非线性双曲守恒律的一种高分辨率冲击捕捉方案
A Class of High Resolution Shock Capturing Schemes for Non-linear Hyperbolic Conservation Laws
AI总结：
本文提出一种构造简单高效的高分辨率TVD方案的方法，通过引入反扩散项和通量限制器，实现了非线性双曲守恒律的高分辨率求解，且在1维标量情况下证明了方案的TVD性质。
摘要：
本文介绍了一种通用方法，用于构造非线性双曲守恒律的简单且高效的高分辨率总变差递减（TVD）方案。通过引入反扩散项和通量限制器来构建数值通量函数，该方法将空间离散化的数值通量函数构造为任意熵满足的一阶准确方案和二阶准确上游方案的组合，利用通量限制器函数。所得高分辨率方案在1维标量情况下被证明为TVD。给出了限制器函数的边界条件。各种测试问题的数值实验表明，所得到的方案相比其对应的首阶方案能提供更高质量的熵一致解。
英文摘要：
A general procedure to construct a class of simple and efficient high resolution Total Variation Diminishing (TVD) schemes for non-linear hyperbolic conservation laws by introducing anti-diffusive terms with the flux limiters is presented. In the present work the numerical flux function for space discretization is constructed as a combination of numerical flux function of any entropy satisfying first order accurate scheme and second order accurate upstream scheme using the flux limiter function. The obtained high resolution schemes are shown to be TVD for 1-D scalar case. Bounds for the limiter function are given. Numerical experiments for various test problems clearly show that the resulting schemes give entropy consistent solution with higher resolution as compared to their corresponding first order schemes.
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