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School of Engineering

Continuous Forcing Approach

Fractional Step Method

  1. Charles S. Peskin (1972), Flow patterns around heart valves: A numerical method

  2. Charles S. Peskin (1977), Numerical analysis of blood flow in the heart

  3. Richard P Beyer Jr. (1991), A computational model of the cochlea using the immersed boundary method

  • Modifications to the flow solver of the original peskin method (Projection Method) also second order accurate forcing approach is used.

4. Charles S. Peskin, Beth Feller Printz (1993), Improved Volume Conservation in the Computation of Flows with Immersed Elastic Boundaries

  • New divergance operator introduced, makes a dramatic improvement in the overall volume conservation that is observed in an immersed-boundary computation.

5. H. S. Udaykumar, et al. (1997), Multiphase Dynamics in Arbitrary Geometries on Fixed Cartesian Grids

  • Used Colocated variables, and Peskian method for dealing with bubbles.

6. Alexandre M. Roma, Charles S. Peskin, Marsha J. Berger. (1999), An Adaptive Version of the Immersed Boundary Method

  • The main contributions of this work concern the formulation and the implementation of a multilevel self-adaptive version of the Immersed Boundary Method on locally refined meshes

7. John M. Stockie, Brian R. Wetton. (1999), Analysis of Stiffness in the Immersed Boundary Method and Implications for Time-Stepping Schemes

  • the effect of time discretisation and the time step restrictions on various explicit schemes, as well as the convergence rates for an iterative, semi-implicit method is studied

8. T. Ye, R. Mittal, H. S. Udaykumar, W. Shyy. (1999), An Accurate Cartesian Grid Method for Viscous Incompressible Flows with Complex Immersed Boundaries

  • Two Step fractional step procedure (second order), A new interpolation procedure preserving the second-order spatial accuracy of the underlying solver. PCCG solver.

9. Ming-Chih Lai, Charles S. Peskin. (2000), An Immersed Boundary Method with Formal Second-Order Accuracy and Reduced Numerical Viscosity

  • Second order accurate Immersed Boundary method, Less numerical viscosity, better choice for the simulation of high Reynolds number flows with immersed boundaries.

10. E. A. Fadlun, R. Verzicco, P. Orlandi, J. Mohd-Yusof. (2000), Combined Immersed Boundary Finite-Difference Methods for Three-Dimensional Complex Flow Simulations

  • Comparison of different forcing and interpolation (zero and second order) experimental data

 11. Jungwoo Kim, Dongjoo Kim, Haecheon Choi. (2001), An Immersed Boundary Finite-Volume Method for Simulations of Flow in Complex Geometries

  • Staggered Grid, Finite Volume formulation Fractional step method. Second order momentum forcing. Experimental Data ( Sphere, Cylider)

12. Luoding Zhu, Charles S. Peskin, (2002), Simulation of a Flapping Flexible Filament in a Flowing Soap Film by the Immersed Boundary Method

  • Mass (nonuniform density function), Air resistance, filament elasticity and gravity are included in formulation, Multigrid solver.

13. Xiaodong Wang, (2003), On the discretized delta function and force calculation in the immerse boundary method

  • Some mathematical discussion of discretisation of delta function

14. Sookkyung Lim, Charles S. Peskin, (2003), Subcritical bifurcation of a rotating elastic filament in a viscous fluid by the immersed buondary method

  • Rotating elastic filament in viscose fluid

15. A. L. F. Lima E Silva, A. Silveira-Neto, J. J. R. Damasceno, (2003), Numerical simulation of two-dimensional flows over a circular cylinder using the immersed boundary method

  • Some Experimental Data, FSM fractional step method.

16. Yu-Heng Tseng, Joel H. Ferziger, (2003), A ghost-cell immersed boundary method for flow in complex geometry

  • Turbulent flow considered, used for both staggered and collocated cartisian grids.

Pressure-Velocity Correction Method

  1. Shen, Chan, (2009), Calculation of hydrodynamic forces acting on a submerged moving object using immersed boundary method

  2. Shen, Chan, (2008), Numerical simulation of fluid–structure interaction using a combined volume of fluid and immersed boundary method