Effective numerical-analytical solution of isoperimetric variational problems of mechanics by an accelerated convergence method

A new numerical-analytical method for solving non-linear variational problems of mechanics is presented. The method enables additional isoperimetric conditions and boundary conditions of different types to be taken into account. Unlike existing approaches, the method is based on the use of residuals of the unknown functions corresponding to abscissae at which they satisfy the required conditions. The method has a clear geometrical interpretation and provides a more confident idea as to the convergence of the iteration algorithm, which is quadratic in nature. The algorithm constructed is used to compute single-mode and multi-mode viscous incompressible flows in a plane convergent channel (Jeffrey-Hamel flow) for a broad range of governing parameters (the aperture angle and Reynolds number). (C) 2003 Elsevier Science Ltd. All rights reserved.