A Study of High-Order Advection Schemes in Variable Resolution

可變解析度的高階平流格式

黃清勇(Ching-Yuang Huang)

《Terrestrial, Atmospheric and Oceanic Sciences》 4卷4期 (1993/12) Pp. 421-440

並列摘要

High-order advection schemes are investigated in linear and nonlinear advection. Numerical tests and theoretical analyses indicate that the performance level of semi-Lagrangian advection schemes using cubic spline interpolation is between those using quintic and seventh-order Lagrange interpolations in uniform resolution. However, higher-order Lagrange interpolations yield larger dispersion in the region of variable resolution in the rotational flow test. The degrading phase preservation can be improved by spline interpolations such as cubic spline or cubic B-spline. For positive definite advection, first-order Lagrange interpolation can be applied in combination with higher-order Lagrange interpolations to suppress the dispersion of negative values. In variable resolution, simple Eulerian formulations generally have insufficient accuracy and stringent stability constraints, but semi-Lagrangian schemes do not. Based on the linear and nonlinear advection tests, it was suggested that variable-resolution mesoscale models may employ cubic spline or cubic B-spline for horizontal advection and cubic Lagrange interpolation for vertical advection without recourse to quintic and higher-order Lagrange interpolations.