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A block matrix formulation for efficient g-function construction
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DOI：10.1016/j.renene.2017.12.092.png)
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Abstract
En 中文
A compact block matrix formulation allowing fast construction of the g-function of a ground heat exchanger is presented. This new formulation is nor sequential nor iterative, doesn't require use of Laplace or Fourier transform and provides a g-function by solving a single system of linear equations assembled in a block matrix system. A method to accelerate the integration of the finite-line source model based on Chebyshev polynomials is also introduced. Although it suffers from a fixed cost in terms of computational time, this approach allows to speed up the g-function assessment even further when used jointly with the block matrix formulation on large fields. By using both strategies, constructing the g-function of a ground heat exchanger composed of 50 regularly spaced boreholes can be achieved in less than half-second while committing only a small relative error. The speed and compactness of the block matrix formulation could be useful to design ground heat exchangers with optimization-based algorithms, which can require the assessment of several thousand g-functions. (C) 2018 Elsevier Ltd. All rights reserved.
Keywords:
g-function
Block matrix notation
Chebyshev polynomials
Ground heat exchanger
Finite line-source model
Convolution matrix
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