满足高阶总变差消减条件的非音速数据极值局部原理方案
Local principle satisfying high order total variation diminishing approximation for non-sonic data extrema
AI总结：
本文提出高阶精度总变差消减方案，通过局部最大原理和非保守形式，在非音速极值处保持高精度且不引入局部振荡。
摘要：
本文的主要贡献是构建高于二阶精度的总变差消减（TVD）方案，能够在非音速极值处保持高精度且不引入局部振荡。该方案基于局部最大原理和非保守形式框架。通过连续梯度的比值将常规二阶精度方案转换为非保守形式。利用局部最大原理分析其非线性LMP/TVD稳定性界限，并基于此构造二阶精度的混合数值方案。数值结果表明，此类混合方案在光滑解和极值处可实现二阶或更高阶的收敛率。
英文摘要：
The main contribution of this work is to construct higher than second order accurate total variation diminishing (TVD) schemes which can preserve high accuracy at non-sonic extrema with out induced local oscillations. It is done in the framework of local maximum principle (LMP) and non-conservative formulation. The representative uniformly second order accurate schemes are converted in to their non-conservative form using the ratio of consecutive gradient. These resulting schemes are analyzed for their non-linear LMP/TVD stability bounds using the local maximum principle. Based on the bounds, second order accurate hybrid numerical schemes are constructed using a shock detector. Numerical results are presented to show that such hybrid schemes yield TVD approximation with second or higher order convergence rate for smooth solution with extrema.
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