Radially Symmetrical Problems for Compressible Fluids with a High-Resolution Boundary Condition

Radially Symmetrical Problems for Compressible Fluids with a High-Resolution Boundary Condition

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

Zijin Zhu

Xiaoyan Hu

Guoxi Ni

  1. 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]