Finite difference schemes and the method of lines for solving incompressible viscous flow problems

• Autorzy: Kosma Z. , Motyl P.
• Języki publikacji: EN

Abstrakty

EN

For the determination of viscous incompressible flows a pure stream-function formulation for the fourth-order equation, the artificial compressibility method, and velocity correction method are employed. Test calculations are performed for various flows inside square, triangular, semicircular and cubic cavities with one uniform wall, the backward-facing step, double bent channels, the flow around an aerofoil at large angle of attack and for flows over models of buildings. Some complex geometrical configurations can be decomposed into a set of simpler subdomains. A practical methodology for the computation of the Navier-Stokes equations in arbitrarily complex geometries is also considered. The simplest approach for specifying boundary conditions near curved or irregular boundaries is to transfer all the variables from the boundaries to the nearest grid knots.

Słowa kluczowe

EN

Navier-Stokes equations; incompressible flows; pure stream-function formulation; artificial compressibility method; velocity correction method; finite difference schemes; method of lines

PL

równania Naviera-Stokesa; przepływy nieściśliwe; metoda sztucznej ściśliwości; metoda korekcji prędkości; metoda różnic skończonych

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2011
• Tom: Vol. 16, no 1
• Strony: 15--35
• Opis fizyczny: Bibliogr. 17 poz., wykr.

Twórcy

autor

Kosma Z.

autor

Motyl P.

• Faculty of Mechanical Engineering, Technical University of Radom ul. Krasickiego 54, 26-600 Radom, POLAND,

Bibliografia

• Gartling D.K. (1990): A test problem for outflow boundary conditions-flow over a backward-facing step. ( Int. J. Numer. Meth. Fluids, vol.11, pp.953-967.
• Ghia U., Ghia K.N. and Shin C.T. (1982): High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. ( J. Comp. Phys., vol.48, pp.387-411.
• Kosma Z. (2005a): Method of lines for the incompressible Navier-Stokes equations in the streamfunction formulation. ( TASK Quarterly, vol.9, No.1, pp.17-35.
• Kosma Z. (2005b): Calculation of viscous incompressible flow around an aerofoil using a modified velocity correction method. ( TASK Quarterly, vol.9, No.1, pp.37-52.
• Kosma Z. (2006): Numerical resolution of incompressible Navier-Stokes equations in the stream function formulation. ( Chem. Process Eng., vol.27, pp.737-760.
• Kosma Z. (2007a): Numerical resolution of incompressible Navier-Stokes equations in the stream-function formulation. ( Tech. Univ. Radom Publ. (in Polish), No.95, pp.1-147.
• Kosma Z. (2007b): Numerical simulations of viscous fluid motions using the artificial compressibility method. ( Tech. Univ. Radom Publ. (in Polish), No.97, pp.1-108.
• Kosma Z. (2008): Fast algorithms for calculations of viscous incompressible flows using the artificial compressibility method. ( TASK Quarterly, vol.12, No.3-4, pp.273-287.
• Kosma Z. (2009): The method of lines for the computation of incompressible viscous flows. ( PAMM, vol.9, pp.483-484.
• Kosma Z. and Motyl P. (2008): Fast algorithms for calculations of viscous incompressible flows using the velocity correction method. ( TASK Quarterly, vol.12, No.3-4, pp.289-301.
• Kosma Z. and Motyl P. (2009a): Fast numerical algorithms for solving incompressible viscous flow problems. ( Tech. Univ. Radom Publ. (in Polish), No.130, pp.1-90.
• Kosma Z. and Motyl P (2009b): Computation of incompressible viscous flows in complex geometries by a velocity correction method. ( PAMM, vol.9, pp.473-474.
• Kosma Z. and Noga B. (2006): Numerical simulations of viscous fluid motions using the artificial compressibility method. ( Chem. Process Eng., vol.27, pp.761-781.
• Lo D.C., Murugesan K. and Young D.L. (2005): Numerical solution of three-dimensional velocity-vorticity Navier-Stokes equations by finite difference method. ( Int. J. Numer. Meth. Fluids, vol.47, pp.1469-1487.
• Murthy P.S., Holla V.S. and Kamath H. (2000): Unsteady Navier-Stokes solutions for a NACA 0012 airfoil. ( Comput. Meth. Appl. Mech. Engrg., vol.186, pp.85-99.
• Shen W.-Z. and Loc T.P. (1995): Simulations of 2D external viscous flows by means of a domain decomposition method using an influence matrix technique. ( Int. J. Numer. Meth. Fluids, vol.20, pp.1111-1136.
• Shu C., Wang L. and Chew Y.T. (2003): Numerical computation of three-dimensional incompressible Navier-Stokes equations in primitive variable form by DQ method. - Int. J. Numer. Meth. Fluids, vol.43, pp.345-368.