In a severe accident of light water reactors, a particulate debris bed of core melt (corium) may form in the core region or the lower head of the reactor pressure vessel (RPV) due to corium-coolant interactions. Melt infiltration in the debris bed will occur due to earlier re-melting of metallic components which have lower melting points. If the melt infiltration process cannot be limited by solidification, the corium is expected to move downwards to the vicinity of the RPV wall, resulting in a strong thermal load there and threatening the RPV integrity. When the RPV fails, corium may be discharged and spread on the basemat of the reactor cavity either in a shallow water pool or a dry cavity. Both the in-vessel and ex-vessel corium behaviors are important to the assessment of severe accident progression and should be investigated deeply. The main goal of this work is to develop and validate the code based on Moving Particle Semi-implicit (MPS) method to address problems associated with in-vessel and ex-vessel behavior of molten corium. In this code, the particles are used to represent the fluid and solid which could be more than millions if the geometry is very large such as the real dimension of reactors. Thus, the calculations will require large computational resources. In addition, the MPS method employs the implicit method to solve the pressure which will take a super long time to solve the simultaneous linear equations. Therefore, the success of this project would greatly depend on the utilization of HPC resources. The application of the MPS code in real reactor to simulate the melt infiltration and melt spreading will be valuable and useful for predicting the reactor severe accidents.