An implicit Lagrangian–Eulerian ÅÌÂ-method for solving two-dimensional hydrodynamic equations on unstructured meshes
E. M. Vaziev, A. D. Gadzhiev, S. Yu. Kuzmin, Yu. G. Panyukov
Russian Federal Nuclear Center – Zababakhin Institute of Applied Physics (RFNC-VNIITF)
The paper presents an ALE method for solving hydrodynamic equations on unstructured
meshes. It is based on an implicit finite-volume scheme derived with Godunov's approach.
The basic quantities — destiny, temperature and velocity are stored in cell centers.
For relations between pressure and velocities in the centers and their analogs in the
nodes, we use those proposed by P.-H. Maire et al. A piecewise linear TVD reconstruction
of pressure and velocity in the cell is used achieve the second order of approximation
keeping monotonicity of smooth solutions.
Mesh rezoning during the calculation is implemented. The quantities are recalculated
through mapping the old mesh onto the new one. A limited piecewise linear representation
is used for quantities in the cells of the old mesh and interface in the mixed cells are
reconstructed with the VOF method. Mass, momentum and total energy are conserved.
implicit finite-volume ALE methods, TVD reconstruction, higher order remapping, VOF method, unstructured mesh.
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E. M. Vaziev, A. D. Gadzhiev, S. Yu. Kuzmin, Yu. G. Panyukov, “An implicit Lagrangian–Eulerian ÅÌÂ-method for solving two-dimensional hydrodynamic equations on unstructured meshes”, Matem. Mod., 30:3 (2018), 118–134
Citation in format AMSBIB
\by E.~M.~Vaziev, A.~D.~Gadzhiev, S.~Yu.~Kuzmin, Yu.~G.~Panyukov
\paper An implicit Lagrangian--Eulerian ÅÌÂ-method for solving two-dimensional hydrodynamic equations on unstructured meshes
\jour Matem. Mod.
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