Year: 2023
Author: Zijin Zhu, Xiaoyan Hu, Guoxi Ni
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 2 : pp. 428–449
Abstract
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'Hospital's rule. Several challenging scenarios are tested to demonstrate the effectiveness and robustness of our approach.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2021-0340
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 2 : pp. 428–449
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Radially symmetrical high-resolution conservation
Author Details
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A high-resolution scheme for axisymmetric hydrodynamics based on the 2D GRP solvers
Zhu, Zijin
Cui, Qingjie
Ni, Guoxi
Computers & Fluids, Vol. 264 (2023), Iss. P.105961
https://doi.org/10.1016/j.compfluid.2023.105961 [Citations: 0]