Spray modeling is a critical component to engine combustion and emissions simulations. Accurate spray modeling often requires a fine computational mesh for better numerical resolutions. This, in turn, will require extensive computer time. A major concern for the successful application of computational methods in an industrial environment is its capability to handle complex configurations with acceptable accuracy at reasonable human and computational costs. To assure the accuracy and reliability of the solution, grid modification and grid refinement studies are often necessary within an iterative process. Adaptive algorithms are a promising approach to realize discretizations that are able to automatically resolve the physically relevant phenomena at reduced costs. The first goal of the dissertation work is to developed a methodology that uses a locally dynamically refined mesh in the spray region for engine spray simulations. An h-refinement adaptive scheme is developed and implemented into an existing computer code. It is a dynamic process that adapts an initial mesh by employing local cell division and recovery. Adaptation of the cells is composed of isotropic division of one hexahedron into eight sub-cells in three dimensions. The concept of polyhedral elements is implemented to treat any possible hanging node configuration that occurs at the interface between the divided and undivided zones in a natural way. This flexibility of this method was demonstrated to handle successive grid adaptation and efficient data management when it is extended to multi-level refinement process. A special data structure based on octree has been developed for high storage efficiency. The solid-cone and hollow-cone sprays under direct-injection gasoline engine conditions were simulated. Predicted spray characteristics using different mesh densities with various refinement levels were compared. Results show that the present mesh refinement scheme can accurately predict spray structures with reduced computer times. A significant computational speed-up was achieved by using a relatively coarse mesh with multi-level refinement while maintaining a good level of accuracy. On the other hand, accurate modeling of the wall heat transfer characteristics within an engine is important for engine design because the amount of heat transfer through the piston, head, and liner surfaces can influence engine efficiency and performance, exhaust emission levels, and engine durability. The surface temperature is a key element for heat transfer, thus an accurate chamber wall surface temperature prediction is crucial for engine heat transfer modeling. The second part of this study developed a conjugate heat transfer model to predict the combustion chamber surface temperature of an engine. First, the code was modified to account for a non-uniform temperature distribution and was run with the uniform temperature profile specified in the input file. The results were compared with the experimental data. The conduction heat transfer modeling capability was added to the code to predict the heat diffusion inside the solid wall by solving a simplified energy equation with the same numerical method used in fluid region. A fully coupled numerical procedure, which conserved the continuous temperature and heat flux condition, was developed to simultaneously solve the heat transfer in fluid flows and heat conduction in solid. Model validation showed the predicted results agreed well with the analytical solutions. The method was applied to simulate a transient diesel engine with fuel spray. The non-uniform spatial temperature distribution on the piston surface caused by fuel spray...