A promising boundary element formulation for three-dimensional viscous flow

International Journal for Numerical Methods in Fluids

Volumn 47, Issue 1, 2005, Pages 19-43

  Gao, Xiao Wei ^a  

^a ZONA TECHNOLOGY INC   (United States)

Author keywords

Boundary element method (BEM); Continuity equation; Domain integral; Navier Stokes equations; Viscous flow

Indexed keywords

BOUNDARY ELEMENT METHOD; INCOMPRESSIBLE FLOW; INTEGRAL EQUATIONS; ITERATIVE METHODS; PRESSURE EFFECTS; PROBLEM SOLVING; THREE DIMENSIONAL; VELOCITY MEASUREMENT;

BOUNDARY POINTS; MOMENTUM EQUATIONS; THREE-DIMENSIONAL VISCUOUS FLOWS; TRACTION;

VISCOUS FLOW;

BOUNDARY ELEMENT METHOD; MATHEMATICAL ANALYSIS; THREE-DIMENSIONAL FLOW; VISCOUS FLOW;

EID: 11344291138     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/fld.800     Document Type: Article

References (31)

1. Roache PJ. Computational Fluid Dynamics (revised edn). Hermosa Press: Albuquerque, 1976.
2. Patankar SV. Numerical Heat Transfer and Fluid Flow. McGraw-Hill: New York, 1980.
3. Reddy JN, Gartling DK. The Finite Element Method in Heat Transfer and Fluid Dynamics. CRC Press: Boca Raton, FL, 1987.
4. Gao XW. A boundary element method without internal cells for two-dimensional and three-dimensional elastoplastic problems. ASME Journal of Applied Mechanics 2002; 69:154-160.
5. Gao XW, Chen PC, Tang L. Deforming mesh for computational aeroelasticity using a nonlinear elastic boundary element method. AIAA Journal 2002; 40:1512-1517.
6. Wu JC, Thompson JF. Numerical solutions of time-dependent incompressible Navier-Stokes equations using an integral-differential formulation. Computers in Fluids 1973; 1:197-215.
7. Skerget P, Alujevic A, Brebbia CA. The solution of Navier-Stokes equations in terms of vorticity-velocity variables by boundary elements. BEM VI. Computational Mechanics Publications: Southampton, 1984.
8. Onishi K, Kuroki T, Tanaka M. An application of the boundary element method to incompressible laminar viscous flow. Engineering Analysis 1984; 1:122-127.
9. Kitagawa K, Brebbia CA, Wrobel LC, Tanaka M. Boundary element analysis of viscous flow by penalty function formulation. Engineering Analysis 1986; 3:194-200.
10. Grigoriev MM, Fafurin AV. A boundary element method for steady viscous fluid flow using penalty function formulation. International Journal for Numerical Methods in Fluids 1997; 25:907-929.
11. Ladyzhenskaya OA. The Mathematical Theory of Viscous Incompressible Flow. Gordon and Breach: New York, 1963.
12. Bush MB, Tanner RI. Numerical solution of viscous flows using integral equation method. International Journal for Numerical Methods in Fluids 1983; 3:71-92.
13. Aydin M, Fenner RT. Boundary element analysis of driven cavity flow for low and moderate Reynolds numbers. International Journal for Numerical Methods in Fluids 2001; 37:45-64.
14. Tosaka N, Onishi K. Boundary integral equations formulations for steady Navier-Stokes equations using the Stokes fundamental solution. Engineering Analysis with Boundary Elements 1985; 2:128-132.
15. Tosaka N, Fukushima N. Integral equation analysis of laminar natural convection problems. BEM VIII. Computational Mechanics Publications: Southampton, Springer: Berlin, 1986.
16. Power H, Partridge PW. The use of Stokes' fundamental solution for the boundary only formulation of the three-dimensional Navier-Stokes equations for moderate Reynolds numbers. International Journal for Numerical Methods in Engineering 1994; 37:1825-1840.
17. Nardini D, Brebbia CA. A new approach for free vibration analysis using boundary elements. In Boundary Element Methods in Engineering, Brebbia CA (ed.). Springer: Berlin, 1982; 312-326.
18. Sarler B, Kuhn G. Primitive variable dual reciprocity boundary element method solution of incompressible Navier-Stokes equations. Engineering Analysis with Boundary Elements 1999; 23:443-455.
19. Power H, Mingo R. The DRM subdomain decomposition approach to solve the two-dimensional Navier-Stokes system of equations. Engineering Analysis with Boundary Elements 2000; 24:107-119.
20. Florez WF, Power H, Chejne F. Multi-domain dual reciprocity BEM approach for the Navier-Stokes system of equations. Communications in Numerical Methods in Engineering 2000; 16:671-681.
21. Dargush GF, Banerjee PK. A boundary element method for steady incompressible thermoviscous flow. International Journal for Numerical Methods in Engineering 1991; 31:1605-1626.
22. Banerjee PK, Honkala KA. Development of BEM for thermoviscous flow. Computer Methods in Applied Mechanics and Engineering 1998; 151 43-62.
23. Gao, XW. A boundary-domain integral equation method in viscous fluid flow. International Journal for Numerical Methods in Fluids 2004; 45:463-484.
24. Liepmann HW, Roshko A. Elements of Gasdynamics. Dover Publications: New York, 2001.
25. Gao XW, Davies TG. Boundary Element Programming in Mechanics. Cambridge University Press: Cambridge, 2002.
26. Gao XW, Liu DD, Chen PC. Internal stresses in inelastic BEM using complex-variable differentiation. Computational Mechanics 2002; 28:40-46.
27. More JB, Hillstrom K. User guide for MINPACK-1. Argonne National Labs Report ANL80-74, Argonne, IL, 1980 (program HYBRJ can be downloaded from: http://netlib.org/minpack/).
28. Granger RA. Fluid Mechanics. Dover Publications: New York, 1995.
29. Ghia U, Ghia KN, Shin CT. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics 1982; 48:387-411.
30. Skerget L, Hribersek M, Kuhn G. Computational fluid dynamics by boundary-domain integral method. International Journal for Numerical Methods in Engineering 1999; 46:1291-1311.
31. Gao XW, Davies TG. 3D multi-region BEM with corners and edges. International Journal of Solids and Structures 2000; 37 1549-1560.