An Oscillation-Free Bound-Preserving Discontinuous Galerkin Method for Multi-component Chemically Reacting Flows

This paper develops an oscillation-free discontinuous Galerkin (OFDG) method for solving the multi-component chemically reacting flows. Two common governing equations are considered: reactive Euler equations and Navier–Stokes equations. Based on our recently developed high-order bound-preserving discontinuous Galerkin method in Du and Yang (J Comput Phys 469:111548, 2022), we add an extra damping term into this scheme to control the spurious oscillations. With the careful construction of the damping term, the proposed method not only achieves non-oscillatory property without sacrificing any order of accuracy but also preserves the conservative property which is the key ingredient of the bound-preserving technique developed in Du and Yang (2022). Therefore, the proposed OFDG method is well-compatible with the bound-preserving limiter in Du and Yang (2022). Similar to Liu et al. (SIAM J Sci Comput 44:A230–A259, 2022), the conservative modified exponential Runge–Kutta method is used to relax the restriction of time step sizes and preserve the conservative property of the fully discrete schemes. Numerical experiments, including one- and two-dimensional space, demonstrate the proposed method has desired properties.