Finite difference Jacobian based Newton-Krylov coupling method for solving multi-physics nonlinear system of nuclear reactor

Liu, Baokun; Wu, Yingjie; Guo, Jiong; Han, Zhang; Niu, Jinlin; Fu, Li

doi:10.1016/j.anucene.2020.107670

Cited by 15 publications

(2 citation statements)

References 21 publications

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“…Since the arrangements to the coupled reaction-diffusion models inspected in this ponder are naturally chaotic, the appropriation of exactness strategies for established consistency, as well as focalize highlights, appears to be critical [9], [36]. In this way, the researcher may observe between the start of numerical vulnerability as well as chaos, which could be a veritable property in terms of a ceaseless show, by utilizing the finitedifference strategies given in this consider with caution [37]- [40].…”

Section: Numerical Solution Of Reaction-diffusion Model a Motivationmentioning

confidence: 95%

Dynamical Behavior of Nonlinear Coupled Reaction-Diffusion Model: A Numerical Study Utilizing ADI and Staggered Grid Finite Volume Method in Matlab

Saqib,

Akhtar,

Hasnain

et al. 2024

IEEE Access

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In this research, we present two Numerical algorithms for studying the dynamics of spatially extended coupled nonlinear reaction-diffusion model. The difference in this work is to model a system of reacting and diffusing chemicals, and how to predict the dynamics of ecologically relevant behavior, including chaos. The goal can be achieved by applying a proposed staggered grid finite volume method for solving the Reaction model, rigorously validating the numerical method and grid generation techniques against established results. Additionally, we integrate an Alternating Direction Implicit formulation to compare the efficiency and accuracy of the model's results. Dynamical system analysis, including linear stability analysis, is applied to comprehend the fundamental qualitative features of the inhibitor-activator system inherent in the coupled reaction-diffusion equations. Results, presented in tables and graphical representations, show that the schemes' high accuracy at fourth-order precision in space and second-order in time, with conditional stability. Numerical results showed that the proposed finite volume approach was exceptionally proficient and accurate for tackling the two-dimensional nonlinear coupled reactiondiffusion model. Overall, the dialog highlights the significance of the proposed staggered grid finite approach and calculations for fathoming coupled reaction-diffusion equations are widely studied in biological and chemical systems of nonlinear differential equations.

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Section: Numerical Solution Of Reaction-diffusion Model a Motivationmentioning

confidence: 95%

Dynamical Behavior of Nonlinear Coupled Reaction-Diffusion Model: A Numerical Study Utilizing ADI and Staggered Grid Finite Volume Method in Matlab

Saqib,

Akhtar,

Hasnain

et al. 2024

IEEE Access

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show abstract

“…The contribution of the new flux to the global Jacobian matrix is computed with the AD tool Tapenade [15], an open source algorithm developed by the Institut National de Recherche en Sciences et Technologies du Numérique (INRIA). AD guarantees that every derivative will be mathematically exact and will not suffer any truncation error, which is typical of the finite differences (FD) approach [40]. In fact, every derivative is obtained with a symbolic optimized differentiation of all the lines of a source code, to generate a new program that will contain the calculations for both the original outputs and their derivatives.…”

Section: Numerical Fluxes and Boundary Conditionsmentioning

confidence: 99%

On the Development of an Implicit Discontinuous Galerkin Solver for Turbulent Real Gas Flows

Mantecca

Colombo

Ghidoni

et al. 2023

Fluids

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The aim of this work is to describe an efficient implementation of cubic and multiparameter real gas models in an existing discontinuous Galerkin solver to extend its capabilities to the simulation of turbulent real gas flows. The adopted thermodynamic models are van der Waals, Peng–Robinson, and Span–Wagner, which differ from each other in terms of accuracy and computational cost. Convective numerical fluxes across elements interfaces are calculated with a thermodynamic consistent linearized Riemann solver, whereas for boundary conditions, a linearized expression of the generalized Riemann invariants is employed. Transport properties are treated as temperature- and density-dependent quantities through multiparameter correlations. An implicit time integration is adopted; Jacobian matrix and thermodynamic derivatives are obtained with the automatic differentiation tool Tapenade. The solver accuracy is assessed by computing both steady and unsteady real gas test cases available in the literature, and the effect of the mesh size and polynomial degree of approximation on the solution accuracy is investigated. A good agreement with experimental and numerical reference data is observed and specific non-classical phenomena are well reproduced by the solver.

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Using a new implementation of reproducing kernel Hilbert space method to solve a system of second-order BVPs

Amoozad,

Allahviranloo,

Abbasbandy

et al. 2023

Int. J. Dynam. Control

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Finite difference Jacobian based Newton-Krylov coupling method for solving multi-physics nonlinear system of nuclear reactor

Cited by 15 publications

References 21 publications

Dynamical Behavior of Nonlinear Coupled Reaction-Diffusion Model: A Numerical Study Utilizing ADI and Staggered Grid Finite Volume Method in Matlab

Dynamical Behavior of Nonlinear Coupled Reaction-Diffusion Model: A Numerical Study Utilizing ADI and Staggered Grid Finite Volume Method in Matlab

On the Development of an Implicit Discontinuous Galerkin Solver for Turbulent Real Gas Flows

Using a new implementation of reproducing kernel Hilbert space method to solve a system of second-order BVPs

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