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) technique offers a versatile layout for the answer of all of the significant sessions of partial differential equations (PDEs) and is very like minded to evolutionary, nonlinear wave PDEs. regardless of its software, although, there are quite few texts that discover it at a extra complicated point and replicate the method's present nation of development.Written by means of individual researchers within the box, Adaptive approach to traces displays the range of innovations and purposes on the topic of the MOL. so much of its chapters specialize in a specific software but additionally offer a dialogue of underlying philosophy and process. specific awareness is paid to the idea that of either temporal and spatial adaptivity in fixing time-dependent PDEs. Many very important principles and techniques are brought, together with relocating grids and grid refinement, static and dynamic gridding, the equidistribution precept and the idea that of a display screen functionality, the minimization of a practical, and the relocating finite aspect strategy. functions addressed contain shallow water movement, combustion and flame propagation, shipping in porous media, gasoline dynamics, chemical engineering tactics, solitary waves, and magnetohydrodynamics.As the 1st complex textual content to symbolize the trendy period of the strategy of traces, this monograph bargains an exceptional chance to find new ideas, examine new recommendations, and discover quite a lot of purposes.

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1 Introduction In recent years, much interest has developed in the numerical treatment of PDEs giving rise to nonlinear wave phenomena, and particularly, solitary waves. , the cubic Schrödinger equation (CSE) and the derivative nonlinear Schrödinger equation (DNLS), as well as several Korteweg-de Vries (KdV)-like equations in one space dimension. These equations have been used extensively to model nonlinear dispersive waves in a wide range of application areas, such as water wave models, laser optics, and plasma physics.

If K is reduced, grid regularity is enforced, resulting in an increase of the number of nodes and, in turn, of the CPU time. 3. 52. It is possible to further increase Nadapt (up to 40) and obtain a satisfactory numerical solution. However, too infrequent grid adaptation yields an increase in the number of nodes (to compensate for their inappropriate placement) and a more difficult time-stepping procedure (characterized by increasing computation time). 3. 2 Influence of c on the grid spacing 47 xi .

4, . . 8. 4 Case Study 4 Consider a laboratory-scale catalytic fixed-bed reactor in which the hydrogenation of small amounts of CO2 to methane is accomplished CO2 + 4H2 → CH4 + 2H2 O . 46) Based on experimental studies, a model of the transient behavior of this plant has been derived in [30], and investigated numerically in [5]. 4. 49) and the boundary and initial conditions cx (0, t) = cx (L, t) = = c(x, 0) vρg cpg v (c − cin ), Tx (0, t) = (T − Tin ) D λ 0, Tx (L, t) = 0 c0 (x), T (x, 0) = T0 (x) .

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