MPI für Dynamik komplexer technischer Systeme / Process Synthesis and Process Dynamics |
|Method of Lines within the Simulation Environment DIVA for Chemical Processes|
|Authors:||Köhler, R.; Mohl, K. D.; Schramm, H.; Zeitz, M.; Kienle, A.; Mangold, M.; Stein, E.; Gilles, E. D.|
|Place of Publication:||Boca Raton|
|Publisher:||Chapmann and Hall|
|Date of Publication (YYYY-MM-DD):||2001|
|Title of Book:||Adaptive Method of Lines|
|Full Name of Book-Editor(s):||Vande Wouwer, A.; Saucez, Ph.; Schiesser, W.E.|
|Review Status:||not specified|
|Intended Educational Use:||No|
|Abstract / Description:||In chemical engineering, detailed process modeling, simulation, nonlinear analysis, and optimization of single process units as well as integrated production plants are issues of growing importance. As a software tool addressing these issues, the simulation environment DIVA is introduced. DIVA comprises tools for process modeling, preprocessing and code generation of simulation models. Furthermore, its simulation kernel contains several advanced methods for simulation, parameter continuation, and dynamic optimization which can be applied to the same process model. These numerical methods require a model description in form of differential algebraic equations (DAE). However, many models of chemical processes derived from first principles lead to partial differential equations (PDE) for distributed parametersystems, to integro partial differential equations (IPDE) for population balances of dispersed phases, and to DAE for lumped parameter systems. In order to transform the PDE and IPDE models into the required DAE model formulation, DIVA employs the "Method-of-Lines" (MOL) approach for one space coordinate. The wide variety of distributed parameter models of chemical processes requires on one hand conventional discretization methods like, e.g.,finite-difference schemes, and on the other hand more sophisticated methods to obtain reliable results in an acceptable computation time. Another approach of so called high-resolution methods uses adaptive approximation polynomials. High-resolution methods are developed forhyperbolic conservation laws with steep moving fronts. Examples areessentially-non-oscillatory (ENO) schemes or the robust upwindkappa-interpolation scheme. In order to support the user of the simulation environment diva, the symbolic preprocessing tool SYPPROT for MOL discretization is developed by means of the computer-algebra-system MATHEMATICA. This tool provides different discretization schemes to transform PDE, IPDE and the related boundary conditions on 1–dimensional spatialdomains into DAE. Discretization options concern fixed spatial grids and moving gridsbased on an equidistribution principle. The toolbox architecture of SYPPROT allows fast testing of various discretization schemes without redefinition of the model equations. This is regarded as an im portant feature to minimize the overall effort for modeling and simulation. A further characteristic that is key to theeasy exchange of discretization schemes is the separation between mode lequations and MOL parameter definitions by means of the mathematica datastructure (MDS).
The resulting overall DAE are written in symbolic form as an inputfile for the DIVA code generator, which automatically generates the DIVA simulation files representing a process unit model in the modellibrary. In the following section 13.2 the architecture of the simulation environment DIVA is presented. This architecture consists of four layers, i.e.the DIVA simulation kernel, the code generator, the symbolic preprocessing tool SYPPROT, and the process modeling tool PROMOT. The MOL discretization of PDE and IPDE as the main preprocessing feature is the focus of Section 13.3. Standard discretizationschemes like finite-difference and finite volume schemes as well as adaptive approaches like high-resolution methods and an equidistribution principle based moving grid method are explained for distributed parameter models with one space coordinate. The application of these discretization methods within the symbolic preprocessing tool SYPPROT follows in Section 13.4, where the PDE and IPDE model representation as well as the implemented MOL discretization capabilities are described.
|External Publication Status:||published|
|Communicated by:||Achim Kienle|
|Affiliations:||MPI für Dynamik komplexer technischer Systeme/Process Synthesis and Process Dynamics|
MPI für Dynamik komplexer technischer Systeme/Systems Biology
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