Comparison of several numerical schemes applied to advection equations
Comparison of several numerical schemes applied to advection equations
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应用于平流方程的几种数值方案的比较
DOI：
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发表时间：
1999
期刊：
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通讯作者：
Z. Sokol
中科院分区：
文献类型：
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作者：
Z. Sokol
通过旋转流场试验和变形流场试验，比较了8种平流方程的数值求解方法。除了跳跃-青蛙差分格式作为参考方法外，其他方法都是正定的或保持单调的。正确定性要么是平流格式的性质，要么是通过应用通量输运限制器得到的。研究了以下格式：由通量输移限制器完成的跳跃-青蛙格式、博特格式、分段抛物方法、总变差递减格式的一种形式和基本非振荡格式的三种修正。目的是比较TVD和ENO方案在高分辨率大气模拟中的应用。试验结果表明，所测试的ENO方案中至少有一种是可行的，但显然以博特方案获得了最好的结果。
Eight numerical‐solution methods of advection equations are compared using two tests: the rotational flowfield test and the deformational flow‐field test. Beside the leap‐frog difference scheme used as a reference method, all the other methods are positive definite or monotonicity preserving. the positive definiteness is either the property of the advection scheme or it is obtained by applying the flux transport limiter. the following schemes are studied: the leap‐frog scheme completed by a flux transport limiter, Bott's scheme, the piecewise parabolic method, one version of the total variation diminishing (TVD) scheme and three modifications of essentially non‐oscillatory (ENO) schemes. the aim is to compare the schemes with respect to the application of TVD and ENO schemes in atmospheric modelling with high resolution. the test results confirm that at least one of the ENO schemes tested may be applied, but apparently the best results are obtained by Bott's scheme.