Joint Optimization of the Spatial and the Temporal Discretization Scheme for Accurate Computation of Acoustic Problems (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 evaluationof the spatial derivative terms. Next, the combination of the OCCS scheme and the fivestage Runge-Kutta time integration (ORK5) scheme has been optimized to reduce numerical diffusion and dispersion error significantly. Proposed OCCS−ORK5 schemeprovides accurate solutions at considerably higher CFL number. In addition, ORK5time integration scheme consists of low storage formulation and requires less memoryas compared to the traditional Runge-Kutta schemes. Solutions of the model problems involving propagation, reflection and diffraction of acoustic waves have beenobtained to demonstrate the accuracy of the developed scheme and its applicability tosolve complex problems.