COMPARATIVE ANALYSIS OF THE PARALLEL COMPUTING EFFICIENCY FOR EXPLICIT AND IMPLICIT DIFFERENCE SCHEMES FOR COMPUTATIONAL AERODYNAMICS PROBLEMS

Abstract

One of the main areas of parallel computing application is solving of computational aerodynamics
problems. The paper considers parallel modeling of gas dynamics with quasi-onedimensional
system of equations. The system describes the gas flow through a channel with variable
cross section using implicit and explicit difference schemes. The purpose of this work is to
study the methods efficiency for organizing parallel computations with implicit and explicit difference
schemes for solving internal aerodynamics problems. The article presents a comparative
analysis of the proposed parallel models for quasi-one-dimensional equations system of gas dynamics.
The system describes flows in a channel of variable cross section. Various parallel algorithms
are used to solve systems of such type numerically. The method of splitting by physical processes
is used for an implicit difference scheme. To suppress the solution oscillations a smoothing
operator at the correction stage is introduced in calculations according to the scheme of the predictor-
corrector type. In scheme fractional steps the parallel scalar sweep algorithm is used to
solve tridiagonal systems with the parametric unknown choice. Besides to compare scheme mentioned
above a parallel algorithm is constructed for McCormack's explicit scheme. Such algorithm
is widely used in computational aerodynamics. Parallel computations are held by computing
structures with distributed memory and by another one – with linear switching dependence between
computing devices of the working field. The paper presents time estimations for each computing
stage (both by implicit and explicit difference schemes). It helped to calculate the developed
parallel algorithms efficiency. It is concluded that the acceleration factor in explicit scheme depends
linearly on the computing devices number.