Application of the GRP Scheme for Cylindrical Compressible Fluid Flows (Communications in Computational Physics, 2018)
This paper contributes to apply both the direct Eulerian and Lagrangiangeneralized Riemann problem (GRP) schemes for the simulation of compressible fluidflows in two-dimensional cylindrical geometry. Particular attention is paid to the treatmentof numerical boundary conditions at the symmetric center besides the zero velocity(momentum) enforced by the symmetry. The new treatment precisely describeshow the thermodynamical variables are discretized near the center using the conservationproperty. Moreover, the Lagrangian GRP scheme is verified rigorously to satisfythe properties of symmetry and conservation. Numerical results demonstrate theperformance of such treatments and the symmetry preserving property of the schemewith second order accuracy both in space and time.
Keywords: Euler equations; cylindrical geometry; the generalized Riemann problem (GRP) scheme.