Using Mesh-free Natural Element Numerical Method in Solving Governing Equations of Free Surface Flow

The present research indicates the ability of mesh-free natural element numerical method in simulation of free-surface flow and consistency of extended second order method of Van-Leer scheme on solving natural element method. The natural element method is based on natural neighbor interpolation. In this study، Sibson interpolation has been used. Nodal integration has been used due to inappropriateness of Gaussian point''s integration. The present method has been validated by two-dimensional heat transfer problem for the diffusion term validation and by one-dimensional dam break problem for the convective term evaluation. Simulation of free-surface flow has been analyzed on non-uniform bed in the channel with a bump. The results obtained are compared with analytical results. In addition، water flow inside the Parshall flume is simulated and results were compared with experimental interpretations. Results of modeling and analytical solutions via normalized root mean square error (NRMSE) for temperature problems، dam break and free-surface flow show NRMSE of less than 2% while 18% for Parshall flume test. In addition، the determination coefficient of numerical model for the first three tests are higher than 0. 99 and 0. 90 for the Parshall flume which suggests high capability of numerical model in simulation of free-surface flow.