Conservation Laws, Hodograph Transformation and Boundary Value Problems of Plane Plasticity [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2012 For the hyperbolic system of quasilinear first-order partial differential equations, linearizable by hodograph transformation, the conservation laws are used to solve the Cauchy problem.
Sergey I. Senashov, Alexander Yakhno
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A Fourth Order Entropy Stable Scheme for Hyperbolic Conservation Laws [PDF]
Entropy, 2019 This paper develops a fourth order entropy stable scheme to approximate the entropy solution of one-dimensional hyperbolic conservation laws. The scheme is constructed by employing a high order entropy conservative flux of order four in conjunction with ...
Xiaohan Cheng
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Statistical solutions of hyperbolic conservation laws I: Foundations [PDF]
Archive for Rational Mechanics and Analysis, 2016 We seek to define statistical solutions of hyperbolic systems of conservation laws as time-parametrized probability measures on $p$-integrable functions.
Fjordholm, Ulrik Skre +2 more
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A proof of Kirchhoff's first law for hyperbolic conservation laws on networks
Networks and Heterogeneous Media, 2023 In dynamical systems on networks, Kirchhoff's first law describes the local conservation of a quantity across edges. Predominantly, Kirchhoff's first law has been conceived as a phenomenological law of continuum physics.
Alexandre M. Bayen +2 more
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Alternating Polynomial Reconstruction Method for Hyperbolic Conservation Laws
Mathematics, 2021 We propose a new multi-moment numerical solver for hyperbolic conservation laws by using the alternating polynomial reconstruction approach. Unlike existing multi-moment schemes, our approach updates model variables by implementing two polynomial ...
Shijian Lin +3 more
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Improvement of the WENO-NIP Scheme for Hyperbolic Conservation Laws
Axioms, 2022 The WENO-NIP scheme was obtained by developing a class of L1-norm smoothness indicators based on Newton interpolation polynomial. It recovers the optimal convergence order in smooth regions regardless of critical points and achieves better resolution ...
Ruo Li, Wei Zhong
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Four-Quadrant Riemann Problem for a 2×2 System II
Mathematics, 2021 In previous work, we considered a four-quadrant Riemann problem for a 2×2 hyperbolic system in which delta shock appears at the initial discontinuity without assuming that each jump of the initial data projects exactly one plane elementary wave.
Jinah Hwang +3 more
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Fully discrete WENO with double entropy condition for hyperbolic conservation laws
Engineering Applications of Computational Fluid Mechanics, 2023 This paper put forward a new fully discrete scheme construction method – double entropy condition solution formula method. With that, we turn the state-of-the-art semi-discrete WENO + RK scheme into a fully discrete scheme, which is named as Full-WENO. A
Haitao Dong, Tong Zhou, Fujun Liu
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Convergence of fully discrete schemes for diffusive dispersive conservation laws with discontinuous coefficient [PDF]
, 2015 We are concerned with fully-discrete schemes for the numerical approximation of diffusive-dispersive hyperbolic conservation laws with a discontinuous flux function in one-space dimension. More precisely, we show the convergence of approximate solutions,
Dutta, Rajib, Koley, Ujjwal, Ray, Deep
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Lagrangian-Eulerian approximation methods for balance laws and hyperbolic conservation laws
Revista UIS Ingenierías, 2018 A new finite control volume in a Lagrangian-Eulerian framework is presented (see papers [1, 28]), in which a local space-time domain is studied, in order to design a locally conservative scheme.
Eduardo Abreu, Jhon Perez, Arthur Santo
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