A New Mapped WENO Scheme Using Order-Preserving Mapping (Communications in Computational Physics, 2022)
Existing mapped WENO schemes can hardly prevent spurious oscillationswhile preserving high resolutions at long output times. We reveal in this paper the essential reason of such phenomena. It is actually caused by that the mapping functionin these schemes can not preserve the order of the nonlinear weights of the stencils.The nonlinear weights may be increased for non-smooth stencils and be decreased forsmooth stencils. It is then indicated to require the set of mapping functions to be order-preserving in mapped WENO schemes. Therefore, we propose a new mapped WENOscheme with a set of mapping functions to be order-preserving which exhibits a remarkable advantage over the mapped WENO schemes in references. For long outputtime simulations of the one-dimensional linear advection equation, the new schemehas the capacity to attain high resolutions and avoid spurious oscillations near discontinuities meanwhile. In addition, for the two-dimensional Euler problems with strongshock waves, the new scheme can significantly reduce the numerical oscillations.
Keywords: Mapped WENO; order-preserving mapping; hyperbolic problems.