Application of the GRP scheme for cylindrical compressible fluid flows

This paper contributes to apply both the direct Eulerian and Lagrangian generalized Riemann problem (GRP) schemes for the simulation of compressible fluid flows in two-dimensional cylindrical geometry. Particular attention is paid to the treatment of numerical boundary conditions at the symmetric center besides the zero velocity (momentum) enforced by the symmetry. The new treatment precisely describes how the thermodynamical variables are discretized near the center using the conservation property. Moreover, the Lagrangian GRP scheme is verified rigorously to satisfy the properties of symmetry and conservation. Numerical results demonstrate the performance of such treatments and the symmetry preserving property of the scheme with second order accuracy both in space and time.