In recent years, a novel adaptive method called fully adaptive multiresolution scheme is used to solve the hyperbolic conservation laws [1, 2].It combines the concepts of Hartens multiresolution scheme [3, 4] and the classic Adaptive Mesh Refinement method [5, 6].Thus, to keep the accuracy of the reference solutions at the finest mesh, a suitable reconstruction interpolation has to be carefully selected according to the spatial discretisation of the finite volume scheme.