The article deals with the possibilities of using local meshless methods for modeling the movement of avalanches and rapid slopes movements. These are dangerous phenomena that can cause extensive damage to the infrastructure of mountainous areas and numerical models are therefore an important tool in their prediction. Today, meshless methods are increasingly developed in many different areas for their potential advantages over conventional numerical methods. For the development of the model of debris flow, the article used the local method of weighted squares, as it proved suitable for addressing this type of differential equations. To verify the possibilities of this method, in the article, we focused on the models of dry granular soil movement and compared the results of the solution to several known cases.

本文探讨了使用局部无网格方法对雪崩运动和快速坡度运动进行建模的可能性。这些危险现象会严重破坏山区的基础设施，因此数值模型是预测的重要工具。如今，无网格方法因其比常规数值方法潜在的优势而在许多不同领域得到了越来越多的发展。为了开发泥石流模型，本文使用了加权平方的局部方法，因为它被证明适合解决这类微分方程。为了验证这种方法的可能性，在本文中，我们重点研究了干燥的颗粒状土壤运动模型，并将该解决方案的结果与几种已知案例进行了比较。