A novel high-order finite difference scheme is proposed based on the Weighted Compact Nonlinear Scheme (WCNS). A two-stage spatial reconstruction is implemented in each cell following the Boundary Variation Diminishing (BVD) principle, which requires the difference between reconstructed values of physical quantity at cell boundaries to be a minimum value. Generally, improvements of weighted nonlinear schemes are achieved by improving a single property of the scheme, such as dispersion and diffusion properties, nonlinear weights, and resolution. Here, they are treated in combination as candidate functions for reconstruction. The new scheme can not only retain each candidate’s own advantages, but also control viscosity of the whole scheme, and is thus applicable for various scenarios. Numerical experiments, including accuracy tests, shock tube problems and double Mach reflection, are conducted, and the results are compared with those of other single-scheme ones. Results reveal that the new scheme is capable of attaining designed accuracy in the smooth area of flow field, and suppressing spurious oscillations near shocks, so that the resolution of high wave number regions can be increased. In addition, precise wave profile can be acquired even after long-time simulation. With extensively developed numerical schemes, other new approaches could be formulated for to provide better results for strong discontinuities and multi-scale structures of compressible flows.
ZHANG Hao
,
XIE Chunhui
,
DONG Yidao
,
WANG Dongfang
,
DENG Xiaogang
. Constructing high-order finite difference scheme based on boundary variation diminishing principle[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021
, 42(S1)
: 726397
-726397
.
DOI: 10.7527/S1000-6893.2021.26397
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