## Highlights:
[PERSON] [35] has developed the HORSMIC model to simulate the shape of the middle section of a horizontal cavern. Both the limits are that the flow area in the cavity is divided in advance and needs to be adjusted manually. [PERSON] [28] conducted physical simulations of TWH salt cavern construction using a high-strength steel mold to shape large rock salt specimens, making the construction process visible and easily observable. The influences of the injection rate, the transferring of the injection well, the oil blanket, and the injection position on cavern development were discussed. [PERSON] [36] performed a physical simulation experiment to investigate the characteristics of horizontal leaching, focusing on how the leaching parameters, like the leaching rate, the brine discharge position, and the back-step length, affect the cavern shape and the brine discharge concentration. This experiment is based on similar principles and uses small salt bricks for the cavity construction experiments. [PERSON] [37] simulated the TWH salt cavern construction process using the TWHSMC code program based on a Navier-Stokes equation to model a U-shaped cavern from a U-shaped borehole. While this model accounts for the fluid flow influences, it overlooks the effects of turbulent flow and heat transfer. Its application to multi-step modeling is limited due to the fixed direction of boundary movements. [PERSON] [38] established an M-SHSCLS model using a time difference method and a finite volume method based on the balance principle, simulated the cavity shape of a salt cavern in multi-step horizontal construction, and optimized the cavity shape. However, the brine concentration is simplified, and the influence of flow field on brine distribution and the dissolution rate was ignored. The previously formed cavity did not expand at the next leaching stage. [PERSON] [32] established a TWHMPC model based on multiple coupled equations of dissolution, transport, and fluid flow to simulate a horizontal salt cavern. This model found the influence of turbulence to be not negligible at the initial stage of solution mining, without considering the influence of heat transfer. This model only simulated the first stage of the cavity leaching process and did not involve multi-step cavity construction. At present, no one has considered the impact of temperature on dissolution and expansion for construction simulations of salt caverns, including vertical caverns, TWH caverns, and horizontal caverns. However, the construction of a multi-step horizontal salt cavern is a complicated process of fluid dynamics, chemical dynamics, and thermodynamics [39; 40]. Heat transfer will affect the fluid flow and brine concentration distribution in the cavity, and also affect the expansion rate of the cavern boundary. The depth of a salt cavern built in a salt rock formation is about 1500-2500 m, and the cavern temperature is about 70-90 \({}^{\circ}\)C. The temperature of injection freshwater is about 20 \({}^{\circ}\)C. Therefore, there is a large temperature difference between the injected fluid and the brine in the cavity, so there is a  
Figure 2: Schematic diagram of a multi-step horizontal salt cavern. thermal convection phenomenon between the forced convection fluid, as shown in Figure 3. The dissolution rate increases with the increase in temperature. The dissolution rate at 80 \({}^{\circ}\)C is 2-3 times larger than that at 20 \({}^{\circ}\)C [41; 42; 43]. In addition, there are few studies on multi-step horizontal cavern construction, and there is currently no criterion for the design of multi-step horizontal caverns. In this study, two critical elements of heat transfer and turbulent flow are considered in developing a 3D multi-physics coupled flow model to simultaneously quantify salt rock dissolution, cavity expansion, heat transfer, brine convection, turbulence flow, and diffusion effects during the construction of multi-step horizontal salt caverns.