Application of implicit Roe-type scheme and Jacobian-Free Newton-Krylov method to two-phase flow problems

Hu, Guojun; Kozłowski, Tomasz

doi:10.1016/j.anucene.2018.05.003

Cited by 18 publications

(8 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Numerical solutions match the analytical solution well. Assessment of the forward solver is ignored in this paper and is referred to [19].…”

Section: Resultsmentioning

confidence: 99%

“…whereF i+1/2 andF i−1/2 are low-order numerical fluxes at cell boundaries. More details of the numerical scheme can be seen in [20]. A first-order Roe-type numerical flux is constructed following the Roe-Pike [21,22] method.…”

Section: Numerical Schemementioning

confidence: 99%

“…( 5) forms a set of algebraic nonlinear equations, which is solved with the JFNK method. More details of the numerical scheme can be seen in [19].…”

Section: Numerical Schemementioning

confidence: 99%

See 2 more Smart Citations

Application of discrete adjoint method to sensitivity and uncertainty analysis in steady-state two-phase flow simulations

Kozłowski

2019

Annals of Nuclear Energy

Self Cite

View full text Add to dashboard Cite

Verification, validation and uncertainty quantification (VVUQ) have become a common practice in thermal-hydraulics analysis. An important step in the uncertainty analysis is the sensitivity analysis of various uncertainty input parameters. The efficient method for computing the sensitivities is the adjoint method. The cost of solving an adjoint equation is comparable to the cost of solving the governing equation. Once the adjoint solution is obtained, the sensitivities to any number of parameters can be obtained with little effort. There are two methods to develop the adjoint equations: continuous method and discrete method. In the continuous method, the control theory is applied to the forward governing equation and produces an analytical partial differential equation for solving the adjoint variable; in the discrete method, the control theory is applied to the discrete form of the forward governing equation and produces a linear system of equations for solving the adjoint variable. In this article, an adjoint sensitivity analysis framework is developed using both the continuous and discrete methods. These two methods are assessed with the one transient test case based on the BFBT benchmark. Adjoint sensitivities from both methods are verified by sensitivities given by the perturbation method. Adjoint sensitivities from both methods are physically reasonable and match each. The sensitivities obtained with discrete method is found to be more accurate than the sensitivities from the continuous method. The continuous method is computationally more efficient than the discrete method because of the analytical coefficient matrices and vectors. However, difficulties are observed in solving the continuous adjoint equation for cases where the adjoint equation contains sharp discontinuities in the source terms; in such cases, the continuous method is not as robust as the discrete adjoint method. arXiv:1805.08083v1 [physics.comp-ph] 18 May 2018 popular in computational fluid dynamics field [1,2]. Within the field of aeronautical computational fluid dynamics, the use of adjoint method has been seen in [3,4,5,6]. Adjoint problems arise naturally in the formulation of methods for optimal aerodynamic design and optimal error control [7,2,8,9]. Adjoint solution provides the linear sensitivities of an objective function (e.g. lift force and drag force) to a number of design variables. These sensitivities can then be used to drive an optimization procedure. In a sequence of papers, Jameson developed the adjoint method for the potential flow, the Euler equation, and the Navier-Stokes equation [3,4,5,6]. The application of the adjoint method to optimal aerodynamic design is very successful. However, to the author's best knowledge, successful adjoint sensitivity analysis to two-phase flow problems is rare. Cacuci performed an adjoint sensitivity analysis to two-phase flow problems using the RELAP5/MOD3.2 numerical discretization [10,11,12]. An application of Cacuci's method was illustrated by [13], where the method was applied to th...

show abstract

“…Numerical solutions match the analytical solution well. Assessment of the forward solver is ignored in this paper and is referred to [19].…”

Section: Resultsmentioning

confidence: 99%

Section: Numerical Schemementioning

confidence: 99%

See 1 more Smart Citation

Application of discrete adjoint method to sensitivity and uncertainty analysis in steady-state two-phase flow simulations

Kozłowski

2019

Annals of Nuclear Energy

Self Cite

View full text Add to dashboard Cite

show abstract

“…Examples of such frames are Sampler in the SCALE code system 7,8 and Paul Scherrer Institute (PSI) methodology. 15 An adjoint framework was also developed in Stripling et al 16 to perform sensitivity analysis (SA) of nuclear reactor depletion calculations (eg, time-dependent reactor calculations). 11 A new framework for adjoint-based sensitivity and uncertainty analysis of nuclear thermal-hydraulics and two-phase flow was developed by Hu and Kozlowski.…”

mentioning

confidence: 99%

“…13,14 Adjoint methods are used in tandem to determine input sensitivities, which can be used for uncertainty propagation if input covariance matrix is provided. 15 An adjoint framework was also developed in Stripling et al 16 to perform sensitivity analysis (SA) of nuclear reactor depletion calculations (eg, time-dependent reactor calculations). Depletion calculations are known to be computationally intensive, which make using Monte Carlo methods prohibitive to identify the sensitive cross-section data under reactor burnup calculations.…”

mentioning

confidence: 99%

Combining simulations and data with deep learning and uncertainty quantification for advanced energy modeling

Radaideh

Kozłowski

2019

Int J Energy Res

Self Cite

View full text Add to dashboard Cite

Summary A novel and modern framework for energy modeling is developed in this paper with a focus on nuclear energy modeling and simulation. The framework combines multiphysics simulations and real data, with validation by uncertainty quantification tasks and facilitation by machine and deep learning methods. The hybrid framework is built on the basis of a wide range of physical models, real data, mathematical and statistical methods, and artificial intelligence techniques. The framework is demonstrated in different applications, including quantifying uncertainties in computer simulations, multiphysics coupling, analysis of variance using machine learning surrogate models, deep learning of time series phenomena, and propagating parametric uncertainties of nuclear data. The applications demonstrated are oriented to nuclear engineering simulations, even though majority of the methods are applicable to other energy sources (eg, renewable). Efficient utilization of this framework is expected to yield a much better understanding of the physical phenomena analyzed as well as an improvement in the performance of the energy design/model under construction.

show abstract

Iteration acceleration methods for solving three‐temperature heat conduction equations on distorted meshes

Yu,

Chen,

Yao

2023

Numerical Methods Partial

View full text Add to dashboard Cite

This article focuses on designing efficient iteration algorithms for nonequilibrium three‐temperature heat conduction equations, which are used to formulate the radiative energy transport problem. Based on the framework of relaxation iteration, we design a new accelerated iteration algorithm by reasonable approximation of the Jacobi matrix, according to the characteristics of the discrete scheme for the three‐temperature equations. Adopting the iteration framework, we analyze the advantages and disadvantages of several iteration algorithms commonly used in practice and the new iteration algorithm. Finally, we compare the new iteration algorithm with some other iteration algorithms by solving several nonlinear models, and show that the new algorithm can achieve significant acceleration effect.

show abstract

Application of implicit Roe-type scheme and Jacobian-Free Newton-Krylov method to two-phase flow problems

Cited by 18 publications

References 23 publications

Application of discrete adjoint method to sensitivity and uncertainty analysis in steady-state two-phase flow simulations

Application of discrete adjoint method to sensitivity and uncertainty analysis in steady-state two-phase flow simulations

Combining simulations and data with deep learning and uncertainty quantification for advanced energy modeling

Iteration acceleration methods for solving three‐temperature heat conduction equations on distorted meshes

Contact Info

Product

Resources

About