AN ITERATIVE NONUNIFORMLY SPACED FINITE DIFFERENCE SCHEME FOR COMPUTATIONAL FLUID DYNAMICS

2001 ◽  
Vol 12 (07) ◽  
pp. 1023-1033
Author(s):  
ANDREAS HORRAS ◽  
GERALD H. RISTOW
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Finite Difference ◽  
Difference Scheme ◽  
Newtonian Fluid ◽  
Finite Difference Scheme ◽  
Infinite System ◽  
System Size ◽  
Terminal Velocity ◽  
Staggered Grid

The settling dynamics of cylinders in a viscous Newtonian fluid are investigated numerically using an iterative finite difference scheme, which uses a nonuniformly spaced staggered grid. Special attention is given to the details of the spatial discretization and how they influence the physical results. The terminal velocity is calculated for different system sizes and cylinder diameters and the extrapolated values for an infinite system size are compared with the Oseen approximation.

Analyses of the Dispersion Overshoot and Inverse Dissipation of the High-Order Finite Difference Scheme

2013 ◽  
Vol 5 (06) ◽  
pp. 809-824 ◽  
Author(s):  
Qin Li ◽  
Qilong Guo ◽  
Hanxin Zhang
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
High Order ◽  
Staggered Grid ◽  
Third Order ◽  
Order Scheme ◽  
Relationship Of ◽  
High Order Finite Difference ◽  
The Relationship

AbstractAnalyses were performed on the dispersion overshoot and inverse dissipation of the high-order finite difference scheme using Fourier and precision analysis. Schemes under discussion included the pointwise- and staggered-grid type, and were presented in weighted form using candidate schemes with third-order accuracy and three-point stencil. All of these were commonly used in the construction of difference schemes. Criteria for the dispersion overshoot were presented and their critical states were discussed. Two kinds of instabilities were studied due to inverse dissipation, especially those that occur at lower wave numbers. Criteria for the occurrence were presented and the relationship of the two instabilities was discussed. Comparisons were made between the analytical results and the dispersion/dissipation relations by Fourier transformation of typical schemes. As an example, an application of the criteria was given for the remedy of inverse dissipation in Weirs & Martín’s third-order scheme.

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