Coordinate Systems, Numerical Objects and Algorithmic Operations of Computational Experiment in Fluid Mechanics

Abstract

Abstract. The paper deals with the computer implementation of direct computational experiments in fluid mechanics, constructed on the basis of the approach developed by the authors. The proposed approach allows the use of explicit numerical scheme, which is an important condition for increasing the efficiency of the algorithms developed by numerical procedures with natural parallelism. The paper examines the main objects and operations that let you manage computational experiments and monitor the status of the computation process. Special attention is given to a) realization of tensor representations of numerical schemes for direct simulation; b) realization of representation of large particles of a continuous medium motion in two coordinate systems (global and mobile); c) computing operations in the projections of coordinate systems, direct and inverse transformation in these systems. Particular attention is paid to the use of hardware and software of modern computer systems.

Interpolation Environment of Tensor Mathematics at the Corpuscular Stage of Computational Experiments in Hydromechanics

“…The constructed scheme ensures unambiguous interpretation of physical processes by means of linear interpolation, which is performed by tensor operators in conjugate coordinate systems [5]. The solution is carried out in three stages:…”

“…Notations are described in details in [5,6]. Now we describe the mathematical and algorithmic features of the build up of a computational experiment.…”