一维单个守恒型方程的二阶熵耗散格式

本文考虑一维单个守恒律方程，对其设计了一种非线性守恒型差分格式，此格式为二阶Godunov型的，用的是分片线性重构，重构函数的斜率是根据熵耗散得到的，格式满足熵条件，且数值实验表明格式具有非线性稳定性，在此格式中一个所谓的熵耗散函数起了很重要的作用，它在每个网格的计算中耗散熵，在文中我们给出了熵耗散函数应满足的条件，并给出了一种具体的构造形式，最后给出了一些数值算例，从中可看出熵耗散函数是如何抑制非物理振荡的，及格式对计算的有效性。

Second-Order Entropy Dissipating Scheme for Scalar Conservation Law in One Space Dimension

In this paper, we are concerned with scalar conservation law in one space dimension. We design a nonlinear conservative difference scheme. The scheme is second-order Godunov type scheme with piecewise-linear reconstruction. The slope of the reconstructed function in each grid cell is computed by dissipating the entropy. Numerical experiments show that the scheme is nonlinearly stable and satisfies the entropy condition. A so-called entropy dissipating function in the scheme plays an important role in stabilizing the computation. Criterions on the entropy dissipating function are given and a design of it is also introduced. Finally, numerical examples are presented to show how the entropy dissipating function suppresses nonphysical oscillations near discontinuities and to illustrate the efficiency of the scheme.