TY - JOUR
T1 - Construction of the High Order Accurate Generalized Finite Difference Schemes for Inviscid Compressible Flows
AU - Xue-Li Li, Yu-Xin Ren & Wanai Li
JO - Communications in Computational Physics
VL - 2
SP - 481
EP - 507
PY - 2018
DA - 2018/10
SN - 25
DO - http://doi.org/10.4208/cicp.OA-2017-0040
UR - https://global-sci.org/intro/article_detail/cicp/12760.html
KW - Cloud of points, high order accurate boundary treatment, high order schemes, generalized
finite difference, shock capturing.
AB - <p style="text-align: justify;">The construction of high order accurate generalized finite difference method
for inviscid compressible flows still remains an open problem in the literature. In this
paper, the high order accurate generalized finite difference schemes have been developed
based on the high order reconstruction and the high order numerical flux evaluation
on a local cloud of points. The WBAP limiter based on the secondary reconstruction
is used to suppress oscillations near discontinuities. The implementation of
high order accurate boundary conditions is of critical importance in the construction of
high order schemes. A new method is proposed for the high order accurate boundary
treatment. Several standard test cases are solved to validate the accuracy, efficiency
and shock capturing capability of the proposed high order schemes.</p>