A gradually implicit method with deferred correction and adaptive relaxation factors for simulation to nonlinear heat transfer

摘要

A gradually implicit method with deferred correction (GIMDC) and adaptive relaxation factors (ARFs) is developed for simulation to nonlinear heat transfer with temperature-dependent properties. GIMDC is equivalent to explicit method initially and approaches implicit method gradually. The theoretical analyses of convergence, error and stability indicate that the accuracy and stability of GIMDC are close to implicit method if ARFs are utilized to guarantee convergence. A strict condition for ARFs is derived. GIMDC is compared with PEM (pure explicit method), NIM (Newton iterative method for implicit solution) and FEM (finite element method) which shows that GIMDC is of acceptable numerical accuracy (similar to NIM and 19.28% and 12.89% higher than PEM and FEM respectively in average) and higher efficiency. The numerical tests are presented which shows that using optimized ARFs (confined by strict condition), efficiency, accuracy and stability are ensured.