Ijaz, Muhammad (2007-12). Implicit Runge-Kutta Methods to Simulate Unsteady Incompressible Flows. Doctoral Dissertation. | Thesis individual record

A numerical method (SIMPLE DIRK Method) for unsteady incompressible
viscous flow simulation is presented. The proposed method can be used to achieve
arbitrarily high order of accuracy in time-discretization which is otherwise limited to
second order in majority of the currently used simulation techniques. A special class of
implicit Runge-Kutta methods is used for time discretization in conjunction with finite
volume based SIMPLE algorithm. The algorithm was tested by solving for velocity field
in a lid-driven square cavity. In the test case calculations, power law scheme was used in
spatial discretization and time discretization was performed using a second-order implicit
Runge-Kutta method. Time evolution of velocity profile along the cavity centerline was
obtained from the proposed method and compared with that obtained from a commercial
computational fluid dynamics software program, FLUENT 6.2.16. Also, steady state
solution from the present method was compared with the numerical solution of Ghia, Ghia,
and Shin and that of Erturk, Corke, and Go?k??l. Good agreement of the solution of the
proposed method with the solutions of FLUENT; Ghia, Ghia, and Shin; and Erturk, Corke,
and Go?k??l establishes the feasibility of the proposed method.

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