An Efficient Mapped WENO Scheme Using Approximate Constant Mapping

We present a novel mapping approach for WENO schemes through the use of an approximate constant function which is constructed by employing approximation classic signum function. The new designed to meet overall criteria proper required in design WENO-PM6 scheme. scheme was proposed overcome potential loss accuracy WENO-M developed recover optimal convergence order WENO-JS at critical points. Our mapped scheme, denoted as WENO-ACM, maintains almost all advantages including low dissipation and high resolution, while decreases number mathematical operations remarkably every process leading significant improvement efficiency. rates WENO-ACM have been shown one-dimensional linear advection equation with various initial conditions. Numerical results Euler equations Riemann problems, Mach 3 shock-density wave interaction Woodward-Colella interacting blastwaves are improved comparison obtained WENO-JS, schemes. experiments two-dimensional problems 2D problem, shock-vortex interaction, explosion double reflection forward-facing step problem modeled via two dimensional conducted demonstrate resolution effectiveness provides significantly better than slightly compared schemes, extra computational cost reduced more 83% 93%, respectively.