Objective  China’s mountains account for more than 2/3 of the country’s land area, and the combination of large topographic elevation differences and numerous landform types endows the generation and development process of topography, water bodies and creatures with significant fluid characteristics. The early development of mountainous cities was constrained by topography, and the mountainous cities then were mostly built on mountains and by water; with the improvement of human construction capacity, the topography endowed by nature can be changed by human transformation behaviors, making mountainous cities gradually integrate into nature and natural elements intersected and fused with urban space, presenting the phenomenon of seepage. Mountainous cities present a unique urban landscape because of their special geographical environment, and the renewal exploration of mountainous cities based on the green urban design method under the background of stock renewal has theoretical significance and practical value for realizing the synergistic symbiosis between cities and nature.

Methods  This research focuses on the dynamic characteristics of natural elements in mountainous cities under complex topographic conditions, introduces the theory of seepage mechanics, analyzes the intrinsic mechanism and changing law of the interaction between natural elements and urban space, digitally identifies and analyzes the characteristics of natural elements relying on multi-source data such as remotely sensed data and urban architectural data. Specifically, the research identifies the three types of flow elements of topography, water body and creature and, based on relevant seepage indicators such as permeability and wettability, analyzes such flow elements including their intrinsic correlation and influence mechanism. Following the law of seepage in mountainous cities, the research proposes “vein darning” as a green urban design path, based on which the research formulates effective measures to promote the realization of perfect seepage of natural flow in mountainous cities, puts forward darning means of ground veins, water veins and green veins, and validates the feasibility of the path with the example of Wanzhou, Chongqing, which is the most famous mountainous city in China. This research provides new perspectives for analyzing the inner mechanism and changing law in the development of mountainous cities, and is of great significance for enhancing the scientific and objective nature of green city design paths.

Results  Taking Wanzhou District of Chongqing as an example, the research, through identifying and analyzing the three types of elements of topographic flow, water body flow and biological flow, finds that the permeability of the central urban area of Wanzhou is low, with the pore space gradually narrowed from the area along the mountain to the waterfront area, and the waterfront interface being highly dense, adhesive and viscous, which blocks the permeation connection between the mountain and the water body. At the same time, the vegetation coverage in waterfront green spaces varies greatly, and the waterfront ecological revetment is fragmented, making the wetting area of part of the river section quite small, thus further affecting the urban seepage. By controlling the height and density of the waterfront building interface, the natural porosity is guaranteed, and the connection between the mountain and the water system is enhanced; for the wedged seepage in the large mountain green space outside the city, the spatial layout is carried out with the current mountain as the core to guarantee the degree of ground vein connection and enhance the urban permeability; combined with the evaluation and analysis of the seepage property of the water body flow, the water body flow is divided into the water vein protection area, water vein restoration area and water vein remediation area for segmented optimization. The corridor flow is improved by adding ecological springboards, expanding the space porosity and improving the permeability. For the urban space with low vegetation coverage, the viscosity is improved by enriching the type and level of vegetation to provide effective space for biological seepage in order to improve the continuity of biological flow.

Conclusion  Based on the seepage characteristics of mountainous cities, this research proposes the green urban design method of vein waving. Starting from the dynamic process of mountainous city and natural development, the research adopts remote sensing data and digital technology to digitally identify and analyze the three types of urban flow elements, namely topography, water body and biology, puts forward the design method of vein darning, and formulates corresponding strategies and methods to enhance the darning of land, water and green veins. Based on the seepage characteristics and seepage influence mechanism of mountainous urban space, the research proposes the “vein darning” design method, and formulates corresponding strategies and methods for the darning enhancement of land, water and green veins; furthermore, taking Wanzhou, Chongqing (a typical mountainous city in China) as an example, the research realizes the methodological practice of green urban design in the object of mountainous city. The research aims to provide a dynamics-based research perspective for the green urban design methodology for the renewal of mountainous cities, so as to maximize the revelation and embodiment of the dynamic characteristics and interaction mechanisms of the elements of mountainous cities, and provide new ideas for the sustainable construction of mountainous cities. However, this research is still problematic such as only involving a single case. In view of this, subsequent researches are supposed to combine more mountainous cities such as Yibin, Qingdao and Hong Kong to summarize their respective models and identify and optimize the seepage characteristics of mountainous cities under different models.