The equations of fluid motion and accompanying boundary conditions are difficult to formulate and solve. For most practical problems, the equations and accompanying boundary conditions must be numerically solved. The types of numerical methods used by the majority of researchers and applications oriented engineers to solve these partial differential equations fall into three categories: 1) finite difference (or finite volume) methods (FDM), 2) finite element methods (FEM), and 3) other approaches (boundary integrals, hybrids, analytical, spectral, etc.). The FDM has been used for a wide variety of problems; nearly all of the early numerical simulations dealing with heat transfer and fluid flow revolved around various solution strategies for the FDM.

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