A high-order nonconservative approach for hyperbolic equations in fluid dynamics

DOI10.1016/j.compfluid.2017.08.019zbMath1410.76277arXiv1702.08847OpenAlexW2591937896MaRDI QIDQ720831

Remi Abgrall, Paola Bacigaluppi, Svetlana Tokareva

Publication date: 18 July 2018

Published in: Computers and Fluids (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.08847

zbMATH Keywords

Euler equationsconservationfluid dynamicsresidual distributionmultiphase flow systemsnonconservative formulation

Mathematics Subject Classification ID

Finite difference methods applied to problems in fluid mechanics (76M20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06)

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Cites Work

• Unnamed Item
• Construction of very high order residual distribution schemes for steady inviscid flow problems on hybrid unstructured meshes
• A five equation reduced model for compressible two-phase flow problems
• A relaxation-projection method for compressible flows. I: The numerical equation of state for the Euler equations
• Explicit Runge-Kutta residual distribution schemes for time dependent problems: second order case
• Multicomponent flow calculations by a consistent primitive algorithm
• High-order fluctuation schemes on triangular meshes
• High order schemes for hyperbolic problems using globally continuous approximation and avoiding mass matrices
• Modelling detonation waves in condensed energetic materials: multiphase CJ conditions and multidimensional computations
• Shock jump relations for multiphase mixtures with stiff mechanical relaxation
• A relaxation-projection method for compressible flows. II: Artificial heat exchanges for multiphase shocks
• An entropy fix for multi-dimensional upwind residual distribution schemes
• Essentially non-oscillatory residual distribution schemes for hyperbolic problems
• Some Failures of Riemann Solvers
• Two-phase modeling of deflagration-to-detonation transition in granular materials: Reduced equations
• A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials
• Why Nonconservative Schemes Converge to Wrong Solutions: Error Analysis
• Hybrid Multifluid Algorithms
• Design of a Second-Order Fully Explicit Residual Distribution Scheme for Compressible Multiphase Flows
• Numerical Approximation of a Compressible Multiphase System
• The Riemann problem for fluid flow of real materials
• Toward the ultimate conservative scheme: Following the quest