, S., and Balaras, E., 2008, “A Strongly-Coupled, Embedded-Boundary Method for Fluid-Structure Interactions of Elastically Mounted Rigid Bodies,” J. Fluids Struct., 24, pp. 167–182.

[CrossRef]Mittal, R., Dong, H., Bozkurttas, M., Najjar, F., Vargas, A., and von Loebbecke, A., 2008, “A Versatile Sharp Interface Immersed Boundary Method for Incompressible Flows With Complex Boundaries,” J. Comput.Phys., 227(10), pp. 4825–4852.

[CrossRef] [PubMed]Luo, H., Dai, H., de Sousa, P. J. F., and Yin, B., 2012, “On the Numerical Oscillation of the Direct-Forcing Immersed-Boundary Method for Moving Boundaries,” Comput. Fluids, 56(0), pp. 61–76.

[CrossRef]Lee, J., Kim, J., Choi, H., and Yang, K.-S., 2011, “Sources of Spurious Force Oscillations From an Immersed Boundary Method for Moving-Body Problems,” J. Comput.Phys., 230(7), pp. 2677–2695.

[CrossRef]Iaccarino, G. and Verzicco, R., 2003, “Immersed Boundary Technique for Turbulent Flow Simulations,” ASME Appl. Mech. Rev., 56(3), pp. 331–347.

[CrossRef]Liu, W. K., Jun, S., and Zhang, Y. F., 1995, “Reproducing Kernel Particle Methods,” Int. J. Numer. Methods Fluids, 20, pp. 1081–1106.

[CrossRef]Li, S. and Liu, W. K., 2004, *Meshfree Particle Methods*, Springer, New York.

Liu, G. R. and Gu, Y. T., 2005, *An Introduction to Meshfree Methods and Their Programming*, Springer, New York.

Johnson, T. A. and Patel, V. C., 1999, “Flow Past a Sphere Up to a Reynolds Number of 300,” J. Fluid Mech., 378(1), pp. 19–70.

[CrossRef]Tomboulides, A. G. and Orszag, S. A., 2000, “Numerical Investigation of Transitional and Weak Turbulent Flow Past a Sphere,” J. Fluid Mech., 416(1), pp. 45–73.

[CrossRef]Nakamura, I., 1976, “Steady Wake Behind a Sphere,” Phys. Fluids, 19(1), pp. 5–8.

[CrossRef]Constantinescu, G. S. and Squires, K. D., 2003, “LES and DES Investigations of Turbulent Flow Over a Sphere at Re = 10,000,” Flow, Turbul. Combus., 70(1–4), pp. 267–298.

[CrossRef]Tomboulides, A. G., 1993.,“Direct and Large-Eddy Simulation of Wake Flows: Flow Past a Sphere,” Ph.D. thesis, Princeton University, Princeton, NJ.

Lee, S., 2000, “A Numerical Study of the Unsteady Wake Behind a Sphere in a Uniform Flow at Moderate Reynolds Numbers,” Comput. Fluids, 29(6), pp. 639–667.

[CrossRef]Khokhlov, A. M., 1998, “Fully Threaded Tree Algorithms for Adaptive Refinement Fluid Dynamics Simulations,” J. Comput. Phys., 143(2), pp. 519–543.

[CrossRef]Ham, F., Lien, F., and Strong, A. B., 2002, “A Cartesian Grid Method With Transient Anisotropic Adaptation,” J. Comput. Phys., 179(2), pp. 469–494.

[CrossRef]Ferm, L. and Lötstedt, P., 2003, “Anisotropic Grid Adaptation for Navier–Stokes Equations,” J. Comput. Phys., 190(1), pp. 22–41.

[CrossRef]Almgren, A. S., Bell, J. B., Colella, P., Howell, L. H., and Welcome, M. L., 1998, “A Conservative Adaptive Projection Method for the Variable Density Incompressible Navier–Stokes Equations,” J. Comput. Phys., 142, pp. 1–46.

[CrossRef]Martin, D. F., Colella, P., and Graves, D., 2008, “A Cell-Centered Adaptive Projection Method for the Incompressible Navier–Stokes Equations in Three Dimensions,” J. Comput. Phys., 227, pp. 1863–1886.

[CrossRef]Peng, Y.-F., Mittal, R., Sau, A., and Hwang, R. R., 2010, “Nested Cartesian Grid Method in Incompressible Viscous Fluid Flow,” J. Comput. Phys., 229(19), pp. 7072–7101.

[CrossRef]Hoffman, R. E., Guerra, F. M., and Humphrey, D. L., 1980, “Practical Applications of Adaptive Mesh Refinement (Rezoning),” Comput. Struct., 12, pp. 639–655.

[CrossRef]Babuska, I. and Rheinboldt, W. C., 1978, “Error Estimating for Adaptive Finite Element Computations,” SIAM J. Numer. Anal., 15(4), pp. 736–759.

[CrossRef]Berger, M. J. and Oliger, J., 1984, “Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations,” J. Comput. Phys., 53(3), pp. 484–512.

[CrossRef]Berger, M. J. and Colella, P., 1989, “Local Adaptive Mesh Refinement for Shock Hydrodynamics,” J. Comput. Phys., 82, pp. 64–84.

[CrossRef]Almgren, A. S., Bell, J. B., and Crutchfield, W. Y., 2000, “Approximate Projection Methods: Part I. Inviscid Analysis,” SIAM J. Sci. Comput., 22, pp. 1139–1159.

[CrossRef]Bell, J. B., Colella, P., and M., G. H., 1989, “A Second-Order Projection Method for the Incompressible Navier–Stokes Equations,” J. Comput. Phys., 85, pp. 257–283.

[CrossRef]Bell, J. B., Colella, P., and Howell, L. H., 1991, “An Efficient Second-Order Projection Method for Viscous Incompressible Flow,” Proceedings of the 10th AIAA Computational Fluid Dynamics Conference, Paper No. AIAA-91-1560-CP, pp. 360–365.

Sussman, M., Almgren, A. S., Bell, J. B., Colella, P., Howell, L. H., and Welcome, M. L., 1999, “An Adaptive Level Set Approach for Incompressible Two-Phase Flows,” J. Comput. Phys., 148(1), pp. 81–124.

[CrossRef]Martin, D. F., Colella, P., and Graves, D., 2008, “A Cell-Centered Adaptive Projection Method for the Incompressible Navier–Stokes Equations in Three Dimensions,” J. Comput. Phys., 227(3), pp. 1863–1886.

[CrossRef]De Zeeuw, D., and Powell, K. G., 1993, “An Adaptively Refined Cartesian Mesh Solver for the Euler Equations,” J. Comput. Phys., 104, pp. 56–68.

[CrossRef]Hornung, R. D. and Kohn, S. R., 2002, “Managing Application Complexity in the SAMRAI Object-Oriented Framework,” Concurr. Comput.: Pract. E., 14, pp. 347–368.

[CrossRef]MacNeice, P., Olson, K. M., Mobarry, C., deFainchtein, R., and Packer, C., 2000, “Paramesh: A Parallel Adaptive Mesh Refinement Community Toolkit,” Comput. Phys. Commun., 126, pp. 330–354.

[CrossRef]Burstedde, C., Wilcox, L. C., and Ghattas, O., 2011, “p4est: Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees,” SIAM J. Sci. Comput., 33(3), pp. 1103–1133.

[CrossRef]Kan, J. V., 1986, “A Second-Order Accurate Pressure-Correction Scheme for Viscous Incompressible Flow,” SIAM J. Sci. Stat. Comput., 7, pp. 870-891.

Brown, D. L., Cortez, R., and Minion, M. L., 2001, “Accurate Projection Methods for the Incompressible Navier–Stokes Equations,” J. Comput. Phys., 168(2), pp. 464–499.

[CrossRef]Löhner, R., 1987, “An Adaptive Finite Element Scheme for Transient Problems in CFD,” Comput. Methods Appl. Mech. Eng., 61(3), pp. 323–338.

[CrossRef]Balsara, D., 2001, “Divergence-Free Adaptive Mesh Refinement for Magnetohydrodynamics,” J. Comput. Phys., 174(2), pp. 614–648.

[CrossRef]Balsara, D. S., 2009, “Divergence-Free Reconstruction of Magnetic Fields and WENO Schemes for Magnetohydrodynamics,” J. Comput. Phys., 228(14), pp. 5040–5056.

[CrossRef]Golub, G. H. and van Van Loan, C. F., 1996, *Matrix Computations* (Johns Hopkins Studies in Mathematical Sciences), 3rd ed., The Johns Hopkins University Press, Baltimore, MD.

Swartzrauber, P. N., 1974, “A Direct Method for the Discrete Solution of Separable Elliptic Equations,” SIAM J. Numer. Anal., 11, pp. 1136–1150.

[CrossRef]Rossi, T. and Toivanen, J., 1999, “A Parallel Fast Direct Solver for Block Tridiagonal Systems With Separable Matrices of Arbitrary Dimension,” SIAM J. Sci. Comput., 20(5), pp. 1778–1796.

[CrossRef]Daley, C., Vanella, M., Dubey, A., Weide, K., and Balaras, E., 2012, “Optimization of Multigrid Based Elliptic Solver for Large Scale Simulations in the FLASH Code,” Concurr.Computat.: Pract. E., 24, pp. 2346–2361.

[CrossRef]Martin, D. F. and Cartwright, K., 1996, “Solving Poisson's Equation Using Adaptive Mesh Refinement,” Technical Report No. UCB/ERL, M96/66.

Huang, J. and Greengard, L., 2000, “A Fast Direct Solver for Elliptic Partial Differential Equations on Adaptively Refined Meshes,” SIAM Journal on Scientific Computing, 21, pp. 1551–1566.

[CrossRef]Ricker, P., 2008, “A Direct Multigrid Poisson Solver for Oct-Tree Adaptive Meshes,” Astroph. J. Suppl. Ser., 176, pp. 293–300.

[CrossRef]Gu, W., Chyu, C., and Rockwell, D., 1994, “Timing of Vortex Formation From an Oscillating Cylinder,” Phys. Fluids, 6(11), pp. 3677–3682.

[CrossRef]Guilmineau, E. and Queutey, P., 2002, “A Numerical Simulation of Vortex Shedding From an Oscillating Circular Cylinder,” J. Fluid Struct, 16(6), pp. 773–794.

[CrossRef]Barad, M., Colella, P., and Schladow, S., 2009, “An Adaptive Cut-Cell Method for Environmental Fluid Mechanics,” Int. J. Numer. Methods Fluids, 60(5), pp. 473–514.

[CrossRef]Vanella, M., 2010, “A Fluid-Structure Interaction Strategy With Application to Low Reynolds Number Flapping Flight,” Ph.D. thesis, School of Engineering, University of Maryland, College Park, MD.