Abstract:
Numerical solutions to partial differential equations form the backbone of mathematical models that simulate gas flow, which in the present case is assumed to be airflow around an arbitrary atmospheric body. Significance of simulating airflow in three dimensions reveals itself with the developing aviation industry and increasing needs for obtaining accurate results during the design process of atmospheric vehicles. A three dimensional approach is deemed necessary for accuracy reasons and the opportunity to compare results with that of 2-D flow assumptions. As the number of nodes in the computational domain increases by a factor of the number of nodes in one dimension, excessive computational work is expected. As such, performance of the numerical solution algorithm gains importance more than anything in the whole burden. Adapting a multi-grid algorithm is hence expected to be a wise step towards solution. The effects of leveling in the multi grid domain are of primary interest. The primary objective of this study is to develop computational tools that facilitate and speed up the solution of three-dimensional external flows around non-symmetric bodies. Adapting multiple domains in the computational space is a sort of domain decomposition technique. Overlapping domains where each domain of coarser mesh encloses that of the finer meshes have been employed. This provided a multi-grid/multilevel formulation which resulted in faster convergence by way of reducing smooth errors. This formulation comprises constant-size sub-problems which might also exhibit good applicability in parallel computation. The effects and the advantages of multi-domains applied for finite difference formulations in three spatial coordinates were numerically experimented. Faster convergence of numerical algorithm using a multi level approach in three dimensions was achieved.
