A truly self-starting composite isochronous integration analysis framework for first/second-order transient systems. (1st January 2023) - Wang, Yazhou; Xie, Ningning; Yin, Likun; Lin, Xinxing; Zhang, Tong; Zhang, Xuelin; Mei, Shengwei; Xue, Xiaodai; Tamma, Kumar
Highlights: A truly self-starting new representation of the ρ ∞ -Bathe method is redesigned. A new composite time integration framework is designed for first-order systems. A novel composite [ i -Integration] design applied to first/second-order systems. In-depth comparisons between the composite method and the well-known GS4 framework. Abstract: Due to the lack of and limited work done for first/second-order systems useful for multidisciplinary problems, this paper proposes a new and novel composite isochronous integration ([ i -Integration]) analysis framework to solve first/second-order transient systems via a single computational framework. The main contributions are summarized as follows: (1) The ρ ∞ -Bathe method is newly reformed to an identical truly self-starting representation with the absence of acceleration and is more efficient for practical applications; (2) The novel [ i -Integration] process is applied to automatically generate a family of time integration algorithms for first/second-order transient systems, whilst preserving features of second-order time accuracy, unconditional stability, controllable numerical dissipation in high-frequency, and truly self-starting; (3) The newly proposed algorithms design framework provides a unified toolkit to solve first/second-order transient systems in a single analysis and hence is more effective for coupled problems and numerical analysis of fluid/heat transfer/structure-type transient simulations. Numerical examples encompassing a manufactured example, the C-F heat conduction model, and the thermal stress wave problem are demonstrated to validate the proposed algorithms.