In the current study, a modified fast converging, mass-conserving, and robust algorithm is proposed for calculation of the pressure distribution of a cavitated axially grooved journal bearing based on the finite volume discretization of the Adams/Elrod cavitation model. The solution of cavitation problem is shown to strongly depend on the specific values chosen for the lubricant bulk modulus. It is shown how the new proposed scheme is capable of handling the stiff discrete numerical system for any chosen value of the lubricant bulk modulus () and hence a significant improvement in the robustness is achieved compared to traditionally implemented schemes in the literature. Enhanced robustness is shown not to affect the accuracy of the obtained results, and the convergence speed is also shown to be considerably faster than the widely used techniques in the literature. Effects of bulk modulus, static load, and mesh size are studied on numerical stability of the system by means of eigenvalue analysis of the coefficient matrix of the discrete numerical system. It is shown that the impact of static load and mesh size is negligible on numerical stability compared to dominant significance of varying bulk modulus values. Common softening techniques of artificial bulk modulus reduction is found to be tolerable with maximum two order of magnitudes reduction of to avoid large errors of more than 3–40% in calculated results.