五阶精度WENO差分型格子波尔兹曼算法求解单守恒方程

给出了五阶精度WENO差分型格子波尔兹曼算法求解单守恒模型方程的计算方法.根据WENO差分格式的特点,定义了广义格子波尔兹曼分布函数,将守恒型方程的求解问题,转化成用WENO格式的差分算法对该分布函数进行求解.该方法的意义在于,将高精度高分辨率的WENO格式差分方法与近几十年发展起来的格子波尔兹曼方法相结合,从而很方便地构造出可以用于求解守恒型方程的格子波尔兹曼模型,使格子波尔兹曼方法在可压缩流领域的使用更简单.利用该方法分别构造了不同初值条件下的一维Burgers守恒型方程的求解模型,求出结果,并分析了模型的精度和稳定性.最后总结了方法的优点和不足,以及有待进一步研究解决的问题.

NUMERICAL SOLUTIONS OF SINGLE CONSERVATION EQUATION BY FIFTH ORDER WENO DIFFERENCE LATTICE BOLTZMANN METHOD

In this paper, a fifth order WENO-Lattice Boltzmann method for solving the one dimension conservation equation was developed. We defined a generalized lattice Boltzmann distribution function, which could be calculated by the WENO difference schemes. Then the solving of the one dimension conservation equation became the solving of the generalized lattice Boltzmann distribution function by the WENO difference schemes. The method remained the benefits of the WENO method such as the high precision and the high resolution, and provided a new way to construct the lattice Boltzmann models for solving the Euler equation. This made the lattice Boltzmann method more convenient to solve the compressible flow problems. As an example, we presented 1D Burgers conservation equation, solved it by using the method we developed in this paper, and analyzed the accuracy and stability of the model. At last, we made a summary of the method, and presented problems to be further studied.