engleski

Finite-difference methods for simulating the solidification of castings

Mathematical models of casting solidification for different geometrical complexities have been developed and checked. Special emphasis is given to the numerical finite-difference methods for solving the partial differential equations for heat conduction in two- and three-dimensions, which are the basis for the simulation of solidification. In the case of three-dimensional mathematical models, the methods of Douglas and Brian are especially efficient because they are unconditionally stable and of the second order with regard to the approximation of time and space. Both methods have a two-dimensional variant and Brian’s method is identical to the implicit alternating direction method. To obtain an algorithm for the solidification with the application of implicit finite-difference methods, the system of the tri-diagonal matrix has to be solved, for which an efficient algorithm exists. In addition to the implicit methods of solving Fourier’s partial differential equation of heat conduction, also the unconditionally stable explicit finite- difference methods are used. These are the methods of partial steps, the classical method and Saulyev’s method. These methods also allow a first-order accuracy. On the basis of the quoted numerical methods for solving the partial differential equation of heat conduction, the algorithms of casting solidification of differential complexity have been obtained and programmed in the computer languages ASCII FORTRAN and FORTRAN 77, and the simulation has been performed with a SPERRY 1106 computer and personal computers.

casting solidification ; heat conduction method of finite differences ; computer simulation

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