The implementation flow of processing incompressible Navier-Stokes equations based on velocity-correction schemes is introduced, and velocity-correction schemes based on Picard iteration is developed by introducing Picard linearization to process the convection term in the velocity governing equation. Compared with the traditional method, the projection method after Picard linearization can be solved with a larger time step, which improves the stability of the solution method, and the convergence accuracy meets the requirements, which confirms the reliability of the solution method.

By employing first-principles based on density functional theory, combined with the Debye model and lattice dynamics theory, the themodynamic properties and state equation of TKX-50 under high temperture and pressure are calculated. It is shown that, the calculated lattice constants of TKX-50 agree well with the available experimental and other theoretical data. And then we calculate the lattice structure and relate thermodynamic properties under different temperature and pressure. The results show that the lattice of TKX-50 is the most difficult to compress along the a-axis; the thermal capacity is influenced by temperature and pressure strongly; the Debye temperature, Gruneison constant, and the thermal expansion coefficient changes rapidly with temperature. The results of this paper not only reveal how the thermodynamic properties of TKX-50 change with temperature and pressure, a guide to predict and explain its temperature pressure performance, but also provide necessary theoretical support, for the engineering application and risk assessment of TKX-50.