A mixed-type modal discontinuous Galerkin approach for solving nonlinear reaction diffusion equations

Abstract

In this study, a mixed-type modal discontinuous Galerkin (DG) algorithm is utilized to simulate the nonlinear reaction-diffusion (RD) equations which describe miscellaneous physical phenomena involving in chemical processes, nuclear reactions, neutron multiplication etc. The current method is based on the concept of introducing an auxiliary unknown in the high or-der derivative diffusion term. The third-order scaled Legendre polynomials are adopted for DG spatial discretization, while the third-order strong stability preserving (SSP) Runge-Kutta scheme is employed for a temporal marching algorithm. To verify the accuracy and reliability of the present DG scheme, three well-known numerical problems are solved. The present DG scheme yields the stable solutions and also shows a good choice to some substituting numerical schemes for approximating the nonlinear RD equations.