Title: An Adaptive Characteristic-wise Reconstruction WENOZ scheme for Gas Dynamic Euler Equations,
Abstract: Due to its excellent shock-capturing capability and high resolution, the WENO
scheme family has been widely used in varieties of compressive flow simulation.
However, for problems containing strong shocks and contact discontinuities,
such as the Lax shock tube problem, the WENO scheme still produces numerical
oscillations. To avoid such numerical oscillations, the characteristic-wise
construction method should be applied. Compared to component-wise
reconstruction, characteristic-wise reconstruction leads to much more
computational cost and thus is not suite for large scale simulation such as
direct numeric simulation of turbulence. In this paper, an adaptive
characteristic-wise reconstruction WENO scheme, i.e. the AdaWENO scheme, is
proposed to improve the computational efficiency of the characteristic-wise
reconstruction method. The new scheme performs characteristic-wise
reconstruction near discontinuities while switching to component-wise
reconstruction for smooth regions. Meanwhile, a new calculation strategy for
the WENO smoothness indicators is implemented to reduce over-all computational
cost. Several one dimensional and two dimensional numerical tests are performed
to validate and evaluate the AdaWENO scheme. Numerical results show that
AdaWENO maintains essentially non-oscillatory flow field near discontinuities
as the characteristic-wise reconstruction method. Besieds, compared to the
component-wise reconstruction, AdaWENO is about 40\% faster which indicates its
excellent efficiency.