Coupled Conduction-Convection Problems

Wrobel, L.C.

doi:10.1007/978-94-011-2902-2_5

Cited by 3 publications

(3 citation statements)

References 10 publications

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“…4 are not generally speaking small, in spite of the fact that they incorporate the small parameter H . The system (4) constitutes imperfect transmission conditions between Π , the following relation between the solution and its flux at T S was derived by means of integral transform method [11]:…”

Section: On-local Boundary Condition -Equivalent Bvpmentioning

confidence: 99%

“…which describes a mass concentration field, induced by a set of point mass sources. Boundary conditions (2) 1 , (2) 2 , (3) are to be taken in accordance with (11). Non-classical boundary condition (9) does not generally speaking satisfy (11).…”

Section: Umerical Verificationmentioning

confidence: 99%

“…Boundary conditions (2) 1 , (2) 2 , (3) are to be taken in accordance with (11). Non-classical boundary condition (9) does not generally speaking satisfy (11). For this reason, the right-hand side of ( 9) is corrected here in the following way:…”

Section: Umerical Verificationmentioning

confidence: 99%

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Numerical Modelling of Mass Transfer Problems in Combined Domains with Non-Linear Imperfect Transmission Conditions

Wróbel

Mishuris²

2009

DDF

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This work deals with a nonlinear mass transfer problem in an infinite combined domain, consisting of half-space matched to a bounded part via a thin intermediate layer. The latter exhibits high contrast material properties, whereas its thickness is assumed to be negligible in comparison with the dimensions of the bounded subdomain. The corresponding problem is reduced to an auxiliary one, defined only in the bounded region with a non-local boundary condition on the transmission surface, which is solved numerically by means of FEM. To introduce the boundary condition, a special iterative subroutine based on the classic Robin type boundary condition is constructed. The accuracy of the procedure and the range of its applicability are investigated for an analytical benchmark. Numerical results for an axisymmetrical stationary mass transfer problem are presented.

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Section: On-local Boundary Condition -Equivalent Bvpmentioning

confidence: 99%

Section: Umerical Verificationmentioning

confidence: 99%

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Numerical Modelling of Mass Transfer Problems in Combined Domains with Non-Linear Imperfect Transmission Conditions

Wróbel

Mishuris²

2009

DDF

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A non‐overlapping domain decomposition dual reciprocity method for solving the forward–backward heat equation in two‐dimension

Shanazari

Banei

2022

Numerical Methods Partial

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We apply a boundary element dual reciprocity method (DRBEM) to the numerical solution of the forward–backward heat equation in a two‐dimensional case. The method is employed for the spatial variable via the fundamental solution of the Laplace equation and the Crank–Nicolson finite difference scheme is utilized to treat the time variable. The physical domain is divided into two non‐overlapping subdomains resulting in two standard forward and backward parabolic equations. The subproblems are then treated by the underlying method assuming a virtual boundary in the interface and starting with an initial approximate solution on this boundary followed by updating the solution by an iterative procedure. In addition, we show that the time discrete scheme is unconditionally stable and convergent using the energy method. Furthermore, some computational aspects will be suggested to efficiently deal with the formulation of the proposed method. Finally, two forward–backward problems, for which the exact solution is available, will be numerically solved for two different domains to demonstrate the efficiency of the proposed approach.

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A note on the matrix analysis of Dual Reciprocity Boundary Element Method

Weng

Rahman

1995

Applied Mathematics Letters

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Coupled Conduction-Convection Problems

Cited by 3 publications

References 10 publications

Numerical Modelling of Mass Transfer Problems in Combined Domains with Non-Linear Imperfect Transmission Conditions

Numerical Modelling of Mass Transfer Problems in Combined Domains with Non-Linear Imperfect Transmission Conditions

A non‐overlapping domain decomposition dual reciprocity method for solving the forward–backward heat equation in two‐dimension

A note on the matrix analysis of Dual Reciprocity Boundary Element Method

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