# Spatial Evolution Analysis of Tailings Flow from Tailings Dam Failure Based on MacCormack-TVD  
[PERSON]  
1 State Key Laboratory of Geomechanics and Geotechnical Engineering Safety, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China; [EMAIL_ADDRESS] (C.Z. ); [EMAIL_ADDRESS] (C.M. ); [EMAIL_ADDRESS] (C.L.) 12 University of Chinese Academy of Sciences, Beijing 100049, China 2  
[PERSON]  
1 State Key Laboratory of Geomechanics and Geotechnical Engineering Safety, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China; [EMAIL_ADDRESS] (C.Z. ); [EMAIL_ADDRESS] (C.M. ); [EMAIL_ADDRESS] (C.L.) 13 Key Laboratory of Slope Safety Risk Warning and Disaster Prevention and Mitigation, Ministry of Emergency Management, Wuhan 430071, China 3  
[PERSON]  
1 State Key Laboratory of Geomechanics and Geotechnical Engineering Safety, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China; [EMAIL_ADDRESS] (C.Z. ); [EMAIL_ADDRESS] (C.M. ); [EMAIL_ADDRESS] (C.L.) 12 University of Chinese Academy of Sciences, Beijing 100049, China 2  
[PERSON]  
1 State Key Laboratory of Geomechanics and Geotechnical Engineering Safety, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China; [EMAIL_ADDRESS] (C.Z. ); [EMAIL_ADDRESS] (C.M. ); [EMAIL_ADDRESS] (C.L.) 12 University of Chinese Academy of Sciences, Beijing 100049, China 2  
Footnote 1: email: {L.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,  
following a tailings dam failure are crucial steps in assessing the severity of dam failure incidents. These measures can significantly mitigate the economic losses in the hazardous areas surrounding the mine. Scholars both domestically and internationally have adopted various numerical methods to address the spatial evolution process of tailing sand flow in tailing dams [5; 6; 7; 8]. These commonly used computational methods can be categorized into three main types: the empirical formula method, the discrete element method (DEM), and the finite element method (FEM). The empirical formula method allows for the easy and quick establishment of the evolution model of dam failure disasters and facilitates the prediction of the inundation depth of disaster fluid. Despite its efficiency and simplicity in model creation, this method has higher demands for experimental or field data, and it lacks a dynamic analysis of the tailing sand flow evolution process [9]. DEM has proven to be highly effective in accurately reproducing particle trajectories, making it particularly suitable for microscopic-scale simulations. However, when applied to the simulation of hazardous fluids, DEM necessitates the use of a substantial number of microscopic particles. Furthermore, the method requires the input of challenging-to-identify micro-mechanical parameters. These requirements can result in significantly prolonged computation times and potentially inaccurate results [10]. FEM aims to model fluid motion by utilizing the incompressible Navier-Stokes equations. To enhance the computational efficiency, these equations are often simplified through various numerical methods, reducing them to two-dimensional (2D) shallow water equations via depth-integrated Navier-Stokes equations [11; 12; 13]. However, the accuracy of such equations is considerably reduced in simulations with wider ranges and longer timescales. Researchers have explored the MacCormack finite difference scheme with decreasing total variation deviation (TVD) and have demonstrated its feasibility and stability for a broader range of mountain hazard simulations over extended periods. This investigation reveals the potential of the MacCormack-TVD method as a reliable computational solution for the long-term predictive modeling in geophysical hazard analysis [14; 15; 16]. [PERSON] et al. proposed a Massflow code utilizing the variable computational domain MacCormack-TVD format [14].