The stimulated Brillouin scattering phase conjugated mirror (SBS-PCM) has garnered significant attention in the laser field due to its ability to compensate for both static and dynamic wavefront distortion in real time and enhance beam quality. However, there remain concerns regarding optical breakdown and degradation of output beam quality under high power pumping. Liquid gain medium is currently the most widely used SBS medium due to its characteristics of high gain, high damage threshold resistance and strong size expansion. However, with the increase of injection power, thermal convection caused by absorption of liquid medium will cause wavefront distortion in reflected Stokes light, resulting in reductions of beam quality.The finite element method was involved, and the 2-dimentional thermal convection at the focus section was solved by coupling the continuity equation, momentum equation, energy equation and the internal heat source equation. The boundary condition was adiabatic, and the numerical model of thermal convection in the medium cell under high power pump was developed. The dimensionless Se number is introduced to calculate the eddy flux to quantify the thermal convection intensity in the medium cell. The variation of the Se number with the interaction time is quantitatively analyzed, and the influence of the pump light repetition rate on the thermal convection intensity distribution is emphatically discussed. The results show that, starting from the pump light injection medium, the Se number firstly increases and then decreases, and finally tends to be stable. In addition, when the repetition rate increases from 10 Hz to 250 Hz,the maximum Se number increases from 10 to 49, and the stable Se number increases from 6 to 31, but the time taken for the Se number to reach the maximum value decreases from 9 s to 3 s. The time taken to reach the stable value is reduced from 37 s to 19 s (Fig.4). The contour of thermal convection velocity and density distribution and corresponding experimental observed spatial profiles at different repetition rates were shown (Fig.5-8). With the increase of repetition rate, the intensity of thermal convection increases, and the distribution of low-density areas in the medium cell expands, leading to the increase of the horizontal and vertical deformation of light spots. The relationship between pump light repetition rate and thermal convection in liquid medium is analyzed from liquid medium flow. The pump light repetition rate is an important factor affecting the thermal convection intensity, the thermal convection intensity is positively correlated to the repetition rate, and the time for the thermal convection intensity to reach the extreme value and the stable value is negatively correlated with the repetition frequency. With the increase of thermal convection intensity, the degree of spot migration increases gradually. This study provides a new perspective for perfecting the model of photothermal effect.