Model of Thermoconvection of Incompressible Viscoelastic Fluid of Nonzero Order. Computational Experiment

The purpose of this paper is the numerical investigation of the solution of the initial-boundary value problem for the model of thermal convection of the nonzero order. We consider the system that models the evolution of the velocity, gradient of the pressure and temperature of the incompressible viscoelastic Kelvin-Voigt fluid of nonzero order. Using the Galerkin method, the algorithm of the numerical solution of the initial-boundary value problem for the system modeling plane-parallel thermal convection of the incompressible fluid of the nonzero order is created, and the program for personal computers to find numerical solutions of this problem is implemented. A graphical illustration of the numerical solution with the given parameters is obtained. The study was based on the results of the theory of semi-linear Sobolev type equations, because the initial boundary value problem for the corresponding system of differential equations in partial derivatives is reduced to the abstract Cauchy problem for the Sobolev type equation.

Keywords

sobolev type equation, thermal convection, incompressible viscoelastic fluid.

References

1. Oskolkov A.P. Initial-Boundary Value Problems for Equations of Motion Kelvin-Voight and Oldroyd Fluids [Nachal'no-kraevye zadachi dlya uravneniy dvizheniya zhidkostey Kel'vina-Foygta i zhidkostey Oldroyta]. Trudy Mat. In-ta AN SSSR, 1988, no. 179, pp. 126-164.
2. Sviridyuk G.A. Solubility of the Thermal Convection of Viscoelastic Incompressible Fluid [Razreshimost' zadachi termokonvektsii vyazkouprugoy neszhimaemoy zhidkosti]. Russian Mathematics (Izvestiya VUZ. Matematika), 1990, no. 12, pp. 65-70.
3. Sviridyuk G.A., Sukacheva T.G. Some Mathematical Problems of the Dynamics of Viscoelastic Incompressible Media [Nekotorye matematicheskie zadachi dinamiki vjazkouprugih neszhimaemyh sred]. Vestnik MaGU, 2005, no. 8, pp. 5-33.
4. Sukacheva T.G. Issledovanie matematicheskikh modeley neszhimaemykh vyazkouprugikh zhidkostey: dis. ... d-ra fiz.-mat. nauk [The Study of Mathematical Models of Incompressible Viscoelastic Fluids: dis. Dr. Science]. Velikiy Novgorod, 2004. 249 p.
5. Sukacheva T.G., Matveeva O.P. The Problem of Thermal Convection of an Incompressible Viscoelastic Kelvin-Voigt Fluid of Nonzero Order [Zadacha termokonvekcii neszhimaemoj vjazkouprugoj zhidkosti Kel'vina-Fojgta nenulevogo porjadka]. Russian Mathematics (Izvestiya VUZ. Matematika), 2001, no. 11, pp. 46-53.