СРАВНИТЕЛЬНЫЙ АНАЛИЗ ЭФФЕКТИВНОСТИ ПАРАЛЛЕЛЬНЫХ ВЫЧИСЛЕНИЙ ПО ЯВНЫМ И НЕЯВНЫМ РАЗНОСТНЫМ СХЕМАМ ДЛЯ ЗАДАЧ ВЫЧИСЛИТЕЛЬНОЙ АЭРОДИНАМИКИ

Abstract

One of the main areas of parallel computing application is solving of computational aerodynamicsproblems. The paper considers parallel modeling of gas dynamics with quasi-onedimensionalsystem of equations. The system describes the gas flow through a channel with variablecross section using implicit and explicit difference schemes. The purpose of this work is tostudy the methods efficiency for organizing parallel computations with implicit and explicit differenceschemes for solving internal aerodynamics problems. The article presents a comparativeanalysis 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 algorithmsare used to solve systems of such type numerically. The method of splitting by physical processesis used for an implicit difference scheme. To suppress the solution oscillations a smoothingoperator 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 tosolve tridiagonal systems with the parametric unknown choice. Besides to compare scheme mentionedabove a parallel algorithm is constructed for McCormack's explicit scheme. Such algorithmis widely used in computational aerodynamics. Parallel computations are held by computingstructures with distributed memory and by another one – with linear switching dependence betweencomputing devices of the working field. The paper presents time estimations for each computingstage (both by implicit and explicit difference schemes). It helped to calculate the developedparallel algorithms efficiency. It is concluded that the acceleration factor in explicit scheme dependslinearly on the computing devices number.