Simulating density current; using Collocation Discrete Least Squares Meshless method

Recently, meshless methods have been widely used in numerical researches. One of these methods is the Collocation Discrete Least Squares Meshless (CDLSM) method, including nodal points and collocation points. Nodal points estimate shape functions, and collocation points discretize the equations. The CDLSM method is used for numerical modeling of density current in this article. Radial Point Interpolation Method (RPIM) is used to calculate Shape functions. The governing equations are solved by the semi incremental fractional step method, and the k-w turbulence model is used to introduce the turbulence. The present study results are compared with Garcia and Akiyama's experimental data. Mean Square Error (MSE), Root Mean Square Error (RMSE), and Mean Absolute Error (MAE) indexes were used as the determination criteria for validating the mathematical model. In all cases, the maximum amount of MSE and MAE are 0.00076 and 0.077, respectively. Hence a good agreement between the numerical study and previous references is obtained.

Automated summary

This article introduces the application of meshless methods in numerical research, with a focus on the Collocation Discrete Least Squares Meshless (CDLSM) method and its use in numerical modeling of density current.