The simulation data are used to produce the figures in the following two manuscripts: “Ocean Circulation on Tide-locked Lava Worlds, Part I: An Idealized 2D Numerical Model” and “Ocean Circulation on Tide-locked Lava Worlds, Part II: Scalings”. All files are nc files created by Matlab scripts. For the codes in detail, please refer to https://github.com/YanhongLai/Two-dimensional-model-for-magma-ocean-on-lava-worlds.git . In each RAR file, several nc files are contained, including the snapshot results (named as Snapshot*.nc) and time series results (named as twod*.nc) of the simulation. The model setup of each simulation is described in detail below. Simulation data used in the manuscript of Part I: An Idealized 2D Numerical Model 1) “PartI-thermal-forcing-Az1E1.rar”: simulation data for the simulation under thermal forcing only, including potential temperature, density, zonal velocity, vertical velocity, pressure, sea surface height, and so on. The baseline values of oceanic and planetary parameters used in this simulation can be found in Table 1 in the manuscript. Figures 1(c & d), 4, 5(a), 7(a & d), and A1(a-c) in the manuscript are generated by these data. 2) “PartI-wind-forcing-Az1E2.rar”: simulation data for the simulation under both thermal and wind forcings. Figures 5(b), 6, 7(b & e), and A1(d-f) in the manuscript are generated by these data. Simulation data used in the manuscript of Part II: Scalings 1) Simulation data under varying vertical viscosities (Az), and the baseline values used in the simulations are summarized in Table 1 of the manuscript. Only thermal forcing is imposed. “PartII-thermal-forcing-Az1E0.rar”: Az = 1e0 m2s-1 “PartII-thermal-forcing-Az1E2.rar”: Az = 1e2 m2s-1 2) Simulation data under varying vertical diffusivities (kz). Only thermal forcing is imposed. “PartII-thermal-forcing-kz1E-5.rar”: kz = 1e-5 m2s-1 “PartII-thermal-forcing-kz1E-6.rar”: kz = 1e-6 m2s-1 3) Simulation data under varying substellar temperatures (Tsub). Only thermal forcing is imposed. “PartII-thermal-forcing-Tsub2500K.rar”: Tsub = 2500 K “PartII-thermal-forcing-Tsub2750K.rar”: Tsub = 2750 K “PartII-thermal-forcing-Tsub3250K.rar”: Tsub = 3250 K 4) Simulation data under varying wind stresses (taux). Both thermal and wind forcings are imposed. “PartII-wind-forcing-over3-Az1E1.rar”: taux = taux0/3, taux0 = 100 Nm-2 is the wind stress amplitude of the control simulation. “PartII-wind-forcing-over5-Az1E1.rar”: taux = taux0/5 “PartII-wind-forcing-over10-Az1E1.rar”: taux = taux0/10 All simulation data in Part II are used to create the scatter points in Figures 3 & 4 in the manuscript.