The LS-STAG method for simulating viscous incompressible flows combines the advantages of immersed boundary methods, the marker-and-cell method, and the level-set method. We developed and verified a general approach for applying the LS-STAG method to RANS (Reynolds-Averaged Navier–Stokes), LES (Large Eddy Simulation), and DES (Detached Eddy Simulation). A modified version of the LS-STAG method was implemented on GPUs, and the computational cost was evaluated for both CPU and GPU architectures. We outline a methodology for designing a profiling tool and identify the most computationally intensive components of the GPU implementation: the ILU preconditioner and ADLJ smoother. An approach for parallelizing these algorithms is presented.