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  1. No Access

    Article

    Stiffened Gas Approximation and GRP Resolution for Compressible Fluid Flows of Real Materials

    The equation of state (EOS) embodies thermodynamic properties of compressible fluid materials and usually has very complicated forms in real engineering applications. The complexity of EOS in form gives rise t...

    Yue Wang, Jiequan Li in Journal of Scientific Computing (2023)

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    Chapter

    An Energy-Splitting High-Order Numerical Method for Multi-material Flows

    This chapter deals with multi-material flow problems by a kind of effective numerical methods, based on a series of reduced forms of the Baer-Nunziato (BN)-type model. Numerical simulations often face a host o...

    **n Lei, Jiequan Li in Numerical Fluid Dynamics (2022)

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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...

    Yanbo Hu, Jiequan Li in Archive for Rational Mechanics and Analysis (2020)

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    Article

    Interaction of Four Rarefaction Waves in the Bi-Symmetric Class of the Two-Dimensional Euler Equations

    The global existence and structures of solutions to multi-dimensional unsteady compressible Euler equations are interesting and important open problems. In this paper, we construct global classical solutions t...

    Jiequan Li, Yuxi Zheng in Communications in Mathematical Physics (2010)

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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 ...

    Jiequan Li, Yuxi Zheng in Archive for Rational Mechanics and Analysis (2009)

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    Article

    Hyperbolic balance laws: Riemann invariants and the generalized Riemann problem

    The Generalized Riemann Problem (GRP) for a nonlinear hyperbolic system of m balance laws (or alternatively “quasi-conservative” laws) in one space dimension is now well-known and can be formulated as follows: Gi...

    Matania Ben-Artzi, Jiequan Li in Numerische Mathematik (2007)

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    Article

    Simple Waves and a Characteristic Decomposition of the Two Dimensional Compressible Euler Equations

    We present a characteristic decomposition of the potential flow equation in the self-similar plane. The decomposition allows for a proof that any wave adjacent to a constant state is a simple wave for the adia...

    Jiequan Li, Tong Zhang, Yuxi Zheng in Communications in Mathematical Physics (2006)