Efficient ADI (Alternating Direction Implicit) and Spline ADI Methods for the Navier-Stokes Equations.

1983 ◽  
Author(s):  
Michele Napolitano
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Adi Methods

Steady Laminar Flow in a Stationary Tank With a Spinning Bottom

1975 ◽  
Vol 42 (4) ◽  
pp. 771-776 ◽  
Author(s):  
C. V. Alonso
Keyword(s):  
Stokes Equations ◽  
Tangential Velocity ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
General Validity ◽  
Alternating Direction Implicit ◽  
Incompressible Viscous Flow ◽  
Alternating Direction ◽  
Alternating Direction Implicit Scheme ◽  
Steady Laminar

The steady incompressible viscous flow induced in a cylindrical tank by the rotation of its bottom was studied both theoretically and experimentally. The complete Navier-Stokes equations are expressed in terms of the tangential velocity, vorticity, and meridional stream function. The transformed equations are solved numerically using an alternating-direction implicit scheme and a nonuniform grid. The general validity of the numerical solution was demonstrated by the agreement between the computed and experimental results.

Laminar Incompressible Recirculating Flow in a Driven Cavity of Polar Cross Section

1977 ◽  
Vol 99 (4) ◽  
pp. 774-777 ◽  
Author(s):  
U. Ghia ◽  
R. K. Goyal
Keyword(s):  
Stream Function ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Cavity Flow ◽  
Rectangular Cavity ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Recirculating Flow ◽  
Alternating Direction

The driven flow in a polar cavity has been analyzed using the complete Navier-Stokes equations formulated in terms of a stream function and vorticity. An alternating-direction implicit method, with careful treatment of the convective terms in the equations, is used to obtain the numerical solutions. Results are obtained for the stream function, vorticity, velocities and pressure for various values of the two characteristic parameters of the problem, namely, the flow Reynolds number Re and the aspect ratio of the cavity. The formulation is general and produces results for the driven rectangular cavity-flow problem as a special case. Good agreement is obtained between the present solutions for this case and available corresponding results. The overall features of the driven polar-cavity flow are found to be generally similar to those for the rectangular cavity.

A High-Accuracy Finite Difference Scheme for Solving Reaction-Convection-Diffusion Problems with a Small Diffusivity

2014 ◽  
Vol 6 (5) ◽  
pp. 637-662 ◽  
Author(s):  
Po-Wen Hsieh ◽  
Suh-Yuh Yang ◽  
Cheng-Shu You
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Stokes Equations ◽  
High Accuracy ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Convection Diffusion ◽  
Alternating Direction ◽  
Diffusion Problems

AbstractThis paper is devoted to a new high-accuracy finite difference scheme for solving reaction-convection-diffusion problems with a small diffusivity ε. With a novel treatment for the reaction term, we first derive a difference scheme of accuracy O(εh2+εh2+h3) for the 1-D case. Using the alternating direction technique, we then extend the scheme to the 2-D case on a nine-point stencil. We apply the high-accuracy finite difference scheme to solve the 2-D steady incompressible Navier-Stokes equations in the stream function-vorticity formulation. Numerical examples are given to illustrate the effectiveness of the proposed difference scheme. Comparisons made with some high-order compact difference schemes show that the newly proposed scheme can achieve good accuracy with a better stability.

Numerical solution of the Navier-Stokes equations for symmetric laminar incompressible flow past a parabola

1972 ◽  
Vol 51 (3) ◽  
pp. 417-433 ◽  
Author(s):  
R. T. Davis
Keyword(s):  
Incompressible Flow ◽  
Stokes Equations ◽  
Alternating Direction Method ◽  
Navier Stokes ◽  
Parabolic Cylinder ◽  
Radius Of Curvature ◽  
Nose Radius ◽  
Navier Stokes Equations ◽  
Flow Past ◽  
Alternating Direction

Symmetric laminar incompressible flow past a parabolic cylinder is considered for all Reynolds numbers. In the limit as the Reynolds number based on nose radius of curvature goes to zero, the solution for flow past a semi-infinite flat plate is obtained. All solutions are found by using an implicit alternating direction method to solve the time-dependent Navier-Stokes equations. The solutions found are compared with various other exact and approximate solutions. Results are presented for skin friction, surface pressure, friction drag and pressure drag. The numerical method developed is of particular interest since it combines the alternating direction method with the implicit method for solving the boundary-layer equations. This leads to fast convergence and may be of use in other problems.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

Sign in / Sign up

Export Citation Format

Share Document