Abstract
Several improved discretization models used in moving particle semi-implicit (MPS) method are briefly described here. Classical MPS is always criticized by its poor pressure calculation. Several improved pressure Poisson equations developed in early years are introduced here. Then researchers found that particle interaction models affected pressure calculation significantly, and several improved models based on corrective matrix are developed. Then least square MPS is developed to obtain a more accurate particle interaction model. However, corrective matrix and least square reconstruction breaks the conservation property of the scheme. Pairwise-relaxing MPS method can achieve both high-order accuracy and conservation properties. Improvements also include couple mesh-based methods such as finite volume method and MPS to take advantage of the two methods.
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