Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List

Full text of this paper is not available in the ETD Center. Copies may be available for inter-library loan from University of Cincinnati or may be available for purchase from Proquest/UMI

ETD Abstract Container

Abstract Header

A NEW METHOD FOR THE SOLUTION OF THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

SAID, HAZEM
http://rave.ohiolink.edu/etdc/view?acc_num=ucin982248241

Abstract Details

2001, PhD, University of Cincinnati, Engineering : Aerospace Engineering.
Numerical Solution of the incompressible Navier-Stokes (INS) equations in primitive variables requires special care to ensure that the resulting flow field will satisfy the discrete governing equations (DGE). However, these equations are not satisfied by the existing solution methods, thus requiring the need to develop a new method. A new method is developed in this work to solve the INS equations in primitive variables. The method uses the velocity and pressure gradients as dependent variables compared to velocity and pressure that are used by all other primitive variables methods. These new dependent variables require additional constraint to be determined. The condition of irrotationality of the gradient of the pressure is employed to give the necessary equations to close the problem. Thus the flow field is represented by a new set of equations that when solved together produces a solution that satisfies the DGE. of the present method are summarized as follows: (1) it eliminates the compatability condition of the pressure equation typical of all pressure-based techniques, (2) it satisfies the discrete continuity and momentum equations. (3) Boundary conditions are physically known for all the dependent variables. (4) It eliminates the inversion of the implicit operator typical of the implicit primitive variables formulation, (5) Robust, stable and more accurate computational codes can be developed. Numerical results are obtained for the driven cavity problem, using both the explicit and the implicit forms of the method. Results are obtained for Reynolds numbers of 100, 400 and 1000. These results show that the present method produces a stable solution and that the resulting flow field does satisfy the DGE to machine zero.
Dr. Shaaban Abdallah (Advisor)
1 p.
Engineering, Aerospace
incompressible flow; navier-stokes equations; implicit; explicit

Recommended Citations

Citations

  • SAID, H. (2001). A NEW METHOD FOR THE SOLUTION OF THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin982248241

    APA Style (7th edition)

  • SAID, HAZEM. A NEW METHOD FOR THE SOLUTION OF THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS. 2001. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin982248241.

    MLA Style (8th edition)

  • SAID, HAZEM. "A NEW METHOD FOR THE SOLUTION OF THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS." Doctoral dissertation, University of Cincinnati, 2001. http://rave.ohiolink.edu/etdc/view?acc_num=ucin982248241

    Chicago Manual of Style (17th edition)

ucin982248241
© 2001, all rights reserved.
This open access ETD is published by University of Cincinnati and OhioLINK.