Integration of Navier-Stokes equations using dual time stepping and a multigrid method

AIAA Journal ◽  
1995 ◽  
Vol 33 (6) ◽  
pp. 985-990 ◽  
Author(s):  
Andrea Arnone ◽  
Meng-Sing Liou ◽  
Louis A. Povinelli
Keyword(s):  
Multigrid Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Time Stepping ◽  
Dual Time Stepping

Numerical Solution of Incompressible Unsteady Flows in Turbomachinery

2000 ◽  
Vol 123 (3) ◽  
pp. 680-685 ◽  
Author(s):  
L. He ◽  
K. Sato
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Time Stepping ◽  
Incompressible Viscous Flow ◽  
Dual Time Stepping

A three-dimensional incompressible viscous flow solver of the thin-layer Navier-Stokes equations was developed for the unsteady turbomachinery flow computations. The solution algorithm for the unsteady flows combines the dual time stepping technique with the artificial compressibility approach for solving the incompressible unsteady flow governing equations. For time accurate calculations, subiterations are introduced by marching the equations in the pseudo-time to fully recover the incompressible continuity equation at each real time step, accelerated with a multi-grid technique. Computations of test cases show satisfactory agreements with corresponding theoretical and experimental results, demonstrating the validity and applicability of the present method to unsteady incompressible turbomachinery flows.

Numerical Simulation on Undulatory Flow of Swimming Fish

2013 ◽  
Vol 353-356 ◽  
pp. 2545-2549
Author(s):  
Xu Zhang ◽  
Xiu Bin He
Keyword(s):  
Numerical Simulation ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Time Stepping ◽  
Dual Time Stepping ◽  
Straight Line ◽  
Volume Method ◽  
Undulatory Swimming

A numerical simulation is carried out to investigate the unsteady flows over a swimming fish. The three-dimensional incompressible Navier-Stokes equations are solved using the finite volume method with artificial compressibility and dual time stepping approaches on unstructured moving grid. A realistic fish-like body is modeled, which undergoes undulatory swimming in a straight line. Both inviscid and viscous flows have been simulated to study the flow structures.

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