The main objective of the current work is to enhance consistency and capabilities of Moving Particle Semi-implicit (MPS) method for simulating a wide range of free-surface flows and convection heat transfer. For this purpose, two novel high-order gradient and Laplacian operators are derived from the Taylor series expansion and are applied for the discretization of governing equations. Furthermore, the combination of the explicit Third-order TVD Runge-Kutta scheme and two-step projection algorithm is employed to approximate transient terms in the Navier-stokes and energy equations. To further improve the accuracy and performance of the method, a new kernel function is constructed by a combination of the Gaussian and cosine functions and then implemented for modeling the 1D Sod shock tube problem. Validation and verification of the proposed model are conducted through the simulations of several canonical test cases such as: dam break, rotation of a square patch of fluid, two-phase Rayleigh-Taylor instability, oscillating concentric circular drop and good agreement are achieved. The proposed model is then employed to simulate three-phase Rayleigh-Taylor instability and entropy generation due to natural convection heat transfer (Differentially Heated Cavity and Rayleigh-Bénard convection). The obtained results reveal that, the newly constructed kernel function provides more reliable results in comparison with two frequently used kernel functions namely; quartic spline and Wendland. Furthermore, it is found that, the enhanced MPS model is capable of handling multiphase flow problems with low and high density contrast.

当前工作的主要目的是增强移动粒子半隐式（MPS）方法的一致性和功能，该方法可模拟各种自由表面流动和对流换热。为此，从泰勒级数展开式推导了两个新颖的高阶梯度算子和拉普拉斯算子，并将其用于控制​​方程的离散化。此外，将显式三阶TVD Runge-Kutta方案与两步投影算法相结合，以近似Navier-stokes和能量方程中的瞬态项。为了进一步提高该方法的准确性和性能，通过结合高斯函数和余弦函数构造新的核函数，然后实施该核函数以对一维Sod激波管问题进行建模。通过对几个规范测试案例的仿真，对提出的模型进行了验证和验证，例如：坝溃，流体正方形斑块的旋转，两相瑞利-泰勒不稳定性，同心圆振动性振荡和良好的一致性。然后，将所提出的模型用于模拟由于自然对流传热（差热腔和Rayleigh-Bénard对流）引起的三相Rayleigh-Taylor不稳定性和熵的产生。所得结果表明，与两个常用的内核函数相比，新构建的内核函数提供了更可靠的结果。四次样条和Wendland。此外，发现增强的MPS模型能够以低密度和高密度对比度处理多相流问题。