Stability and Performance Analysis of the Castillo-Grone Mimetic Operators in Conjunction with RK3 Time Discretization in Solving Advective Equations

In this paper, the performance of the second- and fourth-order accurate Castillo-Grone Mimetic (CGM) gradient and divergence operator for solving advection equations, in conjunction with the RK3 time discretization scheme, is investigated. In addition, the effect of different interpolation schemes on the CGM operator's stability is also studied numerically. It has been shown that, in all cases, the CGM operators were stable for Courant numbers higher than 1, and in some cases, up to a Courant number of 1.8. Furthermore, in the case of the fourth-order accurate CGM divergence operator and linear interpolation, the amplification factor is calculated analytically using the Von Neumann stability analysis method, and the accuracy and stability of the combined CGM and RK3 scheme is also discussed.