Adaptive method of lines by Alain Vande Wouwer, A Vande Wouwer, Ph. Saucez, W.E.

By Alain Vande Wouwer, A Vande Wouwer, Ph. Saucez, W.E. Schiesser

The overall approach to traces (MOL) approach presents a versatile structure for the answer of all of the significant periods of partial differential equations (PDEs) and is especially like minded to evolutionary, nonlinear wave PDEs. regardless of its application, even though, there are rather few texts that discover it at a extra complex point and replicate the method's present nation of development.Written by means of individual researchers within the box, Adaptive approach to strains displays the variety of recommendations and functions concerning the MOL. such a lot of its chapters concentrate on a specific software but additionally offer a dialogue of underlying philosophy and approach. specific cognizance is paid to the idea that of either temporal and spatial adaptivity in fixing time-dependent PDEs. Many vital principles and strategies are brought, together with relocating grids and grid refinement, static and dynamic gridding, the equidistribution precept and the idea that of a video display functionality, the minimization of a practical, and the relocating finite point strategy. purposes addressed contain shallow water circulation, combustion and flame propagation, delivery in porous media, gasoline dynamics, chemical engineering approaches, solitary waves, and magnetohydrodynamics.As the 1st complex textual content to symbolize the trendy period of the tactic of strains, this monograph bargains a superb chance to find new recommendations, examine new ideas, and discover a variety of purposes.

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7] B. Fornberg, Generation of finite difference formulas on arbitrarily spaced grid, Math. , 51, (1988), 699–706. M. G. A. Zegeling, A numerical study of threemoving grid methods for one-dimensional partial differential equations which are based on the method of lines, J. Comp. , 89, (1990), 349–388. [9] R. Gelinas, S. Doss, and K. Miller, The moving finite element method: applications to general equations with multiple large gradients, J. Comp. , 40, (1981), 202–249. [10] E. Hairer and G. Wanner, Solving Ordinary Differential Equations II - Stiff and Differential-Algebraic Problems, Springer-Verlag, Berlin, 1991.

U= ut + x ux = f (u)+ x ux . 29) . , x = g(t), can be derived based on some physical a priori knowledge, such as a flow-related quantity. 30) 18 INTRODUCTION . , x = v, so that . u (x(t), t) = 0 along the characteristic curves. , to minimize the temporal variation of the solution (in the moving reference frame) so as to allow the largest possible time step sizes. 26). In this case, grid point movement ensures a smoothing of the problem in space, but does not necessarily reduce the temporal variation of the solution.

R. Sanders, Numerical modeling of unsteady flame propagation, Sandia National Lab. Livermore Report SAND77-8275, 1978. [5] G. B. Butt, A modified Crank-Nicolson technique with nonequidistant space steps, Chem. Eng. , 31, (1976), 681–691. R. Eiseman, Adaptive grid generation, Comput. Meth. Appl. Mech. , 64, (1987), 321–376. [7] B. Fornberg, Generation of finite difference formulas on arbitrarily spaced grid, Math. , 51, (1988), 699–706. M. G. A. Zegeling, A numerical study of threemoving grid methods for one-dimensional partial differential equations which are based on the method of lines, J.

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