[1] Gingold, R. A., & Monaghan, J. J. (1977). Smoothed particle hydrodynamics: theory and application to non-spherical stars. Monthly notices of the royal astronomical society, 181(3), 375-389.
[2] Koshizuka, S., & Oka, Y. (1996). Moving-particle semi-implicit method for fragmentation of incompressible fluid. Nuclear science and engineering, 123(3), 421-434.
[3] Ataie‐Ashtiani, B., & Shobeyri, G. (2008). Numerical simulation of landslide impulsive waves by incompressible smoothed particle hydrodynamics. International Journal for numerical methods in fluids, 56(2), 209-232.
[4] Shao, S. (2010). Incompressible SPH flow model for wave interactions with porous media. Coastal Engineering, 57(3), 304-316.
[5] Liu, X., Xu, H., Shao, S., & Lin, P. (2013). An improved incompressible SPH model for simulation of wave–structure interaction. Computers & Fluids, 71, 113-123.
[6] Liang, D., Jian, W., Shao, S., Chen, R., & Yang, K. (2017). Incompressible SPH simulation of solitary wave interaction with movable seawalls. Journal of Fluids and Structures, 69, 72-88.
[7] Ng, K. C., Ng, Y. L., Sheu, T. W. H., & Alexiadis, A. (2020). Assessment of Smoothed Particle Hydrodynamics (SPH) models for predicting wall heat transfer rate at complex boundary. Engineering Analysis with Boundary Elements, 111, 195-205..
[8] Zago, V., Bilotta, G., Hérault, A., Dalrymple, R. A., Fortuna, L., Cappello, A., ... & Del Negro, C. (2018). Semi-implicit 3D SPH on GPU for lava flows. Journal of Computational Physics, 375, 854-870.
[9] Wu, J., Zhang, G., Sun, Z., Yan, H., & Zhou, B. (2023). An improved MPS method for simulating multiphase flows characterized by high-density ratios and violent deformation of interface. Computer Methods in Applied Mechanics and Engineering, 412, 116103.
[10] Pan, X. J., Zhang, H. X., & Lu, Y. T. (2008). Numerical simulation of viscous liquid sloshing by moving-particle semi-implicit method. Journal of Marine Science and Application, 7(3), 184-189.
[11] Shibata, K., Koshizuka, S., Sakai, M., & Tanizawa, K. (2012). Lagrangian simulations of ship-wave interactions in rough seas. Ocean Engineering, 42, 13-25.
[12] Sun, Z., Chen, X., Xi, G., Liu, L., & Chen, X. (2017). Mass transfer mechanisms of rotary atomization: A numerical study using the moving particle semi-implicit method. International Journal of Heat and Mass Transfer, 105, 90-101.
[13] Liu, X., Xu, Y., Wang, K., Cheng, S., & Tong, L. (2024). Study on bubble dynamics in sodium using three-dimensional MPS method. Nuclear Engineering and Design, 416, 112810.
[14] Liu, M. B., & Liu, G. R. (2006). Restoring particle consistency in smoothed particle hydrodynamics. Applied numerical mathematics, 56(1), 19-36.
[15] Oger, G., Doring, M., Alessandrini, B., & Ferrant, P. (2007). An improved SPH method: Towards higher order convergence. Journal of Computational Physics, 225(2), 1472-1492.
[16] Schwaiger, H. F. (2008). An implicit corrected SPH formulation for thermal diffusion with linear free surface boundary conditions. International journal for numerical methods in engineering, 75(6), 647-671.
[17] Shao, J. R., Li, H. Q., Liu, G. R., & Liu, M. B. (2012). An improved SPH method for modeling liquid sloshing dynamics. Computers & Structures, 100, 18-26.
[18] Jiang, T., Ouyang, J., Ren, J. L., Yang, B. X., & Xu, X. Y. (2012). A mixed corrected symmetric SPH (MC-SSPH) method for computational dynamic problems. Computer Physics Communications, 183(1), 50-62.
[19] Ikari, H., Khayyer, A., & Gotoh, H. (2015). Corrected higher order Laplacian for enhancement of pressure calculation by projection-based particle methods with applications in ocean engineering. Journal of ocean engineering and marine energy, 1, 361-376.
[20] Huang, C., Lei, J. M., Liu, M. B., & Peng, X. Y. (2016). An improved KGF‐SPH with a novel discrete scheme of Laplacian operator for viscous incompressible fluid flows. International Journal for Numerical Methods in Fluids, 81(6), 377-396.
[21] Zhu, G. X., Zou, L., Chen, Z., Wang, A. M., & Liu, M. B. (2018). An improved SPH model for multiphase flows with large density ratios. International Journal for Numerical Methods in Fluids, 86(2), 167-184.
[22] Violeau, D., & Fonty, T. (2019). Calculating the smoothing error in SPH. Computers & Fluids, 191, 104240.
[23] Shobeyri, G. (2020). Accuracy analysis of different Laplacian models of incompressible SPH method improved by using Voronoi diagram. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 42(10), 527.
[24] Heydari, Z., Shobeyri, G., & Ghoreishi Najafabadi, S. H. (2020). Accuracy analysis of different higher-order Laplacian models of Incompressible SPH method. Engineering Computations, 37(1), 181-202.
[25] Garoosi, F., & Shakibaeinia, A. (2020). An improved high-order ISPH method for simulation of free-surface flows and convection heat transfer. Powder Technology, 376, 668-696.
[26] Rajapriyadharshini, J. R. (2022). An improved smoothed particle hydrodynamics approach using new inverse kernel function. Journal of Ocean Engineering and Science, 7(4), 327-336.
[27] Gao, T., Liang, T., & Fu, L. (2023). A new smoothed particle hydrodynamics method based on high-order moving-least-square targeted essentially non-oscillatory scheme for compressible flows. Journal of Computational Physics, 489, 112270.
[28] Antuono, M., Sun, P. N., Marrone, S., & Colagrossi, A. (2021). The δ-ALE-SPH model: An arbitrary Lagrangian-Eulerian framework for the δ-SPH model with particle shifting technique. Computers & Fluids, 216, 104806.
[29] Rastelli, P., Vacondio, R., & Marongiu, J. C. (2023). An arbitrarily Lagrangian–Eulerian SPH scheme with implicit iterative particle shifting procedure. Computer Methods in Applied Mechanics and Engineering, 414, 116159.
[30] Khayyer, A., & Gotoh, H. (2009). IMPROVED MPS METHODS FOR WAVE IMPACT CALCULATIONS. In Proceedings Of Coastal Dynamics 2009: Impacts of Human Activities on Dynamic Coastal Processes (With CD-ROM) (pp. 1-14).
[31] Khayyer, A., & Gotoh, H. (2010). A higher order Laplacian model for enhancement and stabilization of pressure calculation by the MPS method. Applied Ocean Research, 32(1), 124-131.
[32] Sun, Z., Djidjeli, K., & Xing, J. T. (2015). Modified MPS method for the 2D fluid structure interaction problem with free surface. Computers & Fluids, 122, 47-65.
[33] Wang, L., Jiang, Q., Nie, S., Zhang, J., & Iddy, I. (2018). Improvement on MPS method for simulation of dynamic pressure in dam break flows. Journal of Coastal Research, (85), 971-975.
[34] Shobeyri, G., & Madadi, H. (2018). An improvement in MPS method using Voronoi diagram and a new kernel function. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40, 1-10.
[35] Jandaghian, M., Krimi, A., Zarrati, A. R., & Shakibaeinia, A. (2021). Enhanced weakly-compressible MPS method for violent free-surface flows: Role of particle regularization techniques. Journal of Computational Physics, 434, 110202.
[36] Yamada, D., Imatani, T., Shibata, K., Maniwa, K., Obara, S., & Negishi, H. (2022). Application of improved multiresolution technique for the MPS method to fluid lubrication. Computational Particle Mechanics, 9(3), 421-441.
[37] Matsunaga, T., & Koshizuka, S. (2022). Stabilized LSMPS method for complex free-surface flow simulation. Computer Methods in Applied Mechanics and Engineering, 389, 114416.
[38] Jian, L., Yu, P., Pei, J., Zeng, X., & Yuan, Y. (2022). Development of an MPS Code for Corium Behavior Analysis: 3D Alloy Melting. Science and Technology of Nuclear Installations, 2022(1), 2140729.
[39] Shobeyri, G. (2023). Using a modified MPS gradient model to improve accuracy of SPH method for Poisson equations. Computational Particle Mechanics, 10(5), 1113-1126.
[40] Shobeyri, G. (2024). Improved MPS models for simulating free surface flows. Mathematics and Computers in Simulation, 218, 79-97.
[41] Shao, S., & Lo, E. Y. (2003). Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface. Advances in water resources, 26(7), 787-800.
[42] Xu, R., Stansby, P., & Laurence, D. (2009). Accuracy and stability in incompressible SPH (ISPH) based on the projection method and a new approach. Journal of computational Physics, 228(18), 6703-6725.
[43] Zhang, S., Morita, K., Fukuda, K., & Shirakawa, N. (2006). An improved MPS method for numerical simulations of convective heat transfer problems. International journal for numerical methods in fluids, 51(1), 31-47.
[44] Duan, G., Yamaji, A., Koshizuka, S., & Chen, B. (2019). The truncation and stabilization error in multiphase moving particle semi-implicit method based on corrective matrix: Which is dominant?. Computers & Fluids, 190, 254-273.
[45] Liu, G. R. (2002). Meshfree methods: moving beyond the finite element method. CRC press.
[46] Faraji, S., Afshar, M. H., & Amani, J. (2014). Mixed discrete least square meshless method for solution of quadratic partial differential equations. Scientia Iranica, 21(3), 492-504.
[47] Eini, N., Afshar, M. H., Faraji Gargari, S., Shobeyri, G., & Afshar, A. (2020). A fully Lagrangian mixed discrete least squares meshfree method for simulating the free surface flow problems. Engineering with Computers, 1-21.
[48] Gargari, S. F., Kolahdoozan, M., Afshar, M. H., & Dabiri, S. (2019). An Eulerian–Lagrangian mixed discrete least squares meshfree method for incompressible multiphase flow problems. Applied Mathematical Modelling, 76, 193-224.
[49] Gargari, S. F., Huang, Z., & Dabiri, S. (2024). An upwind moving least squares approximation to solve convection-dominated problems: An application in mixed discrete least squares meshfree method. Journal of Computational Physics, 506, 112931.
[50] Frachon, T., Nilsson, E., & Zahedi, S. (2024). Stabilized Lagrange Multipliers for Dirichlet Boundary Conditions in Divergence Preserving Unfitted Methods. arXiv preprint arXiv:2408.10089.
[51] Afshar, M. H., Lashckarbolok, M., & Shobeyri, G. (2009). Collocated discrete least squares meshless (CDLSM) method for the solution of transient and steady‐state hyperbolic problems. International journal for numerical methods in fluids, 60(10), 1055-1078.
[52] Wang, X., Ouyang, J., & Feng, Z. (2013). Local Kronecker delta property of the MLS approximation and feasibility of directly imposing the essential boundary conditions for the EFG method. Engineering Analysis with Boundary Elements, 37(7-8), 1021-1042.
[53] Li, X., & Wang, Q. (2016). Analysis of the inherent instability of the interpolating moving least squares method when using improper polynomial bases. Engineering Analysis with Boundary Elements, 73, 21-34.
[54] Dehghan, M., & Abbaszadeh, M. (2018). Interpolating stabilized moving least squares (MLS) approximation for 2D elliptic interface problems. Computer Methods in Applied Mechanics and Engineering, 328, 775-803.