Dimension by Dimension Finite Volume HWENO Method for Hyperbolic Conservation Laws

In this paper, we propose a finite volume Hermite weighted essentially non-oscillatory (HWENO) method based on the dimension by dimension framework to solve hyperbolic conservation laws. It can maintain the high accuracy in the smooth region and obtain the high resolution solution when the discontinuity appears, and it is compact which will be good for giving the numerical boundary conditions. Furthermore, it avoids complicated least square procedure when we implement the genuine two dimensional (2D) finite volume HWENO reconstruction, and it can be regarded as a generalization of the one dimensional (1D) HWENO method. Extensive numerical tests are performed to verify the high resolution and high accuracy of the scheme.