The vortex shedding in combustion chamber of solid rocket motor may lead the pressure oscillations, which deteriorates the rocket motor performance and could even damage the payload. Cartesian mesh CFD solver is expected to accurately predict such vortex flows using higher-order scheme and to treat complicated configurations easily. Therefore, blockstructured Cartesian mesh solver, Building-Cube Method (BCM), is applied to Taylor flow analysis, which is the simplified combustion chamber model of solid rocket. Immersed boundary method is extended to treat the wall injection from the grain surface. The approach is also applied to real grain configuration, and the usefulness for the complicated geometry is validated.