The time-line interpolation method for large-time-step Godunov-type schemes

DOI10.1006/jcph.2002.7013zbMath0998.65087OpenAlexW1998743523MaRDI QIDQ1601515

Vincent Guinot

Publication date: 5 August 2002

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jcph.2002.7013

zbMATH Keywords

algorithmstabilityconvergenceNavier-Stokes equationssingularitiesconservation lawsshockscompressible fluidstransonic flowsRiemann-Hilbert problemsStokes equationlinear advection equationinviscid Burgers equationlinear reconstructionshallow water flow

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05) KdV equations (Korteweg-de Vries equations) (35Q53) Transonic flows (76H05) Finite difference methods applied to problems in fluid mechanics (76M20) Gas dynamics (general theory) (76N15) Stokes and related (Oseen, etc.) flows (76D07) Navier-Stokes equations (35Q30) Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Riemann-Hilbert problems in context of PDEs (35Q15)

Related Items (1)

A class of large time step Godunov schemes for hyperbolic conservation laws and applications

Cites Work

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• The piecewise parabolic method (PPM) for gas-dynamical simulations
• A second-order Godunov-type scheme for compressible fluid dynamics
• The numerical simulation of two-dimensional fluid flow with strong shocks
• Application of the generalized Riemann problem method to 1-D compressible flows with material interfaces
• An implicit-explicit hybrid method for Lagrangian hydrodynamics
• Propagation of round-off errors and the role of stability in numerical methods for linear and nonlinear PDEs
• High resolution finite volume methods on arbitrary grids via wave propagation
• Optimal accuracy of unconditionally stable explicit numerical methods for nonlinear evolution PDE's
• An implicit-explicit Eulerian Godunov scheme for compressible flow
• A second-order iterative implicit-explicit hybrid scheme for hyperbolic systems of conservation laws
• The method of space-time conservation element and solution element -- a new approach for solving the Navier-Stokes and Euler equations
• Note on the von Neumann stability of explicit one-dimensional advection schemes
• Iterative implementation of an implicit-explicit hybrid scheme for hydrodynamics
• The space-time conservation element and solution element method: A new high-resolution and genuinely multidimensional paradigm for solving conservation laws
• Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
• Convergence of a large time step generalization of Godunov's method for conservation laws
• Large Time Step Shock-Capturing Techniques for Scalar Conservation Laws
• A flux‐based modified method of characteristics
• The nirvana scheme applied to one‐dimensional advection

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