This work proposes a new spatial reconstruction scheme in finite volume frameworks. Different from long-lastingreconstruction processes which employ high order polynomials enforced with some carefully designed limiting pro-jections to seek stable solutions around discontinuities, the current discretized scheme employs THINC (Tangentof Hyperbola for INterface Capturing) functions with adaptive sharpness to solve both smooth and discontinuoussolutions. Due to the essentially monotone and bounded properties of THINC function, difficulties to solve sharpdiscontinuous solutions and complexities associated with designing limiting projections can be prevented. A newsimplified BVD (Boundary Variations Diminishing) algorithm, so-called adaptive THINC-BVD, is devised to reducenumerical dissipations through minimizing the total boundary variations for each cell. Verified through numericaltests, the present method is able to capture both smooth and discontinuous solutions in Euler equations for com-pressible gas dynamics with excellent solution quality competitive to other existing schemes. More profoundly, itprovides an accurate and reliable solver for a class of reactive compressible gas flows with stiff source terms, such asthe gaseous detonation waves, which are quite challenging to other high-resolution schemes. The stiff C-J detonationbenchmark test reveals that the adaptive THINC-BVD scheme can accurately capture the reacting front of the gaseousdetonation, while the WENO scheme with the same grid resolution generates unacceptable results. Owing also to itsalgorithmic simplicity, the proposed method can become as a practical and promising numerical solver for compress-ible gas dynamics, particularly for simulations involving strong discontinuities and reacting fronts with stiff sourceterm.