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Implicit Virtual Boundary Method for Moving Boundary Problems on Non-Staggered Cartesian Patch Grids

  • S. L. Lee (a1), G. S. Cyue (a1) and K. W. Chen (a1)

Abstract

A simple numerical method is proposed in the paper for fluid flow around a moving boundary of irregular shape. The unsteady term is discretized with the implicit scheme such that large time step is allowed. All of the computations are performed on non-staggered Cartesian grid system. Fine Cartesian patch grid system covering the moving object is employed to resolve the solution around the solid body. A closed curve defined by connecting the solid grid points adjacent to the solid-liquid interface is referred to as virtual boundary. The narrow irregular strip of solid between the virtual boundary and the actual solid-fluid interface is called pseudo-fluid. The general fluid region consisting of both fluid and pseudo-fluid is a regular domain that can be efficiently solved with conventional numerical method. In this connection, external force is imposed at each fluid grid point adjacent to the solid-fluid interface to compensate for the numerical error arising from the assumption of pseudo-fluid. The solution procedure is iterated until the required external force converges. Accuracy of the new numerical method is validated through three test problems. The numerical method then is used to investigate the flow induced by the flapping wings of a tethered dragonfly in literature. The corresponding CFL numbers of the four examples are infinity, 20, 100, and 3.29.

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Copyright

Corresponding author

*Corresponding author (sllee@pme.nthu.edu.tw)

References

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1. Chen, Y. C., Liao, Y. J., Tseng, S. C. and Giacomin, A. J., “Core Deflection in Plastics Iinjection Molding: Direct Measurement, Flow Visualization and 3D Simulation,” Polymer-Plastics Technology and Engineering, 50, pp. 863872 (2011).
2. Sun, M. and Lan, S. L., “A Computational Study of the Aerodynamics Forces and Power Requirements of Dragonfly (Aeschna juncea) Hovering,” Journal of Experimental Biology, 207, pp. 18871901 (2004).
3. Wang, J. K. and Sun, M., “A Computational Study of the Aerodynamics and Forewing-Hindwing Interaction of a Model Dragonfly in Forward Flight,” Journal of Experimental Biology, 208, pp. 37853804 (2005).
4. Chen, H. C., “CFD Simulation of Directional Short-Crested Waves on a Jack-Up Structure,” International Journal of Offshore and Polar Engineering, 23, pp. 3845 (2013).
5. Peskin, C. S., “Flow Pattern around Heart Valves: a Numerical Method,” Journal of Computational Physics, 10, pp. 252271 (1972).
6. Peskin, C. S., “The Immersed Boundary Method,” Acta Numerica, pp. 459571 (2002).
7. Mittal, R. and Iaccarino, G., “Immersed Boundary Methods,” Annual Review of Fluid Mechanics, 37, pp. 239261 (2005).
8. Goldstein, D., Handler, R. and Sirovich, L., “Modeling a No-Slip Flow with External Force Field,” Journal Computational Physics, 105, pp. 354366 (1993).
9. Goldstein, D., Handler, R. and Sirovich, L., “Direct Numerical Simulation of Turbulent Flow over a Modeled Riblet Covered Surface,” Journal of Fluid Mechanics, 302, pp. 333376 (1995).
10. Saiki, E. M. and Biringen, S., “Numerical Simulation of a Cylinder in Uniform Flow: Application of a Virtual Boundary Method,” Journal Computational Physics, 123, pp. 450465 (1996).
11. Lai, M. C. and Peskin, C. S., “An Immersed Boundary Method with Formal Second-Order Accuracy and Reduced Numerical Viscosity,” Journal Computational Physics, 160, pp. 705719 (2000).
12. Lima, E., Silva, A. L. F., Silveira-Neto, A. and Damasceno, J. J. R., “Numerical Simulation of Two-Dimensional Flows over a Circular Cylinder Using the Immersed Boundary Method,” Journal Computational Physics, 189, pp. 351370 (2003).
13. Mohd-Yusof, J., “Combined Immersed-Boundary/B-Spline Methods for Simulations of Flow in Complex Geometries,” Annual Research Briefs, Center for Turbulence Research, NASA Ames/Stanford University, pp. 317327 (1997).
14. Fadlun, E. A., Verzicco, R., Orlandi, P. and Mohd-Yusof, J., “Combined Immersed-Boundary Methods for Three Dimensional Complex Flow Simulations,” Journal of Computational Physics, 161, pp. 3560 (2000).
15. Kim, J., Kim, D. and Choi, H., “An Immersed-Boundary Finite-Volume Method for Simulations of Flow in Complex Geometries,” Journal of Computational Physics, 171, pp. 132150 (2001).
16. Tseng, Y. H. and Ferziger, J. H., “A Ghost-Cell Immersed Boundary Method for Flow in Complex Geometry,” Journal of Computational Physics, 192, pp. 593623 (2003).
17. Balaras, E., “Modeling Complex Boundaries Using an External Force Field on Fixed Cartesian Grids in Large-Eddy Simulations,” Computers and Fluids, 33, pp. 375404 (2004).
18. Gilmanov, A. and Sotiropoulos, F., “A Hybrid Cartesian/Immersed Boundary Method for Simulating Flows with 3D, Geometrically Complex, Moving Bodies,” Journal of Computational Physics, 207, pp. 457492 (2005).
19. Kim, D. and Choi, H., “Immersed Boundary Method for Flow around an Arbitrarily Moving Body,” Journal of Computational Physics, 212, pp. 662680 (2006).
20. Yang, J. and Balaras, E., “An Embedded-Boundary Formulation for Large-Eddy Simulation of Turbulent Flows Interacting with Moving Boundaries,” Journal of Computational Physics, 215, pp. 1224 (2006).
21. Su, S. W., Lai, M. C. and Lin, C. A., “A Simple Immersed Boundary Technique for Simulating Complex Flows with Rigid Boundary,” Computers and Fluids, 36, pp. 313324 (2007).
22. Zhang, N. and Zheng, Z. C., “An Improved Direct-Forcing Immersed-Boundary Method for Finite Difference Applications,” Journal of Computational Physics, 221, pp. 250268 (2007).
23. Choi, J. I., Oberoi, R. C., Edwards, J. R. and Rosati, J. A., “An Immersed Boundary Method for Complex Incompressible Flows,” Journal of Computational Physics, 224, pp. 757784 (2007).
24. Ghias, R., Mittal, R. and Dong, H., “A Sharp Interface Immersed Boundary Method for Compressible Viscous Flows,” Journal of Computational Physics, 225, pp. 528553 (2007).
25. Liao, C. C., Chang, Y. W., Lin, C. A. and McDonough, J. M., “Simulating Flows with Moving Rigid Boundary Using Immersed-Boundary Method,” Computers and Fluids, 39, pp. 152167 (2010).
26. Lee, S. L., “A New Numerical Formation for Parabolic Differential Equations under the Consideration of Large Time Steps,” International Journal for Numerical Methods in Engineering, 26, pp. 15411549 (1988).
27. Lee, S. L., “Weighting Function Scheme and Its Application on Multidimensional Conservation Equations,” International Journal of Heat and Mass Transfer, 32, pp. 20652073 (1989).
28. Patankar, S. V., Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington (1980).
29. Lee, S. L., “A Strongly-Implicit Solver for Two-Dimensional Elliptic Differential Equations,” Numerical Heat Transfer B, 16, pp. 161178 (1989).
30. Lee, S. L. and Tzong, R. Y., “Artificial Pressure for Pressure-Linked Equation,” International Journal of Heat and Mass Transfer, 35, pp. 27052716 (1992).
31. Peng, Y. F., Mittal, R., Sau, A. and Hwang, R. R., “Nested Cartesian Grid Method in Incompressible Viscous Fluid Flow,” Journal of Computational Physics, 229, pp. 70727101 (2010).
32. Majumdar, S., Iaccarino, G. and Durbin, P., “RNS Solvers with Adaptive Structured Boundary Non-Conforming Grids,” Annual Research Briefs, Center for Turbulence Research, NASA Ames/Stanford University, pp. 353366 (2001).
33. Coutanceau, M. and Bouard, R., “Experimental Determination of the Main Features of the Viscous Flow in the Wake of a Circular Cylinder in Uniform Translation. Part 1. Steady Flow,” Journal of Fluid Mechanics, 79, pp. 231256 (1977).
34. Dennis, S. C. R. and Chang, G., “Numerical Solutions for Steady Flow Past a Circular Cylinder at Reynolds Number up to 100,” Journal of Fluid Mechanics, 42, pp. 471489 (1970).
35. Linnick, M. N. and Fasel, H. F., “A High-Order Immersed Interface Method for Simulating Unsteady Iincompressible Flows on Irregular Domains,” Journal of Computational Physics, 204, pp. 157192 (2005).
36. Taira, K. and Colonius, T., “The Immersed Boundary Method: A Projection Approach,” Journal of Computational Physics, 225, pp. 21182137 (2007).
37. Lee, J. and You, D., “An Implicit Ghost-Cell Immersed Boundary Method for Simulations of Moving Body Problems with Control of Spurious Force Oscillations,” Journal of Computational Physics, 233, pp. 295314 (2013).
38. Dutsch, H., Dorst, F., Becker, S. and Lienhart, H., “Low-Reynolds-Number Flow around an Oscillating Circular Cylinder at Low Keulegan-Carperter Number,” Journal of Fluid Mechanics, 360, pp. 249271 (1998).
39. Taneda, S. and Honji, H., “Unsteady Flow past a Flat Plate Normal to the Direction of Motion,” Journal of the Physical Society of Japan, 30, pp. 262272 (1971).
40. Wang, Z. J., “Dissecting Insect Flight,” Annual Review of Fluid Mechanics, 37, pp. 183210 (2005).
41. Wang, Z. J. and Russell, D., “Effect of Forewing and Hindwing Interactions on Aerodynamic Forces and Power in Hovering Dragonfly Flight,” Physical Review Letters, 99, 148101 (2007).
42. Richardson, L. F., “The Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Differential Equations, with an Application to the Stresses in a Masonry Dam,” Philosophical Transactions of the Royal Society A, 210, pp. 307357 (1910).

Keywords

Implicit Virtual Boundary Method for Moving Boundary Problems on Non-Staggered Cartesian Patch Grids

  • S. L. Lee (a1), G. S. Cyue (a1) and K. W. Chen (a1)

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