Very high-order accurate polygonal mesh finite volume scheme for conjugate heat transfer problems with curved interfaces and imperfect contacts

Costa, Ricardo; Nóbrega, J. M.; Clain, Stéphane; Machado, Gaspar J.

doi:10.1016/j.cma.2019.07.029

Cited by 21 publications

(12 citation statements)

References 68 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…General boundary conditions are handled without differentiation, and the method was later extended for heat transfer problems with discontinuous coefficients and solutions on curved interfaces. 73 In that regard, problems with perfect contacts, imposing the temperature continuity and normal conductive heat flux conservation, or imperfect contacts, resulting in temperature discontinuity, were addressed and correctly verified. Comprehensive numerical benchmarks proved that the proposed method is very versatile in solving several situations of conjugate heat transfer and effectively achieves up to the sixth-order of convergence.…”

Section: Conjugate Heat Transfer Modelingmentioning

confidence: 97%

“…The discretization of the conjugate heat transfer problem follows the main ideas proposed in Costa et al, 73 which are herein adapted and applied for the case study of the thermoplastic sheet extrusion cooling stage. The conjugate heat transfer problem is treated as two individual subproblems of heat transfer in each subdomain, and the interface conditions are treated as boundary conditions prescribed on each side of the interface.…”

Section: Generic Finite Volume Formulationmentioning

confidence: 99%

See 1 more Smart Citation

High‐order accurate conjugate heat transfer solutions with a finite volume method in anisotropic meshes with application in polymer processing

Costa

Nóbrega

Clain

et al. 2021

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

The computational modeling has become an indispensable tool to support the engineering design and control of many industrial processes. In polymer processing applications, the simulation of conjugate heat transfer phenomena is critical as rigorous temperature control is necessary to ensure that the produced parts meet the required specifications. In this article, a high-order accurate finite volume method is proposed to improve the numerical accuracy and the computational efficiency of conjugate heat transfer simulations with application in polymer processing. Anisotropic meshes are investigated to significantly reduce the number of unknowns in convection-dominated problems where the higher temperature variations occur perpendicularly to curved boundaries and interfaces. The reconstruction for off-site data method based on polynomial reconstructions is employed to fulfill the prescribed boundary and interface conditions solely using polygonal meshes to avoid the limitations of curved mesh approaches. A code verification benchmark based on manufactured solutions proves that the proposed method provides a fourth-order of convergence and is computationally more cost-effective than the classical second-order of convergence. Moreover, meshes with higher aspect ratios improve the calculation efficiency but suffer from a small accuracy penalty due to conditioning deterioration. Comparison with the classical finite volume discretization techniques, widely implemented in commercial and open-source software packages, is also provided. The applicability and performance of the proposed method are further supported with a practical case study for the sheet extrusion cooling stage. K E Y W O R D Sanisotropic polygonal meshes, conjugate heat transfer problems, curved boundaries and interfaces, high-order accurate finite volume method, OpenFOAM® software, polymer processing applications 1146

show abstract

Section: Conjugate Heat Transfer Modelingmentioning

confidence: 97%

Section: Generic Finite Volume Formulationmentioning

confidence: 99%

High‐order accurate conjugate heat transfer solutions with a finite volume method in anisotropic meshes with application in polymer processing

Costa

Nóbrega

Clain

et al. 2021

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…The study of transfer heat problems between different substances, for instance, solids of different types or solids and fluids, are considered by several researchers [15][16][17][18][19][20][21][22][23]. The motivations are of different types: simple examples, analytical solutions, creation of mathematical models, different applications, theoretical study, and numerical simulations [15].…”

Section: Introductionmentioning

confidence: 99%

A Numerical Method for a Heat Conduction Model in a Double-Pane Window

Coronel

Huancas

Lozada

et al. 2022

Axioms

View full text Add to dashboard Cite

In this article, we propose a one-dimensional heat conduction model for a double-pane window with a temperature-jump boundary condition and a thermal lagging interfacial effect condition between layers. We construct a second-order accurate finite difference scheme to solve the heat conduction problem. The designed scheme is mainly based on approximations satisfying the facts that all inner grid points has second-order temporal and spatial truncation errors, while at the boundary points and at inter-facial points has second-order temporal truncation error and first-order spatial truncation error, respectively. We prove that the finite difference scheme introduced is unconditionally stable, convergent, and has a rate of convergence two in space and time for the L∞-norm. Moreover, we give a numerical example to confirm our theoretical results.

show abstract

“…Several techniques have been recently developed in the unstructured mesh context to preserve the optimal order. We refer to [1,2,3] for a recent review.…”

Section: Introductionmentioning

confidence: 99%

“…The main idea consists in elaborating a mathematical object (a polynomial function for instance) that catches all the information about the location and the boundary condition we shall insert in the numerical scheme. For example, in the finite volume context, the boundary information is converted into flux on the interface edges [1,2]. We tag the method "Reconstruction Off-site Data" (ROD) to highlight the transfer of information located on the physical boundary and not on the grid (Off-site Data) into a polynomial (Reconstruction).…”

Section: Introductionmentioning

confidence: 99%

Very high-order Cartesian-grid finite difference method on arbitrary geometries

Clain,

Lopes,

Pereira

2020

Preprint

Self Cite

View full text Add to dashboard Cite

An arbitrary order finite difference method for curved boundary domains with Cartesian grid is proposed. The technique handles in a universal manner Dirichlet, Neumann or Robin condition. We introduce the Reconstruction Off-site Data (ROD) method, that transfers in polynomial functions the information located on the physical boundary. Three major advantages are: (1) a simple description of the physical boundary with Robin condition using a collection of points; (2) no analytical expression (implicit or explicit) is required, particularly the ghost cell centroids' projection are not needed; (3) we split up into two independent machineries the boundary treatment and the resolution of the interior problem, coupled by the the ghost cell values. Numerical evidences based on the simple 2D convection-diffusion operators are presented to prove the ability of the method to reach at least the 6th-order with arbitrary smooth domains.

show abstract

Very high-order accurate polygonal mesh finite volume scheme for conjugate heat transfer problems with curved interfaces and imperfect contacts

Cited by 21 publications

References 68 publications

High‐order accurate conjugate heat transfer solutions with a finite volume method in anisotropic meshes with application in polymer processing

High‐order accurate conjugate heat transfer solutions with a finite volume method in anisotropic meshes with application in polymer processing

A Numerical Method for a Heat Conduction Model in a Double-Pane Window

Very high-order Cartesian-grid finite difference method on arbitrary geometries

Contact Info

Product

Resources

About