TY - JOUR
T1 - Accuracy of spectral and finite difference schemes in 2D advection problems
AU - Naulin, V.
AU - Nielsen, A.H.
PY - 2003
Y1 - 2003
N2 - In this paper we investigate the accuracy of two numerical procedures commonly used to solve 2D advection problems: spectral and finite difference (FD) schemes. These schemes are widely used, simulating, e.g., neutral and plasma flows. FD schemes have long been considered fast, relatively easy to implement, and applicable to complex geometries, but are somewhat inferior in accuracy compared to spectral schemes. Using two study cases at high Reynolds number, the merging of two equally signed Gaussian vortices in a periodic box and dipole interaction with a no-slip wall, we will demonstrate that the accuracy of FD schemes can be significantly improved if one is careful in choosing an appropriate FD scheme that reflects conservation properties of the nonlinear terms and in setting up the grid in accordance with the problem.
AB - In this paper we investigate the accuracy of two numerical procedures commonly used to solve 2D advection problems: spectral and finite difference (FD) schemes. These schemes are widely used, simulating, e.g., neutral and plasma flows. FD schemes have long been considered fast, relatively easy to implement, and applicable to complex geometries, but are somewhat inferior in accuracy compared to spectral schemes. Using two study cases at high Reynolds number, the merging of two equally signed Gaussian vortices in a periodic box and dipole interaction with a no-slip wall, we will demonstrate that the accuracy of FD schemes can be significantly improved if one is careful in choosing an appropriate FD scheme that reflects conservation properties of the nonlinear terms and in setting up the grid in accordance with the problem.
KW - 2-E tekno
U2 - 10.1137/S1064827502405070
DO - 10.1137/S1064827502405070
M3 - Journal article
SN - 1064-8275
VL - 25
SP - 104
EP - 126
JO - S I A M Journal on Scientific Computing
JF - S I A M Journal on Scientific Computing
IS - 1
ER -