Solution of three-dimensional free boundary problems by variable interchange

The three-dimensional problem of the seepage of fluid through a circular earth dam is solved to illustrate a new approach to more general free boundary problems. The method is based on Boadway's transformation in which the dependent variable, representing velocity potential, is interchanged with one of the independent space variables, which then becomes the new dependent variable to be computed. The need to determine the position of the whole of the free surface in the three-dimensional physical space is reduced to locating the position of the separation line on a fixed plane boundary in the transformed domain. An iterative algorithm approximates within each single loop both a finite-difference solution of the partial differential equation and the position of the separation line

Numerical solution of a free boundary problem by interchanging dependent and independent variables

The classical problem of seepage of fluid through a porous dam is solved to illustrate a new approach to more general free boundary problems. The numerical method is based on the interchange of the dependent variable, representing velocity potential, with one of the independent space variables, which becomes the new variable to be computed. The need to determine the position of the whole of the free boundary in the physical plane is reduced to locating the position of the separation point on a fixed straight—line boundary in the transformed plane. An iterative algorithm approximates within each single loop both a finite-difference solution of the partial differential equation and the position of the free boundary. The separation point is located by fitting a 'parabolic tail' to the finite-difference solution

Numerical solution of free boundary problems by interchanging dependent and independent variables

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A direct variational methods applied to Burgers' equation

WOS: A1996UU48800001In this study, a compact approximate method in limiting form for calculating the solution of Burgers' equation with appropriate boundary conditions is presented. The results obtained by present method are found to be in good agreement with those due to earlier authors and offers appreciable advantages for Burgers' like nonlinear problems

The semi-approximate approach for solving Burgers' equation with high Reynolds number

WOS: 000227044000013This paper presents the solution of Burgers' equation involving very high Reynolds number (Re greater than or equal to 5). We use semi-implicit, time-difference scheme to reduce Burgers' equation to two-point, non-linear ordinary differential equation and solved it by matched asymptotic expansion method. (C) 2004 Elsevier Inc. All rights reserved

Numerical solution of Burgers' equation with restrictive Taylor approximation

WOS: 000235539900042In this paper, we have applied restrictive Taylor approximation classical explicit finite difference method to the Burgers' equation with a set of initial and boundary conditions to obtain its numerical solution. The stability region and truncation error of the new method are discussed. The accuracy of the proposed method is demonstrated by the two test problems. The numerical results are found in good agreement with the exact solutions. (c) 2005 Elsevier Inc. All rights reserved