Abstract: LESAP is a combustion simulation application capable of simulating the chemical reactions and supersonic flows in the scramjet engines. It can be used to solve practical engineering problems and involve a large amount of computations. In this paper, we port and optimize LESAP with the OpenMP 4.0 accelerator model, targeting the heterogeneous many-core platform composed of general CPU and Intel Many Integrated Core (MIC). Based on the application characteristics, a series of techniques are proposed, including OpenMP 4.0 based task offloading, data movement optimization, grid-partition based load-balancing and SIMD optimization. The performance evaluation is done for a real combustion simulation configuration, with 5 320 896 grid cells, on one Tianhe-2 supercomputer node. The results show that the resulting heterogenous code significantly outperforms the original CPU only code. When the heterogenous code runs on two Intel Xeon E5-2692 CPUs and three Intel Xeon Phi 31S1P coprocessors, the runtime per time-steep is reduced from 64.72 seconds to 21.06 seconds. The heterogeneous computing achieves a speedup of 3.07 times over the original code that only runs on the two Intel Xeon E5-2692 CPUs.