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Article
Interaction of Rarefaction Waves of the Two-Dimensional Self-Similar Euler Equations
We construct classical self-similar solutions to the interaction of two arbitrary planar rarefaction waves for the polytropic Euler equations in two space dimensions. The binary interaction represents a major ...
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Article
Entropy convergence of new two-value scheme with slope relaxation for conservation laws
This paper establishes the entropy convergence of a new two-value high resolution finite volume scheme with slope relaxation for conservation laws. This scheme, motivated by the general method of high resoluti...
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Article
Transversal effects of high order numerical schemes for compressible fluid flows
Finite volume schemes for the two-dimensional (2D) wave system are taken to demonstrate the role of the genuine dimensionality of Lax-Wendroff flow solvers for compressible fluid flows. When the finite volume ...
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Article
Sonic-Supersonic Solutions for the Two-Dimensional Steady Full Euler Equations
This paper focuses on the structure of classical sonic-supersonic solutions near sonic curves for the two-dimensional full Euler equations in gas dynamics. In order to deal with the parabolic degeneracy near t...