A high-order pathline Godunov scheme for unsteady one-dimensional equilibrium flows Original Research Article

A time-marching Godunov-type method using control cells consisted of particle pathlines and the coordinate lines is described for the computation of unsteady, quasi-one-dimensional equilibrium flows. An unsteady Riemann problem and its solution for equilibrium gases is described and used in the Godunov method. Tannehillʹs equilibrium air program is used to calculate the equilibrium gas properties. The pathline meshes are automatically solution generated. The use of particle pathline meshes enables a crisp resolution of contact discontinuities and simplifies the Godunov solution procedure. The present particle pathline mesh method shares the same desirable features of Lagrangian description but using an Eulerian description. Extensive computations of various unsteady quasi-one-dimensional equilibrium flows with constant and variable area distribution are included to illustrate the method. Application to a high-temperature shock tube with conical flare indicates that this pathline Godunov method can be useful for estimating the reservoir conditions and the effective time duration for the reflection shock tunnel.