Abstract
The hybrid finite-analytic (HFA) method for discretization of a three-dimensional advection-diffusion equation is developed using the superposition of the HFA solutions of locally linearized one-dimensional advection-diffusion equations. An example calculation of a system of three-dimensional nonlinear equations is conducted to test the convergence and accuracy of the 7-point numerical scheme. Good agreements between calculated and analytical solutions are obtained. An algorithm based on the HFA method with multigrid technique and Gauss-Seidel iteration is also developed to solve the three-dimensional Navier-Stokes equations in a staggered grid system. The stability and efficiency of the method are demonstrated by performing calculations of the fluid flow in a three-dimensional cubic cavity with a moving top wall. The proposed procedure is observed to exhibit good rates of smoothing and almost grid-independent convergence rates in comparison with a single-grid iteration method. The results are in excellent agreement with other published computational results.
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