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Depleting oil reserves and increasing concern over global warming caused by green house gases like carbon dioxide is driving efforts all over the world to improve fuel efficiencies of internal combustion engines. A method of achieving this in spark ignition engines is to use lean air-fuel mixtures. But for burning lean air-fuel mixtures the energy released by conventional spark ignition systems which produce a maximum voltage only of around 20000 V may not be sufficient. A corona discharge spark ignition is a method which can produce voltages as high as 100 kV which can ignite very lean air-fuel mixtures. The objective of this work is to numerically simulate the corona discharge in a point plane configuration and to investigate the applicability of corona discharge to automobile ignition systems. The domain for the simulation is chosen so as to match the engine cylinder and dimensions.