Non-conservative and conservative formulations of characteristics-based numerical reconstructions for incompressible flows

International Journal for Numerical Methods in Engineering

Volumn 66, Issue 9, 2006, Pages 1466-1482

  Shapiro, E ^a   Drikakis, D ^a  

^a CRANFIELD UNIVERSITY   (United Kingdom)

Author keywords

Characteristics based scheme; Eigenvalue analysis; High resolution methods; Incompressible flows; Riemann solvers

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS;

CHARACTERISTICS-BASED SCHEME; HIGH-RESOLUTION METHODS; RIEMANN SOLVERS;

INCOMPRESSIBLE FLOW;

CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; INCOMPRESSIBLE FLOW; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS;

EID: 33744515154     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1606     Document Type: Article

References (34)

1. Chorin AJ. A numerical method for solving incompressible viscous flow problems. Journal of Computational Physics 1967; 2:12-26.
2. Chorin AJ. Numerical solution of the Navier-Stokes equations. Mathematics of Computation 1968; 22: 745-762.
3. Almgren AS, Bell JB, Szymczak WG. A numerical method for the incompressible Navier-Stokes equations based on an approximate projection. SIAM Journal on Scientific Computing 1996; 17:358-369.
4. Bell JB, Colella, P, Glaz HM. A second-order projection method of the incompressible Navier-Stokes equations. Journal of Computational Physics 1989; 85:257-283.
5. Harlow FH, Welch JE. Numerical calculation of time-dependent viscous incompressible flow of fluid with a free surface. Physics of Fluids 1965; 8:2182-2189.
6. Drikakis D, Rider W. High-Resolution Methods for Incompressible and Low-Speed Flows. Springer: Berlin, 2004.
7. Nithiarasu P. An efficient artificial compressibility (AC) method based on the characteristic based split (CBS) method for incompressible flows. International Journal for Numerical Methods in Engineering 2003; 56: 1815-1845.
8. Nithiarasu P, Mathur JS, Weatherill NP, Morgan K. Three-dimensional incompressible flow calculations using the characteristic based split (CBS) scheme. International Journal for Numerical Methods in Fluids 2004; 44:1207-1229.
9. Malan AG, Lewis RW, Nithiarasu P. An improved unsteady, unstructured, artificial compressibility, finite volume scheme for viscous incompressible flows: part I. Theory and implementation. International Journal for Numerical Methods in Engineering 2002; 54:695-714.
10. Malan AG, Lewis RW, Nithiarasu P. An improved unsteady, unstructured, artificial compressibility, finite volume scheme for viscous incompressible flows: part II. Application. International Journal for Numerical Methods in Engineering 2002; 54:715-729.
11. Drikakis D, Iliev OP, Vassileva DP. Acceleration of multigrid flow computations through dynamic adaptation of the smoothing procedure. Journal of Computational Physics 2000; 165:566-591.
12. Drikakis D, Iliev OP, Vassileva DP. A nonlinear multigrid method for the three-dimensional incompressible Navier-Stokes equations. Journal of Computational Physics 1998; 146:301.
13. Drikakis D, Govatsos PA, Papatonis DE. A characteristic-based method for incompressible flows. International Journal for Numerical Methods in Fluids 1994; 19:667.
14. Eberle A. Characteristic flux averaging approach to the solution of Euler's equations. VKI Lecture Series 1987-04, Computational Fluid Dynamics, 1987.
15. Pal S, Patel S, Drikakis D. Effect of anatomosis on fluid flow through the arterial network of a rectus abdominis free flap. British Journal of Anaesthesia 2004; 93:167-168.
16. Neofytou P. Drikakis D. Effects of blood models on flows through a stenosis?. International Journal for Numerical Methods in Fluids 2003; 43:597-635.
17. Zhang B, Zhao Y. Simulations of flow through fluid/porous layers by a characteristic-based method on unstructured grids. International Journal for Numerical Methods in Engineering 2001; 50:2443-2457.
18. Zhao Y, Tai CH. High-order characteristics-based method for incompressible flow computation on unstructured grids. AIAA Journal 2001; 39(7):1280-1287.
19. Govatsos PA, Papantonis DE. A characteristic based method for the calculation of three-dimensional, incompressible and steady flows in hydraulic turbornachines and installations. International Journal for Numerical Methods in Fluids 2000; 34:1-30.
20. Mallinger F, Drikakis D. Instability in three dimensional unsteady stenotic flows. International Journal of Heat and Fluid Flow 2002; 23:657-663.
21. Shapiro E, Drikakis D. Artificial compressibility, characteristics-based schemes for variable density, incompressible, multi-species flows. Part I. Derivation of different formulations and constant density limit. Journal of Computational Physics, 2005, in print, doi:10.1016/ j.jcp.2005.05.001
22. Shapiro E, Drikakis D, Shapiro E, Drikakis E. Artificial compressibility, characteristics-based schemes for variable density, incompressible, multi-species flows. Part II. Multigrid implementation and numerical tests. Journal of Computational Physics, 2005, in print, doi:10.1016/j.jcp.2005.05.002
23. Shu C-W, Osher S. Efficient implementation of essentially non-oscillatory shock capturing schemes. Journal of Computational Physics 1988; 77:439-471.
24. Denham MK, Patrick MA. Laminar flow over a downstream-facing step in a two-dimensional flow channel. Transactions of the Institution of Chemical Engineers 1974; 52(4):361-367.
25. Atkins DJ, Maskell SJ, Patrick MA. Numerical predition of separated flows. International Journal for Numerical Methods in Engineering 1980; 15:129-144.
26. Weigl BH, Yager P. Microfluidic diffusion-based separation and detection. Science 1999; 15:346-347.
27. TeGrotenhuis WE, Cameron RJ, Viswanathan VV, Wegeng RS. Solvent extraction and gas absorption using microchannel contactors. In Microreaction Technology: Industrial Prospects, Ehrfeld W (ed.). Springer: Telos, 2000; 541-550. (ISBN: 3540669647).
28. Wong PK, Lee Y-K, Ho C-M. Deformation of DNA molecules by hydrodynamic focusing. Journal of Fluid Mechanics 2003; 497:55-65.
29. Deshmukh A, Liepmann D, Pisano AP. Characterization of a micro-mixing, pumping, and valving system. Proceedings of the 11th International Conference on Solid State Sensors and Actuators (Transducers '01), Munich, Germany, 10-14 June 2001; 950-953.
30. Engler M, Kockmann N, Kiefer T, Woias P. Numerical and experimental investigations on liquid mixing in static micro mixers. Chemical Engineering Journal 2004; 101:315-322.
31. Kenis PJ, Ismagilov RF, Whitesides GM. Microfabrication inside capillaries using multiphase laminar flow patterning. Science 1999; 285:83-85.
32. Gravesen P, Branebjerg J, Jensen OS. Microfluidics - a review. Journal of Micromechanics and Microengineering 1993; 3:168-182.
33. Lundgren TS, Sparrow EM, Starr JB. Pressure drop due to the entrance region in ducts of arbitrary cross-section. Journal of Basic Engineering 1964; 86:620-626.
34. Rohsenow WM, Hartnett JP, Gani EN. Handbook of Heat Transfer Fundamentals (2nd edn). McGraw-Hill: New York, 1985.