SIMPLE, SIMPLER, SIMPLEC and IDEAL are solution procedures originally developed for incompressible flows and staggered grids. For SIMPLE, SIMPLER and SIMPLEC, extensions for collocated grids and for treatment of flows at all speeds have already been proposed. For IDEAL, only an extension for collocated grids has been found, and an extension for treatment of flows at all speeds is proposed here. Extended versions of SIMPLE and SIMPLER are implemented in Brilliant, a multiphysics CFD-program developed by Petrell AS. These implemented algorithms are compared to the existing solution procedure in Brilliant, an extended version of the SIMPLEC algorithm. As expected, SIMPLE and SIMPLEC gave almost identical solutions for all the three presented test cases. The values given by the SIMPLER algorithm differed slightly from the values given by the two other algorithms. When simulating a shock tube, all three algorithms showed large deviations from the quasi-analytical solution in some regions of the shock tube. The SIMPLER algorithm spent the least CPU time for this simulation example, while SIMPLE and SIMPLEC spent less CPU time than SIMPLER when simulating methane flow in a pipe. Even though the CPU time was not registered for the last simulation example, a pressure relief pipe, it was noticed that the time consumption was much greater for the SIMPLER algorithm than for SIMPLE and SIMPLEC.