A high-accuracy spatiotemporal numerical manifold method with thermal DOF inheritance and its application in rock thermal fracturing analysis

In practical engineering such as deep geothermal extraction and geological disposal of nuclear waste, rock thermal fracturing typically involves large spatial scales, long time spans, and highly time-dependent loading conditions. These characteristics pose significant challenges to the accuracy and computational efficiency of numerical methods. On the basis of recently developed spatial discretization and temporal integration schemes, we propose an innovative thermal DOF inheritance strategy in which the transient temperature field is computed precisely by mapping local approximations of physical patches to Gaussian integration points and temperature loading points during the formation of the heat conduction matrix to handle crack propagation between consecutive time steps, leading to the development of a high-accuracy spatiotemporal numerical manifold method that can accurately model crack propagation under transient heat transfer conditions. Numerical examples illustrate that the proposed method achieves an effective balance between computational accuracy and efficiency when rock thermal fracturing is simulated under transient heat transfer conditions. It therefore provides a scientifically robust and engineering-oriented numerical framework for simulating rock thermal fracturing problems involving large spatial scales, long time spans, and strongly time-dependent thermal loading.