Volume 8, Issue 4
Central Schemes and Second Order Boundary Conditions for 1D Interface and Piston Problems in Lagrangian Coordinates

Riccardo Fazio & Giovanni Russo

Commun. Comput. Phys., 8 (2010), pp. 797-822.

Published online: 2010-08

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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.

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@Article{CiCP-8-797, author = {Riccardo Fazio and Giovanni Russo}, title = {Central Schemes and Second Order Boundary Conditions for 1D Interface and Piston Problems in Lagrangian Coordinates}, journal = {Communications in Computational Physics}, year = {2010}, volume = {8}, number = {4}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.310109.220110a}, url = {http://global-sci.org/intro/article_detail/cicp/7595.html} }
TY - JOUR T1 - Central Schemes and Second Order Boundary Conditions for 1D Interface and Piston Problems in Lagrangian Coordinates AU - Riccardo Fazio & Giovanni Russo JO - Communications in Computational Physics VL - 4 SP - 797 EP - 822 PY - 2010 DA - 2010/08 SN - 8 DO - http://dor.org/10.4208/cicp.310109.220110a UR - https://global-sci.org/intro/cicp/7595.html KW - AB -

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.

Riccardo Fazio & Giovanni Russo. (1970). Central Schemes and Second Order Boundary Conditions for 1D Interface and Piston Problems in Lagrangian Coordinates. Communications in Computational Physics. 8 (4). 797-822. doi:10.4208/cicp.310109.220110a
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