Solution of Partial Differential Equations with a Resistance Network Analogue

Liebmann, G.

doi:10.1088/0508-3443/1/4/303

Cited by 121 publications

(13 citation statements)

References 8 publications

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“…This yielded a network with the highest node density near the well, where the head loss was greatest, and a decreasing node density toward the outer reaches of the system. For a more detailed discussion of graded networks for representing axisymmetric flow systems, see Liebmann [1950] and Bouwer [1960].…”

Section: Evaluation Of Rementioning

confidence: 99%

A slug test for determining hydraulic conductivity of unconfined aquifers with completely or partially penetrating wells

Bouwer¹,

Rice²

1976

Water Resources Research

1,036

854

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Section: Evaluation Of Rementioning

confidence: 99%

A slug test for determining hydraulic conductivity of unconfined aquifers with completely or partially penetrating wells

Bouwer¹,

Rice²

1976

Water Resources Research

1,036

854

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“…The resistive grid was early used to explore some physical problems, such as solution of partial differential equations [13], or mobile robot path planning [27]. In robot path planning, a collision-free environment can be modelled with a resistive grid of uniform resistance, and obstacles are represented by regions of infinite resistance.…”

Section: Simulated Circuitsmentioning

confidence: 99%

The Electron in the Maze

Ayrinhac

2018

Emergence, Complexity and Computation

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“…Flow resistances are commonly used when modeling flow through pipes in fluid systems, as well. Resistance network analogs have also been used in solving other PDE systems, such as in electromagnetic problems [19].…”

Section: A Resistance Network Model For Analyzing Complex Channel Geomentioning

confidence: 99%

Topological design of channels for squeeze flow optimization of thermal interface materials

Bajaj

Subbarayan

Garimella

2012

International Journal of Heat and Mass Transfer

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Performance of thermal interface materials (TIMs) used between a microelectronic device and its associated heat spreader is largely dependent on the bulk thermal conductivity of the TIM, but the bond-line thickness (BLT) of the applied material as well as the interfacial contact resistances are also significant contributors to overall performance. Hierarchically Nested Channels (HNCs), created by modifying the surface topology of the chip or the heatsink with hierarchical arrangements of microchannels in order to improve flow, have been proposed to reduce both the required squeezing force and the final BLT at the interfaces. In the present work, a topological optimization framework that enables the design of channel arrangements is developed. The framework is based on a resistance network approximation to Newtonian squeeze flow. The approximation, validated against finite element (FE) solutions, allows efficient, design-oriented solutions for squeeze flow in complex geometries. A comprehensive design sensitivity analysis exploiting the resistance network approximation is also developed and implemented. The resistance approximation and the sensitivity analysis is used to build an automated optimal channel design framework. A Pareto optimal problem formulation for the design of channels is posed and the optimal solution is demonstrated using the framework.

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Solution of Partial Differential Equations with a Resistance Network Analogue

Cited by 121 publications

References 8 publications

A slug test for determining hydraulic conductivity of unconfined aquifers with completely or partially penetrating wells

A slug test for determining hydraulic conductivity of unconfined aquifers with completely or partially penetrating wells

The Electron in the Maze

Topological design of channels for squeeze flow optimization of thermal interface materials

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