3-DIMENSIONAL SIMULATION OF DIRECT AND INVERSE RAYLEIGH-BENAR AND RAYLEIGH-TAYLOR PROBLEMS
A.I. Korotky, I.A. Tsepelev
VANT. Ser.: Mat. Mod. Fiz. Proc 2002. Вып.3. С. 22-32.
The paper describes one of the possible approaches to numerical simulation of direct and inverse (retrospective) problems of 3-D motions dynamics for highly viscous non-uniform incompressible fluid both with regard of heat transfer into fluid and without it. Mathematical model for fluid dynamics includes a quasi-stationary Stokes equation, a heat balance equation and some equations of physical medium parameter transfer. Many applications of the model for fluid and its motions belong to the geophysics field, though other applications are by far possible. The problems are computed using method with time iterations. For computing rate field of fluid two-component vector potential is used, which is obtained by finite element method with special basis composed of three-cubic splines. Temperature field in direct time is calculated by difference method using a chart of longitudinal-transversal run. In reverse time the equation of heat balance is solved by variational method, consisting in both the construction of sequential approximations and the solution of a series of specially designed direct problems. Transfer equations are alculated by characteristic method with subsequent interpolation of calculated values using three-linear splines. The results of specific examples calculations are demonstrated.
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