A generalized finite-difference (GFD) ALE scheme for incompressible flows around moving solid bodies on hybrid meshfree–Cartesian grids

2006 ◽  
Vol 218 (2) ◽  
pp. 510-548 ◽  
Author(s):  
C.S. Chew ◽  
K.S. Yeo ◽  
C. Shu
Keyword(s):  
Finite Difference ◽  
Incompressible Flows ◽  
Cartesian Grids ◽  
Solid Bodies

Numerical simulation of incompressible flows within simple boundaries: accuracy

1971 ◽  
Vol 49 (1) ◽  
pp. 75-112 ◽  
Author(s):  
Steven A. Orszag
Keyword(s):  
Numerical Simulation ◽  
Finite Difference ◽  
Spectral Methods ◽  
Degrees Of Freedom ◽  
Incompressible Flows ◽  
Finite Difference Methods ◽  
Fourier Method ◽  
Passive Scalar ◽  
Mathematical Basis ◽  
Improved Accuracy

Galerkin (spectral) methods for numerical simulation of incompressible flows within simple boundaries are shown to possess many advantages over existing finite-difference methods. In this paper, the accuracy of Galerkin approximations obtained from truncated Fourier expansions is explored. Accuracy of simulation is tested empirically using a simple scalar-convection test problem and the Taylor–Green vortex-decay problem. It is demonstrated empirically that the Galerkin (Fourier) equations involving Np degrees of freedom, where p is the number of space dimensions, give simulations at least as accurate as finite-difference simulations involving (2N)p degrees of freedom. The theoretical basis for the improved accuracy of the Galerkin (Fourier) method is explained. In particular, the nature of aliasing errors is examined in detail. It is shown that ‘aliasing’ errors need not be errors at all, but that aliasing should be avoided in flow simulations. An eigenvalue analysis of schemes for simulation of passive scalar convection supplies the mathematical basis for the improved accuracy of the Galerkin (Fourier) method. A comparison is made of the computational efficiency of Galerkin and finite-difference simulations, and a survey is given of those problems where Galerkin methods are likely to be applied most usefully. We conclude that numerical simulation of many of the flows of current interest is done most efficiently and accurately using the spectral methods advocated here.

Sign in / Sign up

Export Citation Format

Share Document