바로가기메뉴

본문 바로가기 주메뉴 바로가기

logo

ISSN : 1226-0657

Article Contents

Prev Next
e-Submission

Vol.19 No.2

Citation Share

A HEAVISIDE-FUNCTION APPROACH FOR THE INTERACTION OF TWO-PHASE FLUID AND NON-DEFORMABLE SOLID

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2012, v.19 no.2, pp.147-169
https://doi.org/10.7468/jksmeb.2012.19.2.147
Kang, Myung-Joo
Min, Cho-Hong
Kang,, M. , & Min,, C. (2012). A HEAVISIDE-FUNCTION APPROACH FOR THE INTERACTION OF TWO-PHASE FLUID AND NON-DEFORMABLE SOLID. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 19(2), 147-169, https://doi.org/10.7468/jksmeb.2012.19.2.147

Abstract

We introduce a Heaviside-function formulation of the interaction between incompressible two-phase fluid and a non-deformable solid. Fluid and solid interact in two ways : fluid satises the Dirichlet boundary condition imposed by the velocity field of solid, and solid is accelerated by the surface traction exerted by fluid. The two-way couplings are formulated by the Heaviside function to the interface between solid and fluid. The cumbersome treatment of interface is taken care of by the Heaviside function, and the interaction is discretized in a simple manner. The discretization results in a stable and accurate projection method.

keywords
incompressible fluid, Navier-Stokes equations, fluid-solid interaction, Heaviside function

Reference

1.

(2007). A second order accurate level set method on non-graded adaptive Cartesian grids. J. Comput. Phys., 225, 300-321. 10.1016/j.jcp.2006.11.034.

2.

(2008). Robust second order accurate discretizations of the multi-dimensional heaviside and dirac delta functions. J. Comput. Phys., 227, 9686-9695. 10.1016/j.jcp.2008.07.021.

3.

(2009). An efficient fluid-solid coupling algorithm for single-phase flows. J. Comput. Phys., 228, 8807-8829. 10.1016/j.jcp.2009.08.032.

4.

(1998). Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys., 79, 12-49.

5.

(1979). Prediction of critical mach number for store configurations. AIAA J., 17, 1170-1177. 10.2514/3.7617.

6.

(2008). Two-way coupling of fluids to rigid and deformable solids and shells. ACM Trans. Graph., 27(46).

7.

(2000). A remark on computing distance functions. J. Comput. Phys., 163, 51-67. 10.1006/jcph.2000.6553.

8.

(1968). A two-dimensional interpolation function for irregularly spaced data (517-523). Proc. of the 23rd ACM Nat. Conf..

9.

(1998). An improved level set method for incompressible two-phase flows. Computers and Fluids, 27, 663-680. 10.1016/S0045-7930(97)00053-4.

10.

(1994). A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys., 114, 146-159. 10.1006/jcph.1994.1155.

11.

(2009). Finite difference methods for approximating heaviside functions. J. Comput. Phys., 228, 3478-3489. 10.1016/j.jcp.2009.01.026.

12.

(2001). A semi-Lagrangian high-order method for Navier-Stokes equations. J. Comput. Phys, 172, 658-684. 10.1006/jcph.2001.6847.

13.

(2007). A fast variational framework for accurate solid-fluid coupling. ACM Trans. Graph. (SIGGRAPH Proc.), 26(3).

14.

(1989). A second order projection method for the incompressible Navier-Stokes equations. J. Comput. Phys, 85, 257-283. 10.1016/0021-9991(89)90151-4.

15.

(1998). A new algebraic rigid body collision law based on impulse space considerations. J. Appl. Mech., 65, 939-950. 10.1115/1.2791938.

16.

(1967). A Numerical Method for Solving Incompressible Viscous Flow Problems. J. Comput. Phys., 2, 12-26. 10.1016/0021-9991(67)90037-X.

17.

(2008). Second-order accurate computation of curvatures in a level set framework using novel high-order reinitialization schemes. J. Sci. Comput., 35, 114-131. 10.1007/s10915-007-9177-1.

18.

(2003). Gauge method for viscous incompressible flows. Comm. Math. Sci., 1, 317-332. 10.4310/CMS.2003.v1.n2.a6.

19.

Physics-based animation.

20.

(1985). Application of a fractional-step method to incompressible Navier-Stokes equations. J. Comput. Phys., 59, 308-323. 10.1016/0021-9991(85)90148-2.

21.

Mechanics.

22.

Numerical analysis and scientific computing.

23.

(2010). On reinitializing level set functions. J. Comput. Phys., 229, 2764-2772. 10.1016/j.jcp.2009.12.032.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

e-Submission OA Policy