A new method of solution is presented for the equations governing unsteady flow field during compression and combustion in a spark ignition. The Lagrangian approach, an application of a vortex method to the three-dimensional solution of the continuity and conservation equations, avoids the need for a turbulence model and wall laws close to the surfaces. Vorticity is introduced as blobs close to the wall which diffuse into the main flow. The potential equation is solved by the boundary element method. Combustion is treated as a thin sheet propagating at laminar flame speed using an extension of the simple line interface method to three-dimensions, now called a simple plane interface method. The code is demonstrated in application to a wedge shaped combustion chamber with surface irregularities closely approximating the actual shape.