A Novel Quadratic Exponential B-Spline Based Explicit Time Integration Approach With Energy Corrector Technique for Transient Heat Conduction Analysis

Abstract

This research proposes a novel single-step explicit time integration approach, which is formulated with a quadratic exponential B-spline interpolation function. To obtain enhanced solution accuracy, especially for problems with discontinuous load, the “energy corrector” technique is developed. Through theoretical analysis, four cases of algorithm parameters for the new approach are determined, which achieve high-order accuracy and desirable stability. Numerical simulation demonstrates that the new approach can provide highly precise solutions for transient heat conduction problems, especially for those with discontinuous loads. Furthermore, the new approach possesses a far larger critical stable time step than the traditional approaches, which in return improves computational efficiency greatly.