To address the problems of small cavity volume and long construction period in single vertical well solution mining, and to meet the engineering demand for natural gas peak shaving and supply stability, the cavity expansion law and flow field evolution mechanism of double vertical well solution mining were investigated. The aim was to solve the key technical problems of mesh interweaving and computational divergence encountered when traditional deformed mesh technology is used to simulate the dissolution and connection process of double wells. Based on the multi-field coupling theory of fluid flow, solute transport, and solid-liquid phase transition, an interface tracking method for double vertical well solution mining was proposed. The single-domain method was adopted to couple the Stokes-Brinkman equation describing fluid flow with the dilute species transport equation in porous media, and a solid-liquid interface tracking model for double vertical wells in salt cavern gas storage was established. Mesh independence verification was carried out to determine the optimal mesh scheme, and the reliability of the model was verified using field operation parameters from the Jintan Salt Cavern Gas Storage. Numerical simulations were then performed to analyze the spatial distribution characteristics of the flow field, concentration field, and cavity expansion during double vertical well solution mining, and the influence of water injection displacement on cavity construction efficiency, expansion uniformity, and cavity volume was further investigated. The results show that the flow field of double vertical well solution mining can be divided into three functional zones: the jet zone, convection zone, and seepage zone, with significant differences in driving mechanism,velocity distribution, and concentration diffusion characteristics. Before the two cavities are dissolved and connected, each cavity independently follows a relatively stable jet-convection flow structure. After connection, radial convection occurs at the junction of the two cavities, leading to kinetic energy attenuation and weakening of the overall flow field structure. In addition, a small water injection displacement in the slot construction stage is beneficial for maintaining cavity stability and avoiding local collapse, while a water injection displacement of 70–90 m³/h in the formal solution mining stage can effectively balance cavity construction rate and cavity volume, thereby promoting efficient and relatively uniform cavity expansion. By combining phase change theory with piecewise functions, the topological change of the solid-liquid interface during the double well dissolution process was characterized, and the simulation of the cavity connection process was realized. The proposed method effectively overcomes the computational difficulties of traditional algorithms and provides theoretical support for optimizing the process parameters of double vertical well solution mining in salt cavern gas storage.