(untitled) (Communications in Computational Physics, 2018)
Here, a physical dispersion relation preserving (DRP) scheme has been developed by combined optimization of the spatial and the multi-stage temporal discretization scheme to solve acoustics problems accurately. The coupled compact difference scheme (CCS) has been spectrally optimized (OCCS) for accurate evaluation of the spatial derivative terms. Next, the combination of the OCCS scheme and the five stage Runge-Kutta time integration (ORK5) scheme has been optimized to reduce numerical diffusion and dispersion error significantly. Proposed OCCS−ORK5 scheme provides accurate solutions at considerably higher CFL number. In addition, ORK5 time integration scheme consists of low storage formulation and requires less memory as compared to the traditional Runge-Kutta schemes. Solutions of the model problems involving propagation, reflection and diffraction of acoustic waves have been obtained to demonstrate the accuracy of the developed scheme and its applicability to solve complex problems.