An Effective Multigrid Method for Solving Problemsof High-Frequency Vibrational Convectionстатья
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Дата последнего поиска статьи во внешних источниках: 26 января 2024 г.
Аннотация:The paper describes an implemented algorithm for solving the problem of vibrationalconvection in a rectangular domain filled with an unevenly heated incompressible fluid.The mathematical model is based on the solution of the Simonenko–Zenkovskaya equations obtainedby averaging the Navier-Stokes equations under the assumption that the volume of liquidexecutes high-frequency translational vibrations. To solve the Poisson equations, an algebraicmultigrid method is implemented in combination with a highly efficient dynamic programmingmethod (based on R. Bellman’s optimal control principle) and fast Fourier transform. Mathematicalsoftware written in C/C++ has been developed. Examples of solving model problemswith various directions of the heating flow of a square domain relative to the vibration vectorare given.