Novel TENO schemes with improved accuracy order based on perturbed polynomial reconstruction.

Firstly, an improved TENO scheme based on perturbed polynomial reconstruction (TENO-P) is proposed for hyperbolic conservation laws on the foundation of fifth-order TENO5 scheme. Two different free-parameters are introduced into the reconstruction coefficients to eliminate the third-order errors in the candidate stencils and the fifth-order error in the global stencil, respectively. One-order of accuracy improvement is achieved by adaptively adjusting the values of the free-parameters, resulting a maximum sixth-order accuracy in the smooth stencil. Secondly, to improve the accuracy order of the fifth-order TENO5-THINC scheme, a sixth-order TENO-THINC-P scheme is proposed by combining the proposed TENO-P scheme for smooth regions with the THINC reconstruction for non-smooth discontinuities. Compared to the TENO5 scheme and the TENO5-THINC scheme, the numerical results show the dissipations of the TENO-P scheme and the TENO-THINC-P scheme are reduced, and their resolutions are significantly improved in resolving complicated flow structures with multiple discontinuities. Taking the computational efficiency and the numerical resolution into consideration, the TENO-P scheme is suitable for resolving vortex structures of turbulence while the TENO-THINC-P scheme is more suitable for resolving vortex structures near strong discontinuities. The derivation processes of the TENO-P scheme and the TENO-THINC-P scheme also demonstrate that the perturbed polynomial reconstruction has simple principle and good portability and expandability, so the idea of the TENO-P scheme and the TENO-THINC-P scheme can be easily extended to other improved very-high-order TENO schemes or WENO schemes. • TENO schemes (TENO-P, TENO-THINC-P) with improved accuracy order are proposed by using perturbed polynomial reconstruction. • A maximum sixth-order accuracy method is obtained in smooth stencil by introducing a free-parameter in six-point stencil. • The TENO-P scheme is suitable for resolving vortex structures of turbulence. • The TENO-THINC-P scheme is more suitable for resolving vortex structures near strong discontinuities. • The perturbed polynomial reconstruction method has simple principle and good portability and expandability. [ABSTRACT FROM AUTHOR]