Dispersion analysis of Robert–Asselin type filters for linear non-dispersive and dispersive systems

• Dispersion relation preserving analysis of Robert–Asselin type filters.
• Robustness and computational cost of RA type filters for time dependent systems.
• Effect of spurious mode on numerical solutions of dispersive/non-dispersive systems.
• Comparison with two time-level time advancement methods.

The present paper deals with the dispersion relation preserving (DRP) analysis of the Robert–Asselin type filters coupled with leapfrog time integration method for time dependent non-dispersive and dispersive model systems. As, leapfrog time advancement method is widely used in the numerical modeling of atmosphere and ocean dynamics, despite the fact that in addition to physical mode it also admits a spurious mode. This is the major disadvantage of leapfrog time integration scheme in discrete computing. To suppress the spurious mode associated with leapfrog time integration method, Robert–Asselin type filters are extensively used in the literature. Here, the dispersion analysis is based on the spectral analysis by considering filtered/unfiltered leapfrog time integration method along with spatial discretization schemes. Spatial discretization is performed using second order centered difference and optimized compact schemes. Furthermore, to assess the efficacy of these methods one dimensional convection equation is used as a model equation for the non-dispersive case, while linearized rotating shallow water equations (LRSWE), as a model test problem for the dispersive case.