【摘要】 利用 Taylor级数理论和总变差减小 ( TVD)格式的充分条件构造了时间二阶、空间五点三阶和四阶新 TVD格式 .给出了新 TVD格式与传统 TVD格式及近期建立的二阶新 TVD格式用于线性双曲型方程的计算结果 ,表明本文新格式特别是四阶 TVD格式具有比二阶新 TVD格式和传统 TVD格式峰值衰减更慢、间断更陡 ,而计算工作量具有与传统二阶 TVD格式相当的良好数值性能更多还原

【Abstract】 New five point total variation diminishing (TVD) schemes with third and fourth order accuracy in space and second order accuracy in time were constructed by applying the Taylor series theory and the TVD sufficient conditions. The comparative results for solving linear hyperbolic equation were presented using the present schemes, the second order TVD schemes and the traditional TVD schemes. It demonstrates that the presented high order TVD schemes, especially the fourth order accuracy scheme, have good numerical features that the peak values attenuate more slowly and discontinuities are steeper than the new second order TVD schemes and the traditional TVD schemes. However, the computational time with the present schemes is almost the same as that with the traditional TVD schemes.更多还原