Collocation Method for the Modeling of Membrane Gas Permeation Systems

2015 ◽  
Vol 16 (3-4) ◽  
pp. 141-149
Author(s):  
Anna Feichtinger ◽  
Aleksander Makaruk ◽  
Ewa Weinmüller ◽  
Anton Friedl ◽  
Michael Harasek
Keyword(s):  
Collocation Method ◽  
Numerical Approximation ◽  
Numerical Approach ◽  
Adaptation Strategy ◽  
Gas Permeation ◽  
Computational Time ◽  
Efficient Computation ◽  
Grid Adaptation ◽  
Crucial Feature ◽  
Comparison Of The Results

AbstractIn this work, we describe a numerical method which enables an efficient computation of membrane gas permeation processes that involve multiple membrane stages and multiple gas components. The utilized numerical approach is a collocation method equipped with a grid adaptation strategy based on a dependable error estimate of the numerical approximation. The comparison of the results provided by the collocation method with those calculated from an experimentally validated finite difference method has demonstrated that the accuracy of both numerical approximations is practically the same. However, the current procedure is characterized by a much better computational efficiency that allows to considerably reduce the computational time. This is a crucial feature when combining computation of membrane permeation processes with optimization algorithms. In such a setting the computation of the permeation process is frequently repeated and naturally, results in long computational times when the efficiency is not adequately improved.

Advanced CFD Simulations of free-surface flows around modern sailing yachts using a newly developed openFOAM solver

2016 ◽  
Author(s):  
Janek Meyer ◽  
Hannes Renzsch ◽  
Kai Graf ◽  
Thomas Slawig
Keyword(s):  
Free Surface ◽  
Large Scale ◽  
Breaking Waves ◽  
Free Surface Flows ◽  
Body Motion ◽  
Computational Time ◽  
Efficient Computation ◽  
Surface Flows ◽  
Scale Free ◽  
Wide Range

While plain vanilla OpenFOAM has strong capabilities with regards to quite a few typical CFD-tasks, some problems actually require additional bespoke solvers and numerics for efficient computation of high-quality results. One of the fields requiring these additions is the computation of large-scale free-surface flows as found e.g. in naval architecture. This holds especially for the flow around typical modern yacht hulls, often planing, sometimes with surface-piercing appendages. Particular challenges include, but are not limited to, breaking waves, sharpness of interface, numerical ventilation (aka streaking) and a wide range of flow phenomenon scales. A new OF-based application including newly implemented discretization schemes, gradient computation and rigid body motion computation is described. In the following the new code will be validated against published experimental data; the effect on accuracy, computational time and solver stability will be shown by comparison to standard OF-solvers (interFoam / interDyMFoam) and Star CCM+. The code’s capabilities to simulate complex “real-world” flows are shown on a well-known racing yacht design.

An Efficient Computational Numerical Approach For Nonlinear Mathematical Influenza Disease Modelling

2021 ◽  
Author(s):  
Zulqurnain Sabir ◽  
Muhammad Asif Zahoor Raja ◽  
Mohamed R. Ali ◽  
Adnène Arbi ◽  
Muhammad Kristiawan
Keyword(s):  
Numerical Scheme ◽  
Reference Data ◽  
Disease Model ◽  
Numerical Approach ◽  
Disease Modelling ◽  
Mean Square ◽  
Levenberg Marquardt ◽  
Effectiveness And Efficiency ◽  
Comparison Of The Results ◽  
And Training

Abstract In this study, an advanced computational numerical scheme based on the Levenberg-Marquardt backpropagation (LMB) neural network (NN) process, i.e., LMB-NN is presented for solving the nonlinear mathematical influenza disease model. The nonlinear mathematical influenza disease model depends on four categories named susceptible S(t), infected I(t), recovered R(t) and cross-immune individuals proportion C(t). Six different cases of the nonlinear mathematical influenza disease model have been numerically treated using the LMB-NN process and the comparison of the results has been presented by using the reference data-based solutions designed based on the Adams results. The numerically obtained results of the nonlinear mathematical influenza disease model using the verification, testing, and training procedures are calculated using the LMB-NN process to reduce the functions of mean square error (MSE). For the correctness, competence, effectiveness, and efficiency of the LMB-NN process, the proportional and analysis methods are performed using the analysis of correlation, MSE results, error histograms and regression.

A Fast Approximate Solution of the Laminar Boundary-Layer Equations

1986 ◽  
Vol 108 (2) ◽  
pp. 200-207 ◽  
Author(s):  
Sei-ichi Iida ◽  
Akira Fujimoto
Keyword(s):  
Boundary Layer ◽  
Velocity Profile ◽  
Computational Time ◽  
Computational Techniques ◽  
Boundary Layer Flows ◽  
Boundary Layer Equations ◽  
Laminar Boundary Layers ◽  
Layer Characteristic ◽  
Comparison Of The Results ◽  
Steady Laminar

A new approximate method of calculating steady laminar boundary-layers is presented. This method is based on the mutual relationships between boundary-layer characteristic quantities. The governing equations are efficiently solved without assuming a specific velocity profile. Moreover, a method of estimating the velocity profile using the characteristic quantities is also proposed. Comparison of the results obtained for a wide variety of applications to boundary-layer flows with separations with exact solutions indicates that the present method enables one to obtain solutions with sufficient accuracy and shorter computational time when compared with existing computational techniques.

Advanced Control for Clusters of SOFC/Gas Turbine Hybrid Systems

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Iacopo Rossi ◽  
Valentina Zaccaria ◽  
Alberto Traverso
Keyword(s):  
Fuel Cell ◽  
Power Systems ◽  
Gas Turbine ◽  
Power Plants ◽  
Numerical Approach ◽  
Computational Time ◽  
Target System ◽  
Wide Range ◽  
Advanced Control ◽  
Complex Target

The use of model predictive control (MPC) in advanced power systems can be advantageous in controlling highly coupled variables and optimizing system operations. Solid oxide fuel cell/gas turbine (SOFC/GT) hybrids are an example where advanced control techniques can be effectively applied. For example, to manage load distribution among several identical generation units characterized by different temperature distributions due to different degradation paths of the fuel cell stacks. When implementing an MPC, a critical aspect is the trade-off between model accuracy and simplicity, the latter related to a fast computational time. In this work, a hybrid physical and numerical approach was used to reduce the number of states necessary to describe such complex target system. The reduced number of states in the model and the simple framework allow real-time performance and potential extension to a wide range of power plants for industrial application, at the expense of accuracy losses, discussed in the paper.

scholarly journals A Numerical Approach to Solve Volume-Based Batch Crystallization Model with Fines Dissolution Unit

Processes ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 453 ◽  
Author(s):  
Mukhtar ◽  
Sohaib ◽  
Ahmad
Keyword(s):  
Numerical Approximation ◽  
Chemical Engineering ◽  
Numerical Study ◽  
Moment Generating Function ◽  
Numerical Approach ◽  
Test Problems ◽  
Batch Crystallization ◽  
One Dimensional ◽  
Engineering Sciences ◽  
The Moment

In this article, a numerical study of a one-dimensional, volume-based batch crystallization model (PBM) is presented that is used in numerous industries and chemical engineering sciences. A numerical approximation of the underlying model is discussed by using an alternative Quadrature Method of Moments (QMOM). Fines dissolution term is also incorporated in the governing equation for improvement of product quality and removal of undesirable particles. The moment-generating function is introduced in order to apply the QMOM. To find the quadrature abscissas, an orthogonal polynomial of degree three is derived. To verify the efficiency and accuracy of the proposed technique, two test problems are discussed. The numerical results obtained by the proposed scheme are plotted versus the analytical solutions. Thus, these findings line up well with the analytical findings.

Development of Conservative Form of RELAP5 Thermal Hydraulic Equations: Part I — Theory

2014 ◽  
Author(s):  
Zheng Fu ◽  
Fatih Aydogan ◽  
Richard J. Wagner
Keyword(s):  
Nuclear Power ◽  
Power Plants ◽  
Numerical Approximation ◽  
Numerical Approach ◽  
Phase System ◽  
Hydraulic Systems ◽  
Governing Equations ◽  
Two Phase ◽  
Current Form ◽  
Two Fluids

The design and analysis of the thermal/hydraulic systems of nuclear power plants necessitates system codes that can be used in the analysis of steady state and transient conditions. RELAP5 is one of the most commonly used system codes in nuclear organizations. RELAP5 is based on a two-fluid, non-equilibrium, non-homogeneous, hydrodynamic model for the transient simulation of the two-phase system behavior. This model includes six governing equations to describe the mass, energy, and momentum of the two fluids. The “non-conservative” numerical approximation form (which is the current form of RELAP5 code versions) is obtained through the manipulation of selected derivative terms in the equations including the linearization of the product terms in the time derivatives of the equations. For non-conservative technique, the truncation errors introduced in the linearization process can produce mass and energy errors for some classes of transients during time advancements, either resulting in (a) automatic reduction of time steps used in the advancement of the equations and increased run times or (b) the growth of unacceptably large errors in the transient results. To eliminate these difficulties, a new, optional numerical approach has been introduced in RELAP/SCDAPSIM/MOD4.0. This new option uses a more consistent set of the “conservative” numerical approximation to solve non-linearized mass and energy governing equations. The RELAP/SCDAPSIM/MOD4.0 code, being developed as part of the international SCDAP (Severe Core Damage Analysis Package) Development and Training Program (SDTP), is the first version of RELAP5 completely rewritten to FORTRAN 90/95/2000 standards. This paper provides an overview of the original RELAP5 numerical approximations and describes the new theoretical approach. Then the second article introduces the solution strategy of conservative approach and presents some examples of transient problems that have been run using this new approach.

A NEW MATHEMATICAL MODEL FOR FINITE-DIFFERENCE SOLUTION OF THREE-DIMENSIONAL MIXED-BOUNDARY-VALUE ELASTIC PROBLEMS

2005 ◽  
Vol 02 (01) ◽  
pp. 99-126 ◽  
Author(s):  
M. ZUBAER HOSSAIN ◽  
S. REAZ AHMED ◽  
M. WAHHAJ UDDIN
Keyword(s):  
Finite Difference ◽  
Potential Function ◽  
Solid Mechanics ◽  
Present Model ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Computational Time ◽  
Comparison Of The Results

This paper describes a new mathematical formulation, specifically suitable for finite-difference analysis of stresses and displacements of three-dimensional mixed-boundary-value elastic problems. Earlier, mathematical models of elasticity were very deficient in handling three-dimensional practical stress problems. In the present model, a new scheme of reduction of unknowns is used to formulate the three-dimensional problem in terms of a single potential function, defined in terms of the three displacement components. Compared to the conventional models, the present model provides numerical solution of higher accuracy in a shorter period of computational time. The application of the potential function formulation is demonstrated here through a number of classical problems of solid mechanics, and the results are compared with the available solutions in the literature. The comparison of the results establishes the rationality of the present approach.

Steel Plate Behavior under Blast Loading-Numerical Approach Using LS-DYNA

2016 ◽  
Vol 842 ◽  
pp. 200-207 ◽  
Author(s):  
Vu Minh Thanh ◽  
Sigit P. Santosa ◽  
Djarot Widagdo ◽  
Ichsan Setya Putra
Keyword(s):  
Blast Resistance ◽  
Blast Loading ◽  
Numerical Approach ◽  
Coupling Method ◽  
Steel Plates ◽  
Computational Time ◽  
Arbitrary Lagrangian Eulerian ◽  
Ale Method ◽  
Wide Range ◽  
Coupling Algorithm

Plate is one of the most common structural elements, which appears in a wide range of applications: steel bridges, blast-resistance door, and armored vehicles. In this paper, the behavior of steel plates under blast loading was studied through numerical approaches using LS DYNA and then the results were compared with the experiment results obtained from existing literatures. The study of a clamped square plate exposed to blast loading in three distinct stand-off distances. Three different methods of modeling blast loading were used, namely: empirical blast method, arbitrary Lagrangian Eulerian (ALE) method, and coupling of Lagrangian and Eulerian method. The empirical blast method was deployed by using key card *LOAD_BLAST in LS-DYNA. In ALE method, Langrangian and Eulerian solution were combined in the same model and the fluid-structure interaction (FSI) handled by coupling algorithm. In coupling method, the engineering load blast in LS-DYNA (*LOAD_BLAST_ENHANCED) was coupled with the ALE solver. In terms of central deflection and computational time, the coupling method appeared to be the best method which is very time-effective and showed a good correlation with the experiment data.

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