TY - JOUR
T1 - Radially Symmetrical Problems for Compressible Fluids with a High-Resolution Boundary Condition
AU - Zhu , Zijin
AU - Hu , Xiaoyan
AU - Ni , Guoxi
JO - Advances in Applied Mathematics and Mechanics
VL - 2
SP - 428
EP - 449
PY - 2022
DA - 2022/12
SN - 15
DO - http://doi.org/10.4208/aamm.OA-2021-0340
UR - https://global-sci.org/intro/article_detail/aamm/21275.html
KW - Radially symmetrical, high-resolution, conservation, singularity, numerical boundary condition, GRP, acoustic approximation.
AB - <p style="text-align: justify;">Imposing appropriate numerical boundary conditions at the symmetrical
center $r=0$ is vital when computing compressible fluids with radial symmetry. Extrapolation and other traditional techniques are often employed, but spurious numerical oscillations or wall-heating phenomena can occur. In this paper, we emphasize
that because of the conservation property, the updating formula of the boundary cell
average can coincide with the one for interior cell averages. To achieve second-order
accuracy both in time and space, we associate obtaining the inner boundary value at $r=0$ with the resolution of the corresponding one-sided generalized Riemann problem (GRP). Acoustic approximation is applied in this process. It creates conditions to
avoid the singularity of type $1/r$ and aids in obtaining the value of the singular quantity using L&#39;Hospital&#39;s rule. Several challenging scenarios are tested to demonstrate
the effectiveness and robustness of our approach.</p>