Problem-independent nonlinear switch for newly designed WENO-BO-Z scheme

Abstract

The uniformly third-order WENO-BO-Z scheme has been proposed previously in an attempt to restore third-order accuracy at the second-order critical point via the reduction of nonlinear dissipation followed by the modification of nonlinear weights as well as to improve the intermediate bandwidth property of the linear optimal stencil of the classical WENO-JS scheme with respect to both dispersion and dissipation. However, a problem-dependent nonlinear switch was employed to turn on in the intermediate range of wavenumbers to avoid unnecessary nonlinear adaption of the WENO scheme and was mainly dependent on the trial-and-error threshold value of a switch parameter. In order to avoid the problem-dependent nature of this switch, a problem-independent nonlinear switch is suggested and investigated in this work. Benchmark problems, ranging from non-broadband to broadband, are solved using the WENO-BO-Z scheme, and a comparison of the suggested switch with the problem-dependent switch is made.