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The system of the Navier-Stokes equations represents nature and can solve a wide class of fluid flow problems when coupled with the appropriate boundary conditions. Unfortunately, the system of the Navier-Stokes equations is highly complex; therefore, finding an analytical solution to the system is proving problematic. Then, the only way to obtain reasonable, complete information on fluid flows lies in computational fluid dynamics (CFD). This book presents a simple, robust, and innovative CFD solver for the system of the Navier-Stokes equations. The new algorithm is based on extensive physics consideration and is capable of solving complex fluid dynamics problems. The book covers the detailed steps of the new scheme development and solution methodology for the complete three-dimensional form of the system of the Navier-Stokes equations. The versatility of the new solver was proven by obtaining solution to different types of flow problems, such as the lid driven cavity problem, the shock/boundary interaction problem, and the shock train problem. The book is especially useful for the professional of the CFD field, or any student who wants to learn the art of CFD.