On Symmetrical Finite Volume Scheme Of The Quadrangle Grid And Its Appilication

In this article, aiming at a kind of elliptic problem, three types of preserving-symmetry finite volume schemes under quadrangle partition grids are firstly established . During the course of the establishing, the" vertex-centered" control volume are selected and the balance-equation is discretized by utilizing the finite volume element method. Furthermore, the analysis of the convergence from the theoretical viewpoint is displayed, so is the result that the convergent order of the error is saturated. A number of numerical examples verified the theoretical results. Simultaneously, compared with the nine-point difference scheme which are widely applied , our new schemes have more advantageous on non-orthogonal grids, for example, the convergent accuracy, the fast-solving of the discrete system and so on. At the same time, the three types of schemes are exended to the nonlinear parabolic problem, combining with three types of linearization method(the "Fixed" Coefficients Method, the " Formulation " Newton Iterative Method and the " Algebraic " Newton Iterative Method). The same convergent order of the error is shown by the numerical results. Finally, the schemes for the nonlinear parabolic problem are applied to the two-dimension three-temperature heat conduction equations, some good numeriacl results are achieved.