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

Imposing appropriate numerical boundary conditions at the symmetrical center r = 0 is vital when computing compressible fluids with radial symmetry. Ex-trapolation and other traditional techniques are often employed, but spurious numer-ical 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 prob-lem (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 quan-tity using L'Hospital's rule. Several challenging scenarios are tested to demonstrate the effectiveness and robustness of our approach.

Automated summary

Imposing appropriate numerical boundary conditions at the symmetrical center r = 0 is crucial for computing compressible fluids with radial symmetry. This paper highlights the conservation property, which allows the updating formula for the boundary cell average to coincide with the one for interior cell averages. To achieve second-order accuracy in time and space, the inner boundary value at r = 0 is obtained through the resolution of the corresponding one-sided generalized Riemann problem (GRP), using acoustic approximation and L'Hospital's rule to avoid singularity and obtain the value of the singular quantity. Several challenging scenarios are tested to demonstrate the effectiveness and robustness of this approach.