Finite analytic method and its applications: A review

This paper describes the development of the finite analytic (FA) method and several engineering applications. In the finite analytic method, the governing differential equations are discretized into algebraic equations based on an analytic solution on the small computational element. Nine-point and five-point FA discretization schemes for two-dimensional Navier-Stokes equations are described for simple and complex boundaries. A 19-point FA discretization scheme for three-dimensional Navier-Stokes equations is also presented. The finite analytic method exhibits the properties of stability, convergence and grid independence. It is also shown that the FA method can be successfully used in problems with irregular domains. Evidence of the versatility of the FA method is demonstrated in successful modeling of two-dimensional turbulent sea breeze and three-dimensional channel flow with conjugate heat transfer.