A localized radial basis function-based approach for quenching phenomenon of two-dimensional semilinear wave equation

Source 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.