City Research Online

A CNN-supported Lagrangian ISPH model for free surface flow

Zhang, N., Yan, S. ORCID: 0000-0001-8968-6616, Ma, Q. ORCID: 0000-0001-5579-6454 , Guo, X., Xie, Z. & Zheng, X. (2023). A CNN-supported Lagrangian ISPH model for free surface flow. Applied Ocean Research, 136, article number 103587. doi: 10.1016/j.apor.2023.103587


As a popular method for modeling violent free surface flow, the incompressible Smoothed Particle Hydrodynamics (ISPH) based on the Lagrangian formulation has attracted a great attention worldwide. The Lagrangian ISPH solves the unsteady Navier-Stokes and continuity equations using the projection method, in which the pressure is obtained by solving the pressure Poisson's equation (PPE) that is the most time-consuming part in the ISPH procedure. In this paper, the Convolutional Neural Network (CNN) is combined with ISPH and used to predict the fluid pressure instead of solving the PPE directly. Although limited attempts of using CNN for solving the PPE in Eulerian formulation (referred to as the Eulerian CNN framework) in mesh-based methods are found in the public domain, the present model is the first ISPH model supported by CNN in a Lagrangian formulation. The proposed model overcome several challenges associated with combining CNN with ISPH, including selecting the input parameters, formulating the objective functions, producing the training dataset and dealing with boundary conditions. Two classic free surface problems, i.e. the dam breaking and the wave propagation, are simulated to evaluate the performance of the present model. Quantitative assessments of the numerical error in terms of both the free surface profile and the pressure field are carried out. The assessments show that the new model does not only give results with satisfactory accuracy, but also requires much less computation time for estimating pressure if the number of particles is large, e.g., 100 thousands particles that is usually required in the practical ISPH simulation for free surface flow.

Publication Type: Article
Additional Information: © 2023. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Publisher Keywords: Lagrangian ISPH, PPE, Machine learning, CNN, Free surface flow
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
T Technology > TA Engineering (General). Civil engineering (General)
T Technology > TC Hydraulic engineering. Ocean engineering
Departments: School of Science & Technology > Engineering
SWORD Depositor:
[thumbnail of ISPH-ML revision by Ma final.pdf]
Text - Accepted Version
Available under License Creative Commons Attribution Non-commercial No Derivatives.

Download (1MB) | Preview


Add to AnyAdd to TwitterAdd to FacebookAdd to LinkedinAdd to PinterestAdd to Email


Downloads per month over past year

View more statistics

Actions (login required)

Admin Login Admin Login