Simulation of heat transfer during soil freezing based on peridynamics
Frozen soil is a critical type of porous medium that is widespread in high-latitude and high-altitude re-gions around the world.This soil type is characterized by the freezing of pore water in cold environments,which leads to significant changes in the soil's particle structure and pore configuration.These alterations can compro-mise the structural integrity of the soil,potentially resulting in severe damage or even complete failure of soil-based engineering systems.As such,understanding the mechanical properties and deformation behaviors of fro-zen soil is crucial for the stability and safety of infrastructure in cold climates.The accurate modeling of tempera-ture fields within frozen soils is essential,as these fields directly affect the soil's deformation and mechanical properties.Heat conduction in frozen soil is complicated by phase transitions,particularly the conversion of liq-uid pore water to solid ice at temperatures below the freezing point.This phase transition introduces substantial nonlinearity and discontinuity into the heat conduction problem,which poses significant challenges for tradition-al modeling approaches.Conventional heat transfer models,which rely on continuity assumptions and local par-tial differential equations(PDEs),frequently encounter computational singularities,leading to inaccuracies or instability in predictions.To address these challenges,this paper introduces an innovative numerical approach known as the Differential Operator of Near-Field Dynamics(PDDO).PDDO is a sophisticated non-local opera-tor derived from partial differential(PD)non-local theory and the orthogonality of PD functions.Unlike tradi-tional local PDE methods,PDDO defines the local derivative of any order for a material point as a non-local inte-gral expression within the local space or time domain.This transformation of partial differential equations into non-local integral forms effectively resolves the singularity issues associated with phase transitions,enhancing the accuracy and stability of numerical simulations.The research applies the PDDO method to develop a phase transition heat transfer model based on the enthalpy approach.This model is used to conduct detailed numerical simulations of heat conduction processes in one-dimensional and two-dimensional frozen soil scenarios.Various near-field ranges are systematically tested to identify the optimal range for achieving high precision in simula-tions.The results indicate that PDDO significantly outperforms traditional methods,providing more accurate and stable solutions to the nonlinearity and discontinuity challenges inherent in phase transition problems.Addi-tionally,the study extends the application of PDDO to simulate heat conduction in two-dimensional phase change materials,successfully capturing temperature variations and phase transition behaviors.The accuracy of these simulations validates PDDO's effectiveness in predicting temperature changes during phase transitions,demonstrating its robustness and applicability in handling complex material behaviors.Moreover,the paper in-vestigates the freezing process in two-dimensional soil under various freezing temperatures.The simulations ac-curately capture the phase transition temperature and highlight the distinctive plateau characteristics of the phase transition temperature,which is critical for understanding soil behavior under freezing conditions.This aspect of the research underscores the reliability and practical applicability of the PDDO-based simulation method in pre-dicting frozen soil behavior across a range of temperature conditions.In conclusion,the frozen soil heat conduc-tion simulation method based on PDDO presented in this paper represents a significant advancement in the analy-sis and modeling of frozen soil and phase transition phenomena.This method offers both theoretical and practi-cal improvements,providing a robust tool for accurately predicting the behavior of frozen soils in cold environ-ments.By overcoming the limitations of conventional approaches,PDDO enhances the precision and stability of simulations,thereby improving the design,safety,and stability of engineering projects in challenging frozen soil conditions.The findings and advancements from this research are expected to make a substantial contribu-tion to the development of more reliable and effective engineering solutions for managing and utilizing frozen soils,ultimately benefiting a range of applications from infrastructure development to environmental manage-ment in cold regions.
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