Decomposition and coupling of soil domain for modeling vertical ground heat exchangers using the state model size reduction technique

Numerical modeling of the ground heat exchangers requires important computational resources to accurately reproduce the short-time thermal responses over a long-time period. Considering geometries of the vertical ground heat exchanger, domain decomposition is proposed in the vertical and horizontal directions. As the principal direction of the heat transfer in such a system is horizontal and here the cumbersome finite element method in treating the domain decomposition is adopted, only the horizontal soil domain case is investigated in this work. A new type of boundaries to decomposed sub-zones is proposed, and then a restitution method is developed to keep all the matrix terms inherent in initial matrices ahead of decomposition. The state model size reduction technique is used for each sub-zone model to reduce the model size, and then the reduced models are regrouped into a single state model using the new proposed coupling method. Results show that the developed decomposition and coupling methods are pertinent with negligible errors (less than 0.005 °C for the maximum), and the final reduced model gives acceptable results for typical purposes of geothermal simulations. From some sensitivity tests, it is found that accuracy of the reduced model can be systematically improved by increasing the reduced order or the number of sub-zones. The proposed model is remarkably faster than the reference model (more than 300 times), implying that a detailed 3-D numerical model can be used for long-time simulations.