Analysis of the convergence properties for a non-linear implicit Equilibrium Flux Method using Quasi Newton–Raphson and BiCGStab techniques

Smith, Matthew R.; Lin, Yi-Hsin

doi:10.1016/j.camwa.2016.05.019

Cited by 4 publications

(2 citation statements)

References 19 publications

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“…Newton's method, which is also called the Newton-Raphson method (NRM), is an iterative method or numerical approach for attempting to find the roots of a function or system of equations [21]. NRM is formulated as an expansion of Taylor's series [22], as follows:…”

Section: Newton's Methodsmentioning

confidence: 99%

Application of Solution Strategies for Numerical Estimation of Thermodynamic Equilibrium Parameters for an Acetone–Butanol Mixture

2020

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The development of reliable numerical estimation of thermodynamic parameters is a crucial aspect in the ongoing research about process engineering and design. The consideration of these concepts lets to design more precise processing units and separations stages based on the predicted nature of substances. Therefore, this study presents an application of different solution methods for the estimation of thermodynamic equilibrium parameters of an acetone–butanol mixture. This dissolution is a non-ideal system, so, the non-ideal Raoult’s Law and Wilson’s equation were used to model the liquid–vapor equilibrium. Otherwise, the solution of this system required the application of nonlinear least squares (NLS) for determination of adjustable parameters. As the above step transformed Wilson’s equation into a system of nonlinear equations, solution algorithms such as; Newton–Raphson method (NRM), Broyden’s method (BM) and Levenberg–Marquardt method (LMM) were applied. All algorithms converged towards the same solution ( Λ 12 = 0.689 and Λ 21 = 0.798 ), but Newton’s and Broyden’s methods employed fewer computational time and number of iterations compared to performance showed by the Levenberg–Marquardt algorithm.

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Section: Newton's Methodsmentioning

confidence: 99%

Application of Solution Strategies for Numerical Estimation of Thermodynamic Equilibrium Parameters for an Acetone–Butanol Mixture

2020

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“…When solving non-linear equations in engineering problems, the Bisection method, Secant method, Newton-Raphson method, etc. are usually used [37,38]. Sciniaka et al introduced several iterative algorithms for solving equations and proposed an adaptive method based on the Newton-Raphson rooting method, which can better control the algorithm dynamics [39].…”

Section: Introductionmentioning

confidence: 99%

An Experimental Investigation into Combustion Fitting in a Direct Injection Marine Diesel Engine

Ding

Sui

2018

Applied Sciences

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The marine diesel engine combustion process is discontinuous and unsteady, resulting in complicated simulations and applications. When the diesel engine is used in the system integration simulation and investigation, a suitable combustion model has to be developed due to compatibility to the other components in the system. The Seiliger process model uses finite combustion stages to perform the main engine combustion characteristics and using the cycle time scale instead of the crank angle shortens the simulation time. Obtaining the defined Seiliger parameters used to calculate the engine performance such as peak pressure, temperature and work is significant and fitting process has to be carried out to get the parameters based on experimental investigation. During the combustion fitting, an appropriate mathematics approach is selected for root finding of non-linear multi-variable functions since there is a large amount of used experimental data. A direct injection marine engine test bed is applied for the experimental investigation based on the combustion fitting approach. The results of each cylinder and four-cylinder averaged pressure signals are fitted with the Seiliger process that is shown separately to obtain the Seiliger parameters, and are varied together with these parameters and with engine operating conditions to provide the basis for engine combustion modeling.

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Finite elements in flow problems 2015

Lin

Bazilevs

Brummelen

et al. 2016

Computers & Mathematics with Applications

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Analysis of the convergence properties for a non-linear implicit Equilibrium Flux Method using Quasi Newton–Raphson and BiCGStab techniques

Cited by 4 publications

References 19 publications

Application of Solution Strategies for Numerical Estimation of Thermodynamic Equilibrium Parameters for an Acetone–Butanol Mixture

Application of Solution Strategies for Numerical Estimation of Thermodynamic Equilibrium Parameters for an Acetone–Butanol Mixture

An Experimental Investigation into Combustion Fitting in a Direct Injection Marine Diesel Engine

Finite elements in flow problems 2015

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