大气科学进展（英文版）
大氣科學進展（英文版）
대기과학진전（영문판）
ADVANCES IN ATMOSPHERIC SCIENCES
2010年
3期
594-604
,共11页
黄文誉%伍荣生%方娟
黃文譽%伍榮生%方娟
황문예%오영생%방연
自适应小波%非线性平流方程%配置法%奇异偏微分方程%变网格技术%应用%仿真%有限差分方法
自適應小波%非線性平流方程%配置法%奇異偏微分方程%變網格技術%應用%倣真%有限差分方法
자괄응소파%비선성평류방정%배치법%기이편미분방정%변망격기술%응용%방진%유한차분방법
adaptive wavelet collocation method%efficiency%nonlinear advection%unbalanced frontogenesis
The adaptive wavelet collocation method （AWCM） is a variable grid technology for solving partial differential equations （PDEs） with high singularities. Based on interpolating wavelets, the AWCM adapts the grid so that a higher resolution is automatically attributed to domain regions with high singularities. Accuracy problems with the AWCM have been reported in the literature, and in this paper problems of efficiency with the AWCM are discussed in detail through a simple one-dimensional （1D） nonlinear advection equation whose analytic solution is easily obtained. A simple and efficient implementation of the AWCM is investigated. Through studying the maximum errors at the moment of frontogenesis of the 1D nonlinear advection equation with different initial values and a comparison with the finite difference method （FDM） on a uniform grid, the AWCM shows good potential for modeling the front efficiently. The AWCM is also applied to a two-dimensional （2D） unbalanced frontogenesis model in its first attempt at numerical simulation of a meteorological front. Some important characteristics about the model are revealed by the new scheme.
