Compact finite difference-Fourier spectral method for three-dimensional incompressible Navier-Stokes equations

1996 ◽  
Vol 12 (4) ◽  
pp. 296-306 ◽  
Author(s):  
Xiong Zhongmin ◽  
Ling Guocan
Keyword(s):  
Finite Difference ◽  
Spectral Method ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Fourier Spectral Method ◽  
Navier Stokes Equations ◽  
Compact Finite Difference ◽  
Difference Fourier

A Semi-Staggered Numerical Procedure for the Incompressible Navier-Stokes Equations on Curvilinear Grids

2011 ◽  
Author(s):  
Hessam Babaee ◽  
Sumanta Acharya
Keyword(s):  
Finite Difference ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Second Order ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Benchmark Problems ◽  
Navier Stokes Equations ◽  
Curvilinear Grids

An accurate and efficient finite difference method for solving the three dimensional incompressible Navier-Stokes equations on curvilinear grids is developed. The semi-staggered grid layout has been used in which all three components of velocity are stored on the corner vertices of the cell facilitating a consistent discretization of the momentum equations as the boundaries are approached. Pressure is stored at the cell-center, resulting in the exact satisfaction the discrete continuity. The diffusive terms are discretized using a second-order central finite difference. A third-order biased upwind scheme is used to discretize the convective terms. The momentum equations are integrated in time using a semi-implicit fractional step methodology. The convective and diffusive terms are advanced in time using the second-order Adams-Bashforth method and Crank-Nicolson method respectively. The Pressure-Poisson is discretized in a similar approach to the staggered gird layout and thus leading to the elimination of the spurious pressure eigen-modes. The validity of the method is demonstrated by two standard benchmark problems. The flow in driven cavity is used to show the second-order spatial convergence on an intentionally distorted grid. Finally, the results for flow past a cylinder for several Reynolds numbers in the range of 50–150 are compared with the existing experimental data in the literature.

Computation of Incompressible Three-Dimensional Mixed Convection Flows in Long Aspect Ratio Channels Using an Efficient Finite Difference Method for Vectorial Supercomputers

2005 ◽  
Author(s):  
Xavier Nicolas ◽  
Shihe Xin
Keyword(s):  
Finite Difference ◽  
Aspect Ratio ◽  
Finite Difference Method ◽  
Mixed Convection ◽  
Spectral Decomposition ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Factorization Method ◽  
Navier Stokes ◽  
Navier Stokes Equations

Based on Goda’s algorithm and second-order central finite differences, a very efficient vectorized code is tailored to solve 3D incompressible Navier-Stokes equations for mixed convection flows in high streamwise aspect ratio channels. The code takes advantage of incremental factorization method of ADI type, spectral decomposition of the ID Laplace operators and TDMA algorithm. It is validated through experiments of various Poiseuille-Rayleigh-Be´nard flows with steady longitudinal and unsteady transverse rolls.

Fluid motion inside a spinning nutating cylinder

1985 ◽  
Vol 150 ◽  
pp. 121-138 ◽  
Author(s):  
Harold R. Vaughn ◽  
William L. Oberkampf ◽  
Walter P. Wolfe
Keyword(s):  
Steady State ◽  
Finite Difference ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Navier Stokes Equations ◽  
Internal Fluid

The incompressible three-dimensional Navier–Stokes equations are solved numerically for a fluid-filled cylindrical cannister that is spinning and nutating. The motion of the cannister is characteristic of that experienced by spin-stabilized artillery projectiles. Equations for the internal fluid motion are derived in a non-inertial aeroballistic coordinate system. Steady-state numerical solutions are obtained by an iterative finite-difference procedure. Flow fields and liquid induced moments have been calculated for viscosities in the range of 0.9 × 104−1 × 109 cSt. The nature of the three-dimensional fluid motion inside the cylinder is discussed, and the moments generated by the fluid are explained. The calculated moments generally agree with experimental measurements.

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