Numerical Methods

The Navier-Stokes equations are nonlinear, continuous partial differential equations. To obtain a practical solution, continuous equations are discretized in space and time, resulting in algebraic equations that are then solved using iterative methods. Of the three common methods, finite difference or finite element are generally limited to groundwater modeling or for simple geometries that allow for structured meshing. The finite volume method is most used for practical CFD work. Discretization results in a set of algebraic equations, which are solved iteratively using segregated and coupled solution methods. Simply put, a numerical scheme refers to the method the equations are set up to solve for the primitive variables within RANS equations. There are many types of numerical schemes; however, these schemes are used to treat the temporal differential or the spatial differential terms. Several considerations should be given when choosing the different numerical schemes. These considerations are stability, accuracy, convergence, and computational cost.