长时效的正压原始方程能量完全守恒(拟)谱模式
A LONG VALID TIME ENERGY PERFECT CONSERVATIVE PSEUDOSPECTRAL SCHEME OF BAROTROPIC PRIMITIVE EQUATIONS
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摘要: 遵循误差反演补偿新计算原理,对正压原始方程传统气象全球拟谱模式方案进行了改造,构造了正压原始方程能量完全守恒全球拟增模式新计算方案,解决了正压原始方程的(非线性)计算稳定性问题和能量守恒整体性质保持问题,改进了相应正压原始方程传统气象全球拟谱模式方案的计算效能。新方案的数值试验表明:在计算实践上,新方案在解决能量守恒问题的同时,可解决(非线性)计算稳定性问题,并在一定条件下可解决非线性计算收敛性问题。进一步的比较数值试验还表明:在计算实践上,新方案具有在提高相应传统气象方案的计算精度,减少其计算量的同时,延长其计算时效,解决其中一类特定“气候漂移”问题方面的效用。本工作原理也适用于斜压原始方程情形。Abstract: Here, a meteorological traditional global pseudo-spectral scheme of barotropic primitive equation is restructed and a corresponding perfect energy conservative new scheme is formufated in accordance with the compensation principle of discrete computation. Thus, the problems of both nonlinear computational instability and perfect energy conservation are completely solved, and the computational function of the traditional scheme is improved. As the numerical experiments of the new schemes show, by solving the problem of energy conservation, the new shceme in computational practice can solve their own problem of(nonlinear) computational instability and that of(nonlinear) computational convergence under certain condition. Further contrasts between the new schemes and the traditional one also indicate that, in discrete computational practice the new scheme in case of nondivergence is capable of enlarging the valid integral time of the corresponding traditional scheme, capable of solving its own problem of "climate drift",while at the same time improving its computational accuracy and reducing its amount of computation. The working principle of this paper can also applied in the case of baroclinic primitive equation.
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