This work performs systematic studies for code verification for turbulence modeling in our research CFD code SENSEI. Turbulence modeling verification cases including cross term sinusoidal manufactured solutions and a few exact solutions are used to justify the proper Spalart-Allmaras and Menter's SST turbulence modeling implementation of the SENSEI CFD code. The observed order of accuracy matches fairly well with the formal order for both the 2D/3D steady-state and 2D unsteady flows when using the cross term sinusoidal manufactured solutions. This work concludes that it is important to keep the spatial discretization error in a similar order of magnitude as the temporal error in order to avoid erroneous analysis when performing combined spatial and temporal order analysis. Since explicit time marching scheme typically requires smaller time step size compared to implicit time marching schemes due to stability constraints, multiple implicit schemes such as the Singly-Diagonally Implicit Runge-Kutta multi-stage scheme and three point backward scheme are used in our work to mitigate the stability constraints.