Our objective is to develop a Sharp Interface Level Set Method (SI-LSM) based in-house code on a semi-adaptive Cartesian grid - for an improvement in the performance of similar code on a uniform grid [1]. Proposed partial mesh adaption (only for level set field) involves the un-refinement (based on the evolution of the lower dimensional fluid-fluid interface) of the level set control volumes which are in the non-interfacial region. This semi-adaptive un-refinement is solely based on the cell tagging and does not demand implementation of tree data structure. The performance of the SI-LSM on the semi-adaptive grid as compared to a uniform grid is presented for a Stefan problem involving solidification.