An Efficient Solution Procedure for the Incompressible Navier-Stokes Equations

AIAA Journal ◽  
1977 ◽  
Vol 15 (9) ◽  
pp. 1307-1314 ◽  
Author(s):  
J. D. Murphy
Keyword(s):  
Efficient Solution ◽  
Stokes Equations ◽  
Solution Procedure ◽  
Navier Stokes ◽  
Navier Stokes Equations

Numerical Simulation of Asymmetric Exhaust Flows Using an Actuator Disc Blade Row Model

2002 ◽  
Author(s):  
Jianjun Liu
Keyword(s):  
Numerical Simulation ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Solution Procedure ◽  
Navier Stokes ◽  
Exhaust Hood ◽  
Navier Stokes Equations ◽  
Multigrid Algorithm ◽  
Blade Row ◽  
Actuator Disc

This paper describes the numerical simulation of the asymmetric exhaust flows by using a 3D viscous flow solver incorporating an actuator disc blade row model. The three dimensional Reynolds-Averaged Navier-Stokes equations are solved by using the TVD Lax-Wendroff scheme. The convergence to a steady state is speeded up by using the V-cycle multigrid algorithm. Turbulence eddy viscosity is estimated by the Baldwin-Lomax model. Multiblock method is applied to cope with the complicated physical domains. Actuator disc model is used to represent a turbine blade row and to achieve the required flow turning and entropy rise across the blade row. The solution procedure and the actuator disc boundary conditions are described. The stream traces in various sections of the exhaust hood are presented to demonstrate the complicity of the flow patterns existing in the exhaust hood.

Flow past a row of flat plates at large Reynolds numbers

1993 ◽  
Vol 441 (1912) ◽  
pp. 211-235 ◽  
Keyword(s):  
Stokes Equations ◽  
Solution Procedure ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
Flat Plates ◽  
Navier Stokes Equations ◽  
Element Discretization ◽  
Flow Past ◽  
High Reynolds ◽  
Outflow Boundary

The steady, incompressible, high Reynolds number, viscous flow past a row of flat plates is computed by a Galerkin finite element discretization of the Navier-Stokes equations in the streamfunction/vorticity formulation. A novel implementation of the inflow and outflow boundary conditions is described, which combines numerical stability with computational economy in the solution procedure. The calculations reported here cover the range of medium and small blockage ratios, i. e. 5 ≼ a ≼ 25 (where a is the inverse blockage ratio). A transition is found from narrow wake eddies for small values of a , to wide wake eddies for values of a above a crit ≈ 15. This transition is in general agreement with the trends reported earlier by Fornberg (1991), for the related problem of flow past a row of circular cylinders (for which a crit was approximately 8).

PARALLEL IMPLEMENTATION OF A NAVIER–STOKES SOLVER: TURBULENT EKMAN LAYER DIRECT SIMULATION

2014 ◽  
Vol 11 (05) ◽  
pp. 1350070 ◽  
Author(s):  
SCOTT B. WAGGY ◽  
ALEC KUCALA ◽  
SEDAT BIRINGEN
Keyword(s):  
Stokes Equations ◽  
Parallel Implementation ◽  
Ekman Layer ◽  
Solution Procedure ◽  
Linear Stability Theory ◽  
Navier Stokes ◽  
Implicit Time ◽  
Navier Stokes Equations ◽  
Stable Case ◽  
Strong Scaling

A massively parallel direct numerical solution procedure for the turbulent Ekman layer is presented. The simulations study the dynamics of turbulence in this flow by solving the incompressible Navier–Stokes equations with Coriolis and buoyancy terms. The governing equations are integrated via a semi-implicit time advancement algorithm which is massively parallelized using the Portable, Extensible Toolkit for Scientific Computation (PETSc) libraries. Accuracy of the numerical scheme was validated by comparisons of simulation results with the hydrodynamic linear stability theory for Poiseuille flow. Two cases are presented to demonstrate the capabilities of the code: (a) a neutrally stable case of Reynolds number, Re = 400 and (b) an unstably stratified case at Re = 1,000 requiring very high resolution in all coordinate directions. Results indicate that the scalability is not limited by the overall size of the problem, but rather by the number of mesh points per processor. Strong scaling is demonstrated for both cases with as few as 10,000 unknowns per processor.

Modeling of Three-Dimensional Flow in Turning Channels

1984 ◽  
Vol 106 (3) ◽  
pp. 682-691 ◽  
Author(s):  
I. M. Khalil ◽  
H. G. Weber
Keyword(s):  
Stokes Equations ◽  
Reverse Flow ◽  
Three Dimensional ◽  
Solution Procedure ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Pressure Gradients ◽  
Dean Number ◽  
Navier Stokes Equations ◽  
Curved Channels

The structure of developing flows inside curved channels has been investigated numerically using the time-averaged Navier Stokes equations in three dimensions. The equations are solved in primitive variables using finite difference techniques. The solution procedure involves a combination of repeated space-marching integration of the governing equations and correction for elliptic effects between two marching sweeps. Type-dependent differencing is used to permit downstream marching even in the reverse-flow regions. The procedure is shown to allow efficient calculations of turbulent flow inside strongly curved channels as well as laminar flow inside a moderately curved passage. Results obtained in both cases indicate that the flow structure is strongly controlled by local imbalance between centrifugal forces and pressure gradients. Furthermore, distortion of primary flow due to migration of low momentum fluid caused by secondary flow is found to be largely dependent on the Reynolds number and Dean number. Comparison with experimental data is also included.

Navier–Stokes Solution for Steady Two-Dimensional Transonic Cascade Flows

1988 ◽  
Vol 110 (3) ◽  
pp. 339-346 ◽  
Author(s):  
O. K. Kwon
Keyword(s):  
Stokes Equations ◽  
Solution Procedure ◽  
Curvilinear Coordinates ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Turbine Cascade ◽  
Navier Stokes Equations ◽  
Time Marching ◽  
Transonic Turbine ◽  
Transonic Cascade

A robust, time-marching Navier–Stokes solution procedure based on the explicit hopscotch method is presented for solution of steady, two-dimensional, transonic turbine cascade flows. The method is applied to the strong conservation form of the unsteady Navier–Stokes equations written in arbitrary curvilinear coordinates. Cascade flow solutions are obtained on an orthogonal, body-conforming “O” grid with the standard k–ε turbulence model. Computed results are presented and compared with experimental data.

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