Simple a posteriori slope limiter (Post Limiter) for high resolution and efficient flow computations

A simple and efficient a posteriori slope limiter (“Post Limiter”) is proposed for compressible Navier-Stokes and Euler equations, and examined in 1D and 2D. The Post Limiter tries to employ un-limited solutions where and when possible (even at shocks), and blend the un-limited and (1st-order) limited solutions smoothly, leading to equivalently four times resolution in 1D. This idea was inspired by a posteriori limiting approaches originally developed by Clain et al. (2011) [18] for higher-order flow computations, but proposed here is an alternative suitable and simplified for 2nd-order spatial accuracy with improved both solution and convergence. In fact, any iteration processes are no longer required to determine optimal orders of accuracy, since the limited and un-limited values are available at one time at 2nd-order. In 2D, several numerical examples have been dealt with, and both the κ=1/3 MUSCL (in a structured solver) and Green-Gauss (in an unstructured solver) reconstructions demonstrated resolution improvement (nearly 4×4 times), convergence acceleration, and removal of numerical noises. Even on triangular meshes (on which least-squares reconstruction is used), the unstructured solver showed the improved solutions if cell geometries (cell-orientation angles) are properly taken into account. Therefore, the Post Limiter is readily incorporated into existing codes.