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The accurate prediction of fuel sprays is critical to engine combustion and emissions simulations. A fine computational mesh is often required to better resolve fuel spray dynamics and vaporization. However, computations with a fine mesh require extensive computer time. This study developed a methodology that uses a locally refined mesh in the spray region. Such adaptive mesh refinement will enable greater resolution of the liquid-gas interaction while incurring only a small increase in the total number of computational cells. The present study uses an h-refinement adaptive method. A face-based approach is used for the inter-level boundary conditions. The prolongation and restriction procedure preserves conservation of properties in performing grid refinement/coarsening. The refinement criterion is based on the mass of spray liquid and fuel vapor in each cell. The efficiency and accuracy of the present adaptive mesh refinement scheme is demonstrated.