Vectorized Numerical Algorithms to Solve Internal Problems of Computational Fluid Dynamics

Abstract

The opportunities provided by new information technologies, object-oriented programming tools, and modern operating systems for solving boundary value problems in CFD described by partial differential equations are discussed. An approach to organizing vectorized calculations and implementing finite-difference methods for solving boundary value problems in CFD is considered. Vectorization in CFD problems, eliminating nested loops, is ensured through the appropriate data organization and the use of vectorized operations with arrays. The implementation of numerical algorithms with vectorized mesh structures, including access to internal and boundary mesh cells, is discussed. Specific examples are reported and the implementation of the developed computational algorithms is discussed. Despite the fact that the capabilities of the developed algorithms are illustrated by solving benchmark CFD problems, they enable a relatively simple generalization to more complex problems described by three-dimensional equations.