NDLI: A Cell-Centered Lagrangian Scheme for Two-Dimensional Compressible Flow Problems

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Ovadia, Jean Abgrall, Rmi Maire, Pierre-Henri Breil, Jrme
Copyright Year	2007
Abstract	We present a new Lagrangian cell-centered scheme for two-dimensional compressible flows. The primary variables in this new scheme are cell-centered, i.e., density, momentum, and total energy are defined by their mean values in the cells. The vertex velocities and the numerical fluxes through the cell interfaces are not computed independently, contrary to standard approaches, but are evaluated in a consistent manner due to an original solver located at the nodes. The main new feature of the algorithm is the introduction of four pressures on each edge, two for each node on each side of the edge. This extra degree of freedom allows us to construct a nodal solver which fulfills two properties. First, the conservation of momentum and total energy is ensured. Second, a semidiscrete entropy inequality is provided. In the case of a one-dimensional flow, the solver reduces to the classical Godunov acoustic solver: it can be considered as its two-dimensional generalization. Many numerical tests are presented. They are representative test cases for compressible flows and demonstrate the robustness and the accuracy of this new solver.
Starting Page	1781
Ending Page	1824
Page Count	44
File Format	PDF
ISSN	10648275
DOI	10.1137/050633019
e-ISSN	10957197
Issue Number	4
Volume Number	29
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2007-09-19
Access Restriction	Subscribed
Subject Keyword	Godunov-type schemes Shock waves and blast waves hyperbolic conservation laws Lagrangian gas dynamics Finite difference methods
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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