6 research outputs found

    The numerical solution of two-dimensional moving boundary problems using curvilinear co-ordinate transformations

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    A numerical method is described for the solution of two-dimensional moving boundary problems by tansforming the curved, fixed and moving boundaries in the originalco-ordinate system (x,y) into an orthogonal or, in general, nonorthogonal curvilinear system (ξ,η) such that the curved boundaries become (ξ,η) co-ordinate lines. All computations are then carried out in the transformed region using a fixed, rectangular (ξ,η) mesh which corresponds to a moving, non-rectangular (x,y) mesh. A one-phase, two-dimensional problem is solved by using two different such transformations and the results are compared with those from finite-element, enthalpy and isotherm migration methods

    Modified finite-difference approximations near the singularitiy in the problem of motz

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    A simple, modified finite-difference method is described for solving Laplace's equation with boundary singularities of the infinite derivative type. Modified approximations for the derivatives of the Laplacian equation are employed near the singularity. These are developed from a truncated series form of the local analytical solution. The method is applied to the problem of Motz. The numerical results compare favourably with those obtained by other techniques
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