Parareal Time-Stepping for Limit-Cycle Computation of the Incompressible Navier-Stokes Equations with Uncertain Periodic Dynamics

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.

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Multigrid Computation of Incompressible Flows Using Two-Equation Turbulence Models: Part II—Applications

Journal of Fluids Engineering ◽

10.1115/1.2819514 ◽

1997 ◽

Vol 119 (4) ◽

pp. 900-905 ◽

Cited By ~ 4

Author(s):

X. Zheng ◽

C. Liao ◽

C. Liu ◽

C. H. Sung ◽

T. T. Huang

Keyword(s):

Turbulent Flows ◽

Incompressible Flows ◽

Stokes Equations ◽

Three Dimensional ◽

Turbulence Models ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Time Stepping ◽

Grid Algorithm ◽

High Reynolds

In this paper, computational results are presented for three-dimensional high-Reynolds number turbulent flows over a simplified submarine model. The simulation is based on the solution of Reynolds-Averaged Navier-Stokes equations and two-equation turbulence models by using a preconditioned time-stepping approach. A multiblock method, in which the block loop is placed in the inner cycle of a multi-grid algorithm, is used to obtain versatility and efficiency. It was found that the calculated body drag, lift, side force coefficients and moments at various angles of attack or angles of drift are in excellent agreement with experimental data. Fast convergence has been achieved for all the cases with large angles of attack and with modest drift angles.

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Numerical Simulation on Undulatory Flow of Swimming Fish

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.353-356.2545 ◽

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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