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Two-Dimensional Riemann Problems for the Compressible Euler System

Chinese Annals of Mathematics,Series B 2009年第6期30卷 845-858页

作者： Yuxi ZHENG Dedicated to Professor Andrew Majda for his 60th Birthday

Riemann problems for the compressible Euler system in two space dimensions are complicated and difficult,but a viable alternative remains *** author lists merits of one-dimensional Riemann problems and compares them with those for the current two-dimensional Riemann problems,to illustrate their ***-dimensional Riemann problems are approached via the methodology promoted by Andy Majda in the spirits of modern applied mathematics;that is,simplified model is built via asymptotic analysis,numerical simulation and theoretical analysis.A simplified model called the pressure gradient system is derived from the full Euler system via an asymptotic ***-of-the-art numerical methods in numerical simulations are used to discern small-scale structures of the solutions,e.g.,semi-hyperbolic *** methods are used to establish the validity of the structure revealed in the numerical *** entire process,used in many of Majda's programs,is shown here for the two-dimensional Riemann problems for the compressible Euler systems of conservation laws.

关键词： Characteristic decomposition Guderley reflection hodograph transform Pressure gradient system Self-similar Semi-hyperbolic wave Triple point paradox Riemann problem Riemann variable

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Reflection and Refraction of Waves Across an Interface of Two-phase Flow

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Acta Mathematicae Applicatae Sinica 2021年第1期37卷 137-147页

作者： Kai HU Hui KAN Chun-lei TANG Xiao-zhou YANG School of Mathematics and Statistics Southwest UniversityChongqing 400715China Wuhan Institute of Physics and Mathematics Chinese Academy of SciencesWuhan 430071China

We investigate a hyperbolic system of one-dimensional isothermal fluid with liquid-vapor phase *** refraction-reflection phenomena are intensively analyzed when elementary waves travel across the two-phase *** apply the characteristic method and hodograph transform of Riemann to reduce the nonlinear PDEs to a concise *** for the case of incident rarefaction wave,reduced linear equations are convenient to solve by Laplace *** an integral formula in wave interaction region is derived in this paper,instead of the hypergeometric functions solutions for non-isothermal polytropic *** is also observed that when incident waves travel from the vapor phase to the liquid phase,the refracted waves must be accelerated and move forward.

关键词： p-system two-phase fluid hodograph transform Volterra equation

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