天气和流体力学中许多问题的核心框架都是一套依赖于时间的微分方程组，求解时误差的大小主要取决于空间和时间方向的算法精度，以往对空间导数的精确计算研究较多，但时间积分方案多采用较低的阶数，这导致了一些模式空间、时间计算精度不匹配，影响了模式长时间计算的准确性。本项目拟研究高精度且时空匹配的数值格式的理论和方法，对典型的方程如：Lorenz方程、平流方程、Burgers方程，正压涡度方程等采用新的格式进行计算，以验证其合理性。解决算法实用性中的科学问题，包括时间积分的高阶递归计算格式设计及其并行计算，然后，根据各模型方程的特点，采用高阶差分算法和谱方法等精确计算空间导数项，推导与其匹配的时间积分方案。此外，对时空匹配的高精度计算格式进行误差分析，并与低阶格式对比，研究高阶格式对模拟结果的改进，最后，以球面浅水方程和一个实际的大气环流模式为例，探讨其应用于未来实际数值模拟研究中的可行性。

The core of many weather and fluid dynamics problems are sets of time-dependent differential equations. The numerical errors in computing the equations are mainly affected by the orders of spatial and temporal schemes. Previous studies mainly focus on the precise computation of spatial derivate, while the order of applied scheme is low on the temporal direction. The mismatch influences the accuracy of long-time computation due to temporal error accumulation. The proposal proposes a high-order method which has cooperative spatial and temporal accuracy and can be applied to solve classical equations such as Lorenz equation, advection equation, Burgers equation and barotropic vorticity equation. Then, methods, such as the high-order difference scheme and spectral method, are used to accurately obtain spatial derivatives and formulate the corresponding high-order temporal items for Taylor integration scheme. The parallel computation is applied to speed up the computation of recurrent high-order derivate. We also compare the performance of new scheme with previous low order scheme. In addition, the new schemes are adopt in the spherical shallow water model and an atmospheric general circulation model to study the feasibility of applying the schemes in the real numerical simulation.