基于Runge-Kutta不连续Galerkin方法的斜率限制器研究

采用高阶Runge-Kutta不连续Galerkin方法对欧拉方程进行数值研究。针对高分辨率数值流通量格式中斜率限制器展开研究,采用虚拟流体法这种界面处理方法和斜率限制器共同抑制数值振荡。结果表明：斜率限制器计算稳定,计算精度高,能实现计算的高精度和高分辨率；在数值计算方法采用不连续Runge-KuttaGalerkin方法,界面处理方法采用虚拟流体法的计算环境下,斜率限制器十分高效和精确,在工程应用中有广阔的前景。

Slope limiter based on Runge-Kutta discontinuous Galerkin method

The Euler equation is studied numerically by the high order Runge - Kutta method of discontinuous Galerkin method .. In this paper, we study the slope limiter in the high resolution numerical flow format, and use the ghost fluid method to suppress the numerical oscillation. The results show that the slope limiter is stable in calculation, high accuracy, high precision and high resolution can be achieved in the calculation; numerical calculation method by using the discontinuous Runge-KuttaGalerkin method, computing environment interface processing method using ghost fluid method, slope limiter is very efficient and accurate, and has broad prospects in engineering application.