Numerical solution of differential and integral equations
The numerical method based on the idea of splitting on physical processes (G.I. Marchuk, 1988) is proposed for investigations of convective motions of fluid in 2-dimensional and 3-dimensional domains. Convection transfer and diffusion transfer are the stages of splitting. It allows to combine effectively the computations using the physical functions and the variables of type “vortex – stream function” for 2-dimensional problems or of type “rotor of velocity – vector potential” for 3-dimensional problems. The stage of convection is realized only for the velocity field on the displaced grids (V.M. Belolipecky, V.Yu. Kostyuk, Yu.I. Shokin, 1991) with help of two-cyclic reduction based on the Crank – Nicholson schemes. Such approach ensures a property of the energy neutrality of the velocity field. On the diffusion stage a transition to the new required functions gives a possibility to avoid the computation of pressure and to have the solenoidality of the velocity field. The no-slip conditions are fulfilled due to some variant of Thomas’s algorithm with parameters. This algorithm with parameters permits to carry out the boundary conditions without iterations.
In this report the computation algorithms and the results of testing are presented. For testing the known problems of applied hydrodynamics such as free convection in quadratic or cubic domains with heating of one of boundaries are used.
Note. Abstracts are published in author's edition
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