Firstly, a new reconstruction strategy is proposed to improve the accuracy of the fifth-order Weighted Essentially Non-Oscillatory (WENO) scheme. It has been noted that conventional WENO schemes still suffer from excessive numerical dissipation near critical regions. One of the reasons is that they tend to under-use all adjacent smooth sub-stencils thus fail to realize optimal interpolation. Hence in this work, a modified WENO (MWENO) strategy is designed to restore the highest possible order interpolation when three target sub-stencils or two target adjacent sub-stencils are smooth.Since the new detector is formulated under the original smoothness indicators, no obvious complexity and cost are added to the simulation. This idea has been successfully implemented into two classical fifth-order WENO schemes, which improve the accuracy near the critical region but without destroying essentially non-oscillatory properties. Secondly, the Tangent of Hyperbola for INterface Capturing (THINC) scheme is introduced as another reconstruction candidate to better represent the discontinuity. Finally, the MWENO and THINC schemes are implemented with the Boundary Variation Diminishing (BVD) algorithm to further minimize the numerical dissipation across discontinuities. Numerical verifications show that the proposed scheme accurately capture both smooth and discontinuous flow structures simultaneously with high-resolution quality. Meanwhile, the presented scheme effectively reduce numerical dissipation error and suppress spurious numerical oscillation in the presence of strong shock or discontinuity for compressible flows and compressible two-phase flows.