守恒律方程的导数人工压缩法

将高分辨率差分格式用于守恒律方程的导数方程,可以克服传统高分辨率格式在极值点精度退化的缺点,类似于Harten的人工压缩法,新方法称为导数人工压缩法.本方法既能提高间断的分辨率,又能提高极值点处的分辨率,是一种高分辨率低耗散低扩散格式.用单个守恒律方程带间断和多极值的初值问题和一维激波管问题进行了验证,比较了Harten-TVD,人工压缩,导数人工压缩方法的在间断和极值点的分辨率问题.

Derivative artificial compression method of conservation laws

Applying high resolution difference schemes on the derivative equations of conservation laws could overcome the shortcoming of accuracy decay at extreme points that has plagued almost all high resolution schemes.Similar to Harten’s artificial compression method,the new method is called derivative artificial compression method,which has high resolution,low dissipation and low diffusion properties,and could enhance the resolution(of numerical solution) both at discontinuities and at extreme points.Numerical experiments are implemented on a single conservation law with initial values of discontinuities and extremes,and on one dimensional shock tube problem.The resolution problem of discontinuities and extremes is compared with Harten’s TVD scheme,artificial compression method and derivative artificial compression method.