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This paper is concerned with the construction of a fast algorithm for computing the maximum speed of propagation in the Riemann solution for the Euler system of gas dynamics with the co-volume equation of state. The novelty in the algorithm…

Numerical Analysis · Mathematics 2016-07-20 Jean-Luc Guermond , Bojan Popov

In this paper, we consider Riemann solvers with phase transition effects based on the Euler-Fourier equation system. One exact and two approximate solutions of the two-phase Riemann problem are obtained by modelling the phase transition…

Fluid Dynamics · Physics 2022-07-06 Steven Jöns , Claus-Dieter Munz

We construct centered rarefaction wave solutions given background solutions to the compressible Euler equations. The flow considered in this article is the homentropic flow of perfect gas governed by compressible Euler equations and the…

Analysis of PDEs · Mathematics 2025-12-02 Ruotong Zhang

We study the slightly compressible Darcy-Forchheimer equations modeling gas flow in porous media, particularly in applications related to combustion processes. The equations are discretized in time using the backward Euler method and in…

Numerical Analysis · Mathematics 2026-04-16 Laura Portero , Andrés Arrarás , Francisco J. Gaspar , Florin A. Radu

We investigate various analytical and numerical techniques for the coupling of nonlinear hyperbolic systems and, in particular, we introduce here an augmented formulation which allows for the modeling of the dynamics of interfaces between…

Analysis of PDEs · Mathematics 2021-10-01 Benjamin Boutin , Frédéric Coquel , Philippe G. LeFloch

We give sufficient conditions on the regularity of solutions to the inhomogeneous incompressible Euler and the compressible isentropic Euler systems in order for the energy to be conserved. Our strategy relies on commutator estimates…

Analysis of PDEs · Mathematics 2016-12-21 Eduard Feireisl , Piotr Gwiazda , Agnieszka Świerczewska-Gwiazda , Emil Wiedemann

We introduce new coupling conditions for isentropic flow on networks based on an artificial density at the junction. The new coupling conditions can be derived from a kinetic model by imposing a condition on energy dissipation. Existence…

Analysis of PDEs · Mathematics 2020-06-17 Yannick Holle , Michael Herty , Michael Westdickenberg

A novel numerical scheme to solve coupled systems of conservation laws is introduced. The scheme is derived based on a relaxation approach and does not require information on the Lax curves of the coupled systems, which simplifies the…

Numerical Analysis · Mathematics 2023-04-28 Michael Herty , Niklas Kolbe , Siegfried Müller

We develop a general framework for studying non-uniqueness of the Riemann problem for the isentropic compressible Euler system in two spatial dimensions, and in this paper we present the most delicate result of our method: non-uniqueness of…

Analysis of PDEs · Mathematics 2025-05-23 Sam G. Krupa , László Székelyhidi

The method of characteristics is a classical method for gaining understanding in the solution of a partial differential equation. It has recently been applied to the adjoint equations of the 2D Euler equations and the first goal of this…

Fluid Dynamics · Physics 2023-05-08 Kevin Ancourt , Jacques Peter , Olivier Atinault

This paper is concerned with the Riemann problem for the two-dimensional barotropic compressible Euler system with a general strictly increasing pressure law. By means of convex integration, the existence of infinitely many admissible weak…

Analysis of PDEs · Mathematics 2026-03-26 Kotaro Horimoto

This paper is concerned with a set of novel coupling conditions for the $3\times 3$ one-dimensional Euler system with source terms at a junction of pipes with possibly different cross-sectional areas. Beside conservation of mass, we require…

Analysis of PDEs · Mathematics 2018-03-21 Jens Lang , Pascal Mindt

We consider two laminar incompressible flows coupled by the continuous law at a fixed interface. We approach the system by one that satisfies a friction Navier law, and we show that when the friction coefficient goes to infinity, the…

Analysis of PDEs · Mathematics 2022-06-22 François Legeais , Roger Lewandowski

We consider the Cauchy problem for a damped Euler-Maxwell system with no ionic background. For smooth enough data satisfying suitable so-called dispersive conditions, we establish the global in time existence and uniqueness of a strong…

Analysis of PDEs · Mathematics 2024-02-02 Bernard Ducomet , Šárka Nečasová , John Sebastian H. Simon

We develop a method to compute effectively the Young measures associated to sequences of numerical solutions of the compressible Euler system. Our approach is based on the concept of $\mathcal{K}$-convergence adapted to sequences of…

Numerical Analysis · Mathematics 2019-10-09 Eduard Feireisl , Maria Lukacova , Bangwei She , Yue Wang

We introduce a tool for simulation and optimization of gas pipeline networks coupled to power grids by gas-to-power plants. The model under consideration consists of the isentropic Euler equations to describe the gas flow coupled to the AC…

Optimization and Control · Mathematics 2019-03-25 Eike Fokken , Simone Göttlich , Oliver Kolb

In this work, we prove the convergence of residual distribution schemes to dissipative weak solutions of the Euler equations. We need to guarantee that the residual distribution schemes are fulfilling the underlying structure preserving…

Numerical Analysis · Mathematics 2022-12-06 Rémi Abgrall , Mária Lukácova-Medvid'ová , Philipp Öffner

We consider the barotropic Euler equations with pairwise attractive Riesz interactions and linear velocity damping in the periodic domain. We establish the global-in-time well-posedness theory for the system near an equilibrium state. We…

Analysis of PDEs · Mathematics 2023-09-04 Young-Pil Choi , Jinwook Jung , Yoonjung Lee

We report on the development of a computational framework for the parallel, mesh-adaptive solution of systems of hyperbolic conservation laws like the time-dependent Euler equations in compressible gas dynamics or Magneto-Hydrodynamics…

Computational Physics · Physics 2007-05-23 J. Dreher , R. Grauer

We present a modified Front Tracking (mFT) scheme for hyperbolic systems of conservation laws in one space dimension, in which we allow arbitrarily large nonlinear waves. We build the scheme by introducing and solving a ``generalized…

Analysis of PDEs · Mathematics 2025-04-30 Manas Bhatnagar , Robin Young