TY - JOUR
T1 - An Adaptive High Order WENO Solver for Conservation Laws
AU - Cheng Liu & Changhong Hu
JO - Communications in Computational Physics
VL - 3
SP - 719
EP - 748
PY - 2019
DA - 2019/04
SN - 26
DO - http://doi.org/10.4208/cicp.OA-2018-0059
UR - https://global-sci.org/intro/article_detail/cicp/13144.html
KW - Block-structured AMR, WENO, Euler equations, Navier-Stokes equations, large scale
computation.
AB - <p style="text-align: justify;">This paper presents an implementation of the adaptive hybrid WENO
(weighted essentially non-oscillatory) scheme based on our previous investigations
for compressible multi-medium flows (Liu and Hu, J. Comput. Phys., 342 (2017),
43-65). In this study a simple and efficient method is developed for Euler equations
and Navier-Stokes equations arising from the conservation laws. A class of high order weighted essentially non-oscillatory (WENO) schemes are applied to resolve the
complicated flow structures and shock waves. Classical WENO schemes are computationally expensive in calculating the non-linear weight and smoothness indicators. We
propose a block-structured adaptive mesh method together with a modified hybrid-WENO scheme to reduce the cost, the reconstruction is only performed at non-smooth
region. Comparisons of WENO scheme with various smoothness indicators and different Lax-Friedrich flux vector splitting methods are performed on block structured
adaptive mesh. Benchmark tests show present adaptive hybrid WENO method is low-dissipative and highly robust. The 2-D/3-D shock wave boundary layer interaction are
simulated to verify the efficiency of present AMR (adaptive mesh refinement) solver
in predicting turbulent flow</p>