Domain decomposition methods to model heat exchanges between a well and a rock mass
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![Figure 2: Both |G RR (k)| and |G DN (k)| (top) and 1 − |G DN (k)| (bottom) as a function of k ∈ [0, k max ] obtained with Q n = 30000 nm 3 .h −1 , ∆t = 6 h and with β ff = h, β rock = DtN [ rock (0), θ given by (16)](https://thumb-eu.123doks.com/thumbv2/123doknet/13539837.418498/13.892.136.767.131.365/figure-rr-function-obtained-rock-dtn-rock-given.webp)
![Figure 4: |G RR (k)| as a function of k ∈ [0, k max ] obtained with the Robin coefficients given by a numerical approximation of the min-max problem, by the choice β rock = DtN [ rock (0), β ff = h (denoted DtN0-h) and by the choice β rock = DtN [ rock (0)](https://thumb-eu.123doks.com/thumbv2/123doknet/13539837.418498/14.892.125.766.128.579/figure-function-obtained-coefficients-numerical-approximation-problem-denoted.webp)
![Figure 5: Convergence rate (defined as the maximum of |G RR (k)| in k ∈ [0, k max ]) as a function of the normal flow rate Q n for the Robin coefficients obtained by a numerical approximation of the min-max problem (min-max), by the choice β rock = DtN [ r](https://thumb-eu.123doks.com/thumbv2/123doknet/13539837.418498/15.892.239.657.132.426/figure-convergence-defined-function-coefficients-obtained-numerical-approximation.webp)
![Figure 7: Convergence of the DDM residual (23) with one curve for each time step as a function of the cumulative number of DDM iterations for the 3D radial test case with random thermal conductivity λ rock ∈ [2, 5] W.K −1 .m −1 on the mesh 50 × 50 × 200 wi](https://thumb-eu.123doks.com/thumbv2/123doknet/13539837.418498/22.892.131.765.128.355/figure-convergence-residual-function-cumulative-iterations-thermal-conductivity.webp)
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