An error parameter in TLM diffusion modelling

Gui, Xiang; Webb, Paul W.; Cogan, Donard de

doi:10.1002/jnm.1660050207

Cited by 30 publications

(22 citation statements)

References 6 publications

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“…, and R d (x) satisfy Equations (10), (7), and (8), then the fourth term in Equation (2) becomes (10) and (11) gives the distributed inductance in terms of u…”

Section: The Methodsmentioning

confidence: 99%

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A transmission line modelling (TLM) method for steady‐state convection–diffusion

Kennedy

O’Connor

2007

Numerical Meth Engineering

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SUMMARYThis paper describes how the lossy transmission line modelling (TLM) method for diffusion can be extended to solve the convection-diffusion equation. The method is based on the correspondence between the convection-diffusion equation and the equation for the voltage on a lossy transmission line with properties varying exponentially over space. It is unconditionally stable and converges rapidly to highly accurate steady-state solutions for a wide range of Peclet numbers from low to high. The method solves the non-conservative form of the convection-diffusion equation but it is shown how it can be modified to solve the conservative form. Under transient conditions the TLM scheme exhibits significant numerical diffusion and numerical convection leading to poor accuracy, but both these errors go to zero as a solution approaches steady state.

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“…, and R d (x) satisfy Equations (10), (7), and (8), then the fourth term in Equation (2) becomes (10) and (11) gives the distributed inductance in terms of u…”

Section: The Methodsmentioning

confidence: 99%

“…This is equivalent to the one-dimensional diffusion equation with one extra term (the third term in (1)). If this (wave propagation) term is negligible then solving for the voltage on a lossy TL is equivalent to solving the diffusion equation [6][7][8]. This is the basis for the TLM method for modelling diffusion.…”

Section: Introductionmentioning

confidence: 99%

A transmission line modelling (TLM) method for steady‐state convection–diffusion

Kennedy

O’Connor

2007

Numerical Meth Engineering

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“…and solution of the parabolic equation has generally been accomplished by the parameterization of the TLM network and choice of a suitably short timestep [4][5][6][7] so that the second term on the right-hand side of Equation (1) is negligible. In the traditional TLM description, a pulse incident on any node via the link transmission lines is scattered in accordance with the scattering matrix equation…”

Section: Review Of the Operation Of The Tlm Algorithm In Heat Transfementioning

confidence: 99%

TLM nodal state estimator: An alternative method of initializing a two‐dimensional diffusion model

Koay

Wilkinson

Pulko

2008

Int J Numerical Modelling

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SUMMARYThe transmission line matrix (TLM) method is an established technique for modelling thermal transients in heat transfer systems. However, initial and boundary conditions have always been slightly problematic, particularly when the boundary condition is specified as a temperature (Transmission Line Matrix (TLM) Techniques for Diffusion Applications. Gordon & Breach: London, 1998), for example, when the body of interest is suddenly exposed to a different temperature on its surface. In such a case the modelled solution contains additional dynamics that are associated with the two sub-meshes in the TLM network and the two timesteps necessary for the temperature change to be fully communicated. These initialization problems are related to the fact that the boundary temperature in merely imposed as a fixed value on the network; the fundamental information-carrying quantity, on the other hand, is the pulse, the thermal state of the body being represented by the distribution of pulses. Here, we aim to provide an alternative initialization approach, using nodal state estimation to derive pulse distributions from boundary and initial conditions specified by temperature. Consideration is given to the accuracy of the estimator by comparison with the first timestep solution proposed by Enders (Int. J. Numer. Model. 2002; 15:251-259).

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“…In solving diffusion processes using TLM the magnitude of the second term on the right-hand side of Equation (1) has been rendered negligible by use of a suitably short timestep [2][3][4]. However, heat transfer in some materials is better described by the hyperbolic heat conduction equation, which is [5,6] …”

Section: Introductionmentioning

confidence: 99%

TLM representation of the hyperbolic heat conduction equation

Pulko

Wilkinson

Saïdane

2002

Int J Numerical Modelling

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SUMMARYMany heat transfer situations are adequately described by the parabolic thermal diffusion equation. However, in situations in which very rapid heating occurs or in slower heating regimes for particular materials, the hyperbolic heat conduction equation is a better representation. Here, a parameterized nodal structure for transmission line modelling (TLM) representation of hyperbolic heat conduction processes is devised. A TLM model based on the nodal structure is implemented and temperature field predicted by the model are compared with analytical results for the same physical situation.

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An error parameter in TLM diffusion modelling

Cited by 30 publications

References 6 publications

A transmission line modelling (TLM) method for steady‐state convection–diffusion

A transmission line modelling (TLM) method for steady‐state convection–diffusion

TLM nodal state estimator: An alternative method of initializing a two‐dimensional diffusion model

TLM representation of the hyperbolic heat conduction equation

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