Investigating the shock-capturing properties of some composite numerical schemes for the 1-D linear advection equation
Investigating the shock-capturing properties of some composite numerical schemes for the 1-D linear advection equation
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研究一维线性平流方程的一些复合数值格式的冲击捕获特性
DOI：
10.1504/ijcat.2012.046038
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
A. Appadu
中科院分区：
文献类型：
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作者：
A. Appadu
这使我们能够更好地理解复合格式的激波捕捉特性。这项研究使我们能够理解为什么在求解一维线性平流问题时，并不是所有的组合格式都能有效地控制激波区的扩散和耗散。我们使用了一种称为低色散低耗散的最小积分指数误差的技术来分析一些用于一维线性平流方程的数值方法的激波捕捉特性。这一技术还允许我们获得最优的CFL数。进行了数值实验，并利用Takacs设计的技术将误差量化为色散和耗散。可以看出，误差取决于所使用的CFL数。与其他CFL数相比，在最佳CFL数下，色散和耗散误差最小。
This paper enables us to understand better the shock-capturing property of composite schemes. The study allows us to understand why not all composite schemes can be effective to control dispersion and dissipation in regions of shocks when used to solve 1-D linear advection problems. We use a technique called the Minimised Integrated Exponential Error for Low Dispersion and Low Dissipation to analyse the shock-capturing property of some selected numerical methods applied to the 1-D linear advection equation. This technique also allows us to obtain the optimal cfl number. Numerical experiments are performed and the errors are quantified into dispersion and dissipation using a technique devised by Takacs. It is seen that the errors are dependent on the cfl number used. At the optimal cfl, we observe that the dispersion and dissipation errors are least as compared to other cfl numbers.