Numerical analysis of higher order singularities in chemical process models

Krasnyk, Mykhaylo; Ginkel, Martin; Mangold, Michael; Kienle, Achim

doi:10.1016/j.compchemeng.2006.09.010

Cited by 12 publications

(8 citation statements)

References 14 publications

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“…First, we convert BVP (14) and (15) into an equivalent integral equation by integrating it twice. For doing so, we set v(x) = xy ′ (x) and then integrating (14) between 0 to x, yields…”

Section: Drawbacks Of Ham [34 35]mentioning

confidence: 99%

“…Because of the lack of space we have not listed higher order approximations. To obtain more accurate solution of BVP (14) to (15), the method requires more number of terms in the solution series (21). Now one needs to use a root finding approach, such as Newton's method, to solve (22) for the undetermined coefficient a at each order approximation.…”

Section: Drawbacks Of Ham [34 35]mentioning

confidence: 99%

“…In the study of nonlinear phenomena in engineering and applied sciences, many mathematical models lead to singular boundary value problems (SBVP), see previous studies. [5][6][7][8][9][10][11][12][13][14][15][16] Several methods have been developed for solving (1) with q(x) = 1, g(x) or x and f(x, y, gy ′ ) = f(x, y). For example, finite difference methods, 17,18 spline methods, 19,20 finite element method, 21 collocation method, 22 variational iteration method, 23 homotopy perturbation method, [24][25][26][27] Adomian decomposition method (ADM), 28 and B-spline collocation method.…”

Section: Introductionmentioning

confidence: 99%

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Doubly singular boundary value problems with derivative dependent source function: A fast‐converging iterative approach

Roul

2018

Math Methods in App Sciences

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In this paper, a fast-converging recursive scheme is presented to approximate the solution of a class of derivative dependent doubly singular boundary value problems (DDSBVP). First, the original problem is reformulated as an equivalent integral equation. The resulting integral equation is then efficiently tackled by an improved homotopy analysis method (IHAM). This method contains a parameter, which greatly accelerates the convergence of the series solution. The convergence of the method is carried out. To illustrate the efficiency and accuracy of the proposed recursive approach, we consider three nonlinear examples, including one physical model problem, which describes stress distribution on a rotationally shallow membrane cap. Results show that our method excels over the existing methods.

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“…First, we convert BVP (14) and (15) into an equivalent integral equation by integrating it twice. For doing so, we set v(x) = xy ′ (x) and then integrating (14) between 0 to x, yields…”

Section: Drawbacks Of Ham [34 35]mentioning

confidence: 99%

Section: Drawbacks Of Ham [34 35]mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Doubly singular boundary value problems with derivative dependent source function: A fast‐converging iterative approach

Roul

2018

Math Methods in App Sciences

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“…The TMBR model was implemented in ProMoT and simulated with the tool Diana [25,26]. This tool also allows analysis of simple zero eigenvalues bifurcation points and the calculation of higher order singularities as well.…”

Section: Parameters and Numerical Simulation Techniquesmentioning

confidence: 99%

Theoretical Analysis of Heat Integration in a Periodically Operated Cascade of Catalytic Fixed‐Bed Reactors

et al. 2009

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Forced periodic operation can lead to improved reaction processes. Such operation is studied for the example of the application of a cascade of connected adiabatic fixed-bed reactors to perform catalytic total oxidation. It is shown that the periodic operation of the configuration considered allows an autothermal operation. The concept can outperform classical reverse-flow operation concerning the reduction of slips of unconverted feed. A simple model based on the assumption of a hypothetical countercurrent of the solid phase is derived and compared with a standard dynamical model of the reactor cascade. By evaluation of steady state profiles and application of bifurcation theory, it is demonstrated that the reduced model describes the limiting case for an infinitely segmented cascade and allows assessment of important properties of the periodic process. It permits a fast and detailed analysis of limit point bifurcations, which result in curves enclosing the region of desired ignited states of the reactor. Using singularity analysis further helps to understand the influence of secondary parameters and to identify operational limits. Copyright © 2009 John Wiley & Sons, Inc. All Rights Reserved. [accessed November 25, 2009

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“…Diana contains powerful methods for parameter continuation and bifurcation analysis of equilibrium points states, steady state singularities and periodic solutions [11,12]. A predictor-corrector algorithm with step size control is used for continuation.…”

mentioning

confidence: 99%

Development and Nonlinear Analysis of Dynamic Plant Models in ProMoT /Diana

Mangold

Khlopov

Danker

et al. 2014

Chemie Ingenieur Technik

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In the process design of chemical production plants, dynamic simulation plays an important role. This paper gives a short introduction to the process modeling tool ProMoT and the simulation tool Diana. Both are open‐source programs intended for the dynamic analysis of chemical engineering and biological systems. They support the implementation and analysis of large nonlinear differential algebraic systems. An overview is given on the functionality of ProMoT and Diana. The use of the tools is illustrated by their application to an innovative fluidized bed crystallization process.

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Numerical analysis of higher order singularities in chemical process models

Cited by 12 publications

References 14 publications

Doubly singular boundary value problems with derivative dependent source function: A fast‐converging iterative approach

Doubly singular boundary value problems with derivative dependent source function: A fast‐converging iterative approach

Theoretical Analysis of Heat Integration in a Periodically Operated Cascade of Catalytic Fixed‐Bed Reactors

Development and Nonlinear Analysis of Dynamic Plant Models in ProMoT /Diana

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