We present theoretical models to simulate spark discharge and ignition. Two models are presented. The first model considers simplified fluid mechanics with chemistry effects. The second model utilizes more sophisticated flow with no chemistry. The simplified model incorporates physical models of breakdown and chemical kinetics of combustion with species and energy equations solved using a control volume method. A three-step mechanism is used to simulate chemical kinetics for fuel combustion and nitrogen chemistry. Dissociation and ionization in the plasma are included by assuming local thermal equilibrium. The second model simulates a spark discharge in air with more complete physics of flow using a high order numerical method, which shows the evolution of the shock wave and a torus-like plasma kernel.

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