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 strains (MOL) method offers a versatile structure for the answer of all of the significant sessions of partial differential equations (PDEs) and is very compatible to evolutionary, nonlinear wave PDEs. regardless of its software, in spite of the fact that, there are fairly few texts that discover it at a extra complex point and mirror the method's present nation of development.Written by way of distinctive researchers within the box, Adaptive approach to strains displays the variety of strategies and functions on the topic of the MOL. such a lot of its chapters specialize in a specific software but additionally offer a dialogue of underlying philosophy and procedure. specific realization 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 computer screen functionality, the minimization of a useful, and the relocating finite point strategy. purposes addressed contain shallow water move, combustion and flame propagation, delivery in porous media, fuel dynamics, chemical engineering methods, solitary waves, and magnetohydrodynamics.As the 1st complicated textual content to symbolize the trendy period of the tactic of traces, this monograph bargains an exceptional chance to find new options, research new thoughts, and discover a variety of purposes.

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39) is a degenerate parabolic equation. The flux function including gravitational effects is given by u2 1 − 5(1 − u)2 . 42) and Dirichlet boundary conditions in xL = 0 and xR = 1 u(0, t) u(1, t) = = 0 1. 01 using the moving grid code AGE [26], which is based on a method published by Sanz-Serna and Christie [25] and an extension proposed by Revilla [24]. , xi xi−1 m(u)dx = m(u) = © 2001 by CRC Press LLC xi+1 xi m(u)dx, (α + uxx ∞) 2≤i ≤N −1 . 4. 6 Substrate concentration in a fixed-bed bioreactor; adaptive grid solution using PARAB every 5000 units in time.

4. CASE STUDIES 19 of the grid point spacing and the smoothness of the ODE temporal trajectories. ). These regularization procedures always make the method more complicated in the sense that they involve a set of additional tuning parameters. 4 Case Studies This section is devoted to the numerical study of several application examples taken from physics and engineering. At this stage, we would like to illustrate the various concepts introduced thus far, to show the diversity of adaptive grid algorithms and to demonstrate their potential to address challenging applications.

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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