TY - JOUR
T1 - High Order Well-Balanced Weighted Compact Nonlinear Schemes for the Gas Dynamic Equations under Gravitational Fields
AU - Zhen Gao & Guanghui Hu
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 697
EP - 713
PY - 2018
DA - 2018/02
SN - 7
DO - http://doi.org/10.4208/eajam.181016.300517g
UR - https://global-sci.org/intro/article_detail/eajam/10714.html
KW - Euler equations, gravitational fields, source term, steady state solution, weighted compact nonlinear Scheme.
AB - <p style="text-align: justify;">In this study, we propose a high order well-balanced weighted compact nonlinear
(WCN) scheme for the gas dynamic equations under gravitational fields. The proposed
scheme is an extension of the high order WCN schemes developed in (S. Zhang,
S. Jiang, C.-W Shu, J. Comput. Phys. 227 (2008) 7294-7321). For the purpose of maintaining
the exact steady state solution, the well-balanced technique in (Y. Xing, C.-W
Shu, J. Sci. Comput. 54 (2013) 645-662) is employed to split the source term into two
terms. The proposed scheme can maintain the isothermal equilibrium solution exactly,
genuine high order accuracy and resolve small perturbations of the hydrostatic balance
state on the coarse meshes. Furthermore, in order to capture the strong discontinuities
and large gradients, the fifth-order upwind weighted nonlinear interpolations together
with the fourth/sixth order cell-centered compact schemes with local characteristic projections
are used to construct different WCN schemes. Several representative one- and
two-dimensional examples are simulated to demonstrate the good performance of the
proposed schemes.</p>