TY - JOUR
T1 - High-Order Hybrid WCNS-CPR Schemes on Hybrid Meshes with Curved Edges for Conservation Laws I: Spatial Accuracy and Geometric Conservation Laws
AU - Huajun Zhu, Zhenguo Yan, Huayong Liu, Meiliang Mao & Xiaogang Deng
JO - Communications in Computational Physics
VL - 5
SP - 1355
EP - 1392
PY - 2018
DA - 2018/04
SN - 23
DO - http://doi.org/10.4208/cicp.OA-2017-0032
UR - https://global-sci.org/intro/article_detail/cicp/11219.html
KW - Weighted compact nonlinear scheme (WCNS), Correction procedure via reconstruction (CPR), hybrid schemes, hybrid grid, high-order accuracy.
AB - <p style="text-align: justify;">A type of hybrid WCNS and CPR method for solving conservation laws on
hybrid structured and unstructured meshes is proposed. WCNS on structured grid
is conjoined with CPR on unstructured grid through CPR on structured grid. The
main hybrid technique becomes coupling WCNS and CPR on curvilinear structured
grid. Calculation of grid metrics, interpolation methods of physical coordinates and
state variables, and computation of Riemann flux near coupling interface are designed
to maintain the expected high order accuracy and to satisfy discrete geometric conservation
laws in the whole computational domain. Third-order schemes and fifth-order
schemes are considered. Numerical simulations show that the proposed hybrid
WCNS-CPR schemes can obtain designed accuracy, satisfy geometric conservation law
and have good balance of computational efficiency and grid flexibility.</p>