热喀斯特湖是其周边多年冻土重要的热源,也是排向大气的温室气体的重要源泉,对湖下及周边多年冻土中发生的物理、化学、生物、地貌和水文过程能产生重要的作用,严重影响冻土区环境和建筑物的稳定性.数值模拟为量化分析热喀斯特湖及其演化对周边多年冻土热状况长期影响的效果提供了有效的方法,极大地深化了人们对热喀斯特湖作用的认识,总结热喀斯特湖对多年冻土热状况数值模拟研究的进展对运用和改进现有数学模型以及开发更加有效的模型具有重要的指导作用.综述了最近10多年开发的描述热喀斯特湖对多年冻土热状况影响的相变热传导模型、热融滑塌模型、湖塘-冻土耦合模型、组合热量传递与质量传输过程的湖扩张模型、温度场与水分场耦合运移模型,以及基于移动网格方法的热喀斯特湖动态演化模型等主要数学模型的构成、功能、优点和不足,提出了未来数值模拟研究中值得重视的问题,包括建立更有效的模型,确定更符合实际的初始条件,深入研究土壤的热和物理参数,充分考虑湖水补给的作用,进一步研究热喀斯特湖周边冻土层上水的热效果,建立耦合相变热传导与对流传热过程的控制方程,在模型中嵌入气候变暖的效应,研究热喀斯特湖干涸对多年冻土区环境变化的长期影响,量化分析多个热喀斯特湖对冻土共同作用的效果,模拟热喀斯特湖邻近湖岸浅水区下面融区发展的过程与特点,并继续做好系统全面的现场观测等.“,”Thermokarst lakes are a major heat source for the adjacent permafrost and a significant source of atmospheric methane.These lakes have important impacts on the physical,chemical,biological,geomorphological and hydrological processes occurring in the ground under and around thermokarst lakes,and seriously affect the local environment and the stability of the structures constructed in permafrost regions.Numerical simulation methods provide an effective method for quantitative analysis of the long-term impact of thermokarst lakes and their evolution on permafrost surrounding the lakes,and have deepened our knowledge about the impact of thermokarst lakes immensely.Summarizing the research progresses in numerical simulation of long-term impact of thermokarst lakes on thermal regime of surrounding permafrost has an important guiding function to improve mathematical models and develop more effective models.In this study,the components,functions,advantages and defects of several typical mathematical models having developed over the past ten years or so were reviewed,such as the heat conduction model with phase change,thaw slumping model,the coupled lake-permafrost model,thaw lake expansion model combining thermal processes with mass wasting and thaw-driven subsidence,the coupled heat conduction and moisture migration model,and the moving mesh method based thermokarst lake dynamic evolution model.Several issues deserving to be paid further attention in the future researches were proposed,including creating more effective models,determining the more realistic initial condition,lucubrating thermal and physical parameters of the typical soils,consider the impact of lake water replenishment,quantitative analysis of the thermal effect of supra-permafrost water flow around the thermokarst lakes,creating the coupled governing equation of heat conduction with phase change and convective heat transfer,embed ding the effect of climate warming in the model,numerical investigation of the long-term influence of thermokarst lake drainage on the environment change in permafrost regions,analyzing the long-term joint impact of multiple lakes on adjacent permafrost,simulating the near-shore talik development process and feature beneath shallow water in expanding thermokarst lakes,and continuing to do the systemic and comprehensive field measurements.