Radially Symmetrical Problems for Compressible Fluids with a High-Resolution Boundary Condition (Advances in Applied Mathematics and Mechanics, 2022)
Imposing appropriate numerical boundary conditions at the symmetricalcenter $r=0$ 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 emphasizethat because of the conservation property, the updating formula of the boundary cellaverage can coincide with the one for interior cell averages. To achieve second-orderaccuracy 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 toavoid 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 demonstratethe effectiveness and robustness of our approach.