Quasi-linear analysis of dispersion relation preservation for nonlinear schemes

Abstract In numerical simulations of complex flows with discontinuities, it is necessary to use nonlinear schemes. The spectrum the scheme used has a significant impact on resolution and stability computation. Based approximate dispersion relation method, we combine corresponding spectral property preservation proposed by De Eswaran (J Comput Phys 218:398–416, 2006) propose quasi-linear (QL-GRP) analysis through which group velocity can be determined. particular, derive when high-order Runge–Kutta compare performance different time schemes QL-GRP. rationality QL-GRP method verified simulation discrete Fourier transform method. To further evaluate in finding velocity, new hyperbolic equations are designed. validity several investigated using two examples equation for one-dimensional wave propagation equations. results show that integrated determine their reasonably efficiently.