The development of computational fluid dynamics (CFD) can be traced back as far as the early 1900’s. The pioneering efforts by Richardson [1], Courant, Friedrichs, and Lewy [2], Southwell [3], Von Neumann [4], Lax [5], as well as Godunov [6] address the fundamental issues in numerical analyses for CFD. It is immediately clear that a major portion of these efforts was focused on one of the most difficult problems in resolving the discontinuous fluid phenomena in a discretized space — the Riemann problem [7]. As it will be seen later, it remains the most studied problem in CFD. However, if one is interested in the viscous flow simulation, Thom [8] probably obtained the first-ever numerical solution by solving the partial differential equation for a low speed flow past a circular cylinder. For a scholarly description of the CFD historical perspective, the books by Roach [9] and Tannehill, Anderson, and Pletcher [10] are highly recommended.

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