Numerical discretization of the compressible Navier-Stokes equations requires computing gradients as- sociated with inviscid and viscous fluxes. These gradients are also used in shock-capturing techniques such as WENO schemes and to compute turbulent statistics such as enstrophy. The primary motivation of this talk is to compute these gradients with high-order accuracy and superior spectral properties once and reuse them wherever necessary to reduce simulation computational cost, while resolving flow features and interfaces with high resolution. The objectives of this presentation are: a) demonstrate that the spec- tral properties of the viscous flux discretization play an important role in preventing odd-even decoupling for flows with and without discontinuities [1]; b) show how the gradients used for the viscous fluxes can be reused for convective fluxes, resulting in what is called gradient-based reconstruction. The novel fea- ture of the proposed algorithm is the efficient reconstruction via derivative sharing between the inviscid and viscous schemes: highly accurate explicit and implicit gradients are used for the solution recon- struction expressed in terms of derivatives [2]; c) two different shock-capturing strategies are presented for the gradient-based reconstruction. One is based on the boundary variation diminishing (BVD) ap- proach and the other is the monotonicity preserving (MP) approach. The MP approach is also improved by reusing the gradients; d) show how the MP algorithm works for primitive and conservative variable reconstruction, and highlight the differences.