Journal:International Journal of Numerical Methods for Heat & Fluid Flow
Abstract:Purpose Semilinear wave equations with different source terms describe acoustic wave motion in fluids, shock wave formation that decelerates fluid from supersonic to subsonic speeds and quenching phenomena in micro-electro mechanical systems devices with fluid mechanical applications. This paper aims to investigate the quenching behavior of numerical solutions for a two-dimensional semilinear wave equation with an inverse power law term. Design/methodology/approach The localized radial basis function-generated finite difference (RBF-FD) method is used for approximating numerical solutions in space, and the finite difference scheme is used for temporal discretization. A discrete energy analysis is conducted to evaluate the local stability of the developed numerical scheme. Findings The energy functional of the classical solution is defined. The numerical results demonstrate finite-time quenching, and the influence of various parameters is assessed through detailed numerical simulation. Originality/value An RBF-FD approach is applied to confront the quenching phenomena in one- and two-dimensional cases. Stability and the computational performance of the proposed numerical scheme are verified numerically. The impact of various parameters and domains on quenching time is studied in detail.
Co-author:Shreya Singh, Riya Kumari Burman, Rajesh K. Pandey*, Yufeng Xu
Indexed by:Journal paper
Discipline:Natural Science
First-Level Discipline:Mathematics
Document Type:J
Volume:2026
Page Number:1--32
Translation or Not:no
Included Journals:SCI
Links to published journals:https://doi.org/10.1108/HFF-11-2025-0872