Информационная система "Конференции"

Abstracts

Numerical solution of differential and integral equations

At present time several tens of various finite-difference algorithms for numerical implementation of the Navier-Stokes equations are in use [1], but retrieval of new efficient methods is continued. In this paper authors discuss the difference scheme, which can be obtained after transformation of the original equations given in divergence form. The algorithm suggested is illustrated by one-dimensional model problem , 00, t0=0, tN=T, where hi=xi+1-xi, =(hi+hi-1)/2, i=1,...,I, then in case of implicit approximation of the original equation (3) we yield the following set of equations on the n-th time step , i=1,…,I, where , , , , and the value of ui1/4 is defined as ui1/4=u(xi1/4) or ui1/4=(3u(xi)+u(xi1))/4. Note that under the conditions of u=const and ux0, x[xi-3/4,xi+3/4] the system is monotonic, otherwise the monotonicity condition is determined by value of n. The algorithm described above is validated by solving the test problem of the convective heat transfer in rectangular cross section cavity heated from one side. The solution matches well the results presented in [2].

Note. Abstracts are published in author's edition

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