Density-based and pressure-based approaches in solving the Navier-Stokes equations for computational field simulations for compressible and incompressible flows have been presented. For the density-based flow solver, a generalized grid based framework has been developed and employed to simulate the complex-geometry problems with ease. The integral form of the standard and artificial compressibility form of Navier-Stokes equations has been taken as the governing form for the density-based method. For the pressure-based flow solver, the differential form of the conservation equations in the curvilinear coordinates was solved with a non-staggered structure-grid topology. A predictor plus multi-corrector algorithm (which can handle the flow with a wide range of Mach numbers without using the artificial compressibility and the preconditioning method) is utilized in the pressure-based method. Also, the capability has been developed to model the gas-particle (liquid and/or solid) multi-phase flows in the Eulerian-LaGrangian particle-tracking framework. Though the strengths and weaknesses of these two methods have been well documented, there is yet an extensive study to compare these two methods in terms of their numerical accuracies, computational efficiencies, and limitations. In this paper, these two models are validated separately, and the results are presented. Comparisons of these two methods with various benchmark test cases will be assessed and addressed in the future. © 2005 IMACS. Published by Elsevier B.V. All rights reserved.