Central Schemes and Second Order Boundary Conditions for 1D Interface and Piston Problems in Lagrangian Coordinates (Communications in Computational Physics, 2010)
We study high-resolution central schemes in Lagrangian coordinates for theone-dimensional system of conservation laws describing the evolution of two gasesin slab geometry separated by an interface. By using Lagrangian coordinates, the interfaceis transformed to a fixed coordinate in the computational domain and, as aconsequence, the movement of the interface is obtained as a byproduct of the numericalsolution. The main contribution is the derivation of a special equation of state to beimposed at the interface in order to avoid non-physical oscillations. Suitable boundaryconditions at the piston that guarantee second order convergence are described.We compare the solution of the piston problem to other results available in the literatureand to a reference solution obtained within the adiabatic approximation. Ashock-interface interaction problem is also treated. The results on these tests are ingood agreement with those obtained by other methods.