An Integrated Quadratic Reconstruction for Finite Volume Schemes to Scalar Conservation Laws in Multiple Dimensions

We proposed a piecewise quadratic reconstruction method, which is in an integrated style, for finite volume schemes to scalar conservation laws. This quadratic reconstruction is parameter-free, is of third-order accuracy for smooth functions, and is flexible on structured and unstructured grids. The finite volume schemes with the new reconstruction satisfy a local maximum principle. Numerical examples are presented to show that the proposed schemes with a third-order Runge-Kutta method attain the expected order of accuracy.