Central Schemes and Second Order Boundary Conditions for 1D Interface and Piston Problems in Lagrangian Coordinates

Central Schemes and Second Order Boundary Conditions for 1D Interface and Piston Problems in Lagrangian Coordinates

Year:    2010

Communications in Computational Physics, Vol. 8 (2010), Iss. 4 : pp. 797–822

Abstract

We study high-resolution central schemes in Lagrangian coordinates for the one-dimensional system of conservation laws describing the evolution of two gases in slab geometry separated by an interface. By using Lagrangian coordinates, the interface is transformed to a fixed coordinate in the computational domain and, as a consequence, the movement of the interface is obtained as a byproduct of the numerical solution. The main contribution is the derivation of a special equation of state to be imposed at the interface in order to avoid non-physical oscillations. Suitable boundary conditions at the piston that guarantee second order convergence are described. We compare the solution of the piston problem to other results available in the literature and to a reference solution obtained within the adiabatic approximation. A shock-interface interaction problem is also treated. The results on these tests are in good agreement with those obtained by other methods.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.310109.220110a

Communications in Computational Physics, Vol. 8 (2010), Iss. 4 : pp. 797–822

Published online:    2010-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    26

Keywords:   

  1. Finite difference schemes on quasi-uniform grids for BVPs on infinite intervals

    Fazio, Riccardo | Jannelli, Alessandra

    Journal of Computational and Applied Mathematics, Vol. 269 (2014), Iss. P.14

    https://doi.org/10.1016/j.cam.2014.02.036 [Citations: 22]
  2. Numerical validation of homogeneous multi-fluid models

    Phan, Duyen T.M. | Gavrilyuk, Sergey L. | Russo, Giovanni

    Applied Mathematics and Computation, Vol. 441 (2023), Iss. P.127693

    https://doi.org/10.1016/j.amc.2022.127693 [Citations: 0]
  3. Progress in Exergy, Energy, and the Environment

    Numerical Simulation of 1-D Compression Stroke Using Smoothed Particle Hydrodynamics

    El-Gammal, Tarek | Khalil, Essam Eldin | Haridy, Hatem | Abo-Serie, Essam

    2014

    https://doi.org/10.1007/978-3-319-04681-5_61 [Citations: 0]