Multiscale Finite Element Method for heat transfer problem during artificial ground freezing

Vasilyeva, Maria; Stepanov, Sergei; Spiridonov, Denis; Васильев, В. И.

doi:10.1016/j.cam.2019.112605

Cited by 27 publications

(8 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(2a)), the temperatures and enrichment variables of control points are solved with Eq. (6). It is noted that the temperature approximation presented in Eq.…”

Section: Xiga For Steady-state Heat Transfer In Heterogeneous Mediamentioning

confidence: 99%

“…Heat transfer in heterogeneous media widely exist in many fields. Numerical simulation is an efficient method for solving the common heat transfer problem, and heat transfer problem in heterogeneous media has been investigated with various numerical methods, such as meshless method [1], discrete element method [2], finite element method [3][4][5][6] and lattice Boltzmann method [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Adaptive Extended Isogeometric Analysis for Steady-State Heat Transfer in Heterogeneous Media

Fang¹,

Yu²,

Yang³

2021

Computer Modeling in Engineering &Amp; Sciences

View full text Add to dashboard Cite

Steady-state heat transfer problems in heterogeneous solid are simulated by developing an adaptive extended isogeometric analysis (XIGA) method based on locally refined non-uniforms rational B-splines (LR NURBS). In the XIGA, the LR NURBS, which have a simple local refinement algorithm and good description ability for complex geometries, are employed to represent the geometry and discretize the field variables; and some special enrichment functions are introduced into the approximation of temperature field, thus the computational mesh is independent of the material interfaces, which are described with the level set method. Similar to the approximation of temperature field, a temperature gradient recovery technique for heterogeneous media is proposed, and based on the Zienkiewicz-Zhu recovery technique a posteriori error estimator is defined to automatically identify the locally refined regions. The convergence and performance properties of the developed method are verified by using three numerical examples. The numerical results show that (1) The convergence speed of the adaptive local refinement is faster than that of the uniform global refinement; (2) The convergence rate of the high-order basis functions is faster than that of the low-order basis functions; and (3) The existing inclusions change the local distributions of the temperature, and the extreme values of the temperature gradients take place around the inclusion interfaces.

show abstract

“…(2a)), the temperatures and enrichment variables of control points are solved with Eq. (6). It is noted that the temperature approximation presented in Eq.…”

Section: Xiga For Steady-state Heat Transfer In Heterogeneous Mediamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adaptive Extended Isogeometric Analysis for Steady-State Heat Transfer in Heterogeneous Media

Fang¹,

Yu²,

Yang³

2021

Computer Modeling in Engineering &Amp; Sciences

View full text Add to dashboard Cite

show abstract

“…So we choose the Generalized Multiscale Finite Element Method (GMsFEM [13]) as the model reduction technique here. The GMsFEM provides a systematic way of reducing the computational cost in solving various types of highly heterogeneous partial differential equations [15,16,48,11]. This method reduces the degrees of freedom of large systems by constructing appropriate multiscale basis functions, which are only needed to calculate one time.…”

Section: Gmsfemmentioning

confidence: 99%

Recovery of the time-dependent source term in the stochastic fractional diffusion equation with heterogeneous medium

Fu¹,

Zhang²

2020

Preprint

View full text Add to dashboard Cite

In this work, an inverse problem in the fractional diffusion equation with random source is considered. The measurements used are the statistical moments of the realizations of single point data u(x 0 , t, ω). We build the representation of the solution u in integral sense, then prove that the unknowns can be bounded by the moments theoretically. For the numerical reconstruction, we establish an iterative algorithm with regularized Levenberg-Marquardt type and some numerical results generated from this algorithm are displayed. For the case of highly heterogeneous media, the Generalized Multiscale finite element method (GMsFEM) will be employed.

show abstract

“…We previously created a GMsFEM algorithm with an additional basis function for artificial ground freezing [46]. We expand our technique and employ multiscale online basis functions to predict phase change in the heat and mass transfer problem with artificial ground freezing in this study.…”

Section: Introductionmentioning

confidence: 99%

An Online Generalized Multiscale finite element method for heat and mass transfer problem with artificial ground freezing

Spiridonov¹,

Степанов²,

Vasiliy³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

The Online Generalized Multiscale Finite Element Method (Online GMsFEM) is presented in this study for heat and mass transfer problem in heterogeneous media with artificial ground freezing process.The mathematical model is based on the classical Stefan model, which depicts heat transfer with a phase change and includes filtration in a porous media. The model is described by a set of temperature and pressure equations. We employ a finite element method with the fictitious domain method to solve the problem on a fine grid. We apply a model reduction approach based on Online GMsFEM to derive a solution on the coarse grid. We can use the online version of GMsFEM to take less offline multiscale basis functions. We use decoupled offline basis functions built with snapshot space and based on spectral problems in our method. This is the standard approach of basis construction. We calculate additional basis functions in the offline stage to account for artificial ground freezing pipes. We use online multiscale basis functions to get a more precise approximation of phase change. We create an online basis that reduces error using local residual values. The accuracy of standard GMsFEM is greatly improved by using an online approach. Numerical results in a two-dimensional domain with layered heterogeneity are presented. To test the method's accuracy, we show results from a variety of offline and online basis functions. The results suggest that Online GMsFEM can deliver high-accuracy solutions with minimal processing resources.

show abstract

Multiscale Finite Element Method for heat transfer problem during artificial ground freezing

Cited by 27 publications

References 14 publications

Adaptive Extended Isogeometric Analysis for Steady-State Heat Transfer in Heterogeneous Media

Adaptive Extended Isogeometric Analysis for Steady-State Heat Transfer in Heterogeneous Media

Recovery of the time-dependent source term in the stochastic fractional diffusion equation with heterogeneous medium

An Online Generalized Multiscale finite element method for heat and mass transfer problem with artificial ground freezing

Contact Info

Product

Resources

About