Unsplit schemes for hyperbolic conservation laws with source terms in one space dimension

DOI10.1006/jcph.1997.5692zbMath0880.65074OpenAlexW1990521895WikidataQ115149546 ScholiaQ115149546MaRDI QIDQ1360436

Paul E. Dimotakis, Miltiadis V. Papalexandris, Anthony Leonard

Publication date: 8 January 1998

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

Full work available at URL: https://authors.library.caltech.edu/51564/

zbMATH Keywords

numerical examplesfinite difference schemeEuler equationsmethod of characteristicshyperbolic systems of conservation lawsdetonationchemically reacting flows

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs (65M25) Combustion (80A25) Chemically reacting flows (80A32)

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Computation of Flashing Flows In Variable Cross-Section Ducts, Mapped hybrid central-WENO finite difference scheme for detonation waves simulations, High order weighted essentially non-oscillation schemes for two-dimensional detonation wave simulations, An \(h\)-adaptive RKDG method with troubled-cell indicator for one-dimensional detonation wave simulations, A conservative approximation to compressible two-phase flow models in the stiff mechanical relaxation limit, MOL solvers for hyperbolic PDEs with source terms, Convection Systems with Stiff Source Terms, Second-order Godunov-type scheme for reactive flow calculations on moving meshes, Construction of second-order TVD schemes for nonhomogeneous hyperbolic conservation laws, Hybrid Compact-WENO Finite Difference Scheme For Detonation Waves Simulations, FRONT TRACKING FOR SCALAR BALANCE EQUATIONS, Numerical resolution of pulsating detonation waves, Unsplit algorithms for multidimensional systems of hyperbolic conservation laws with source terms

Cites Work

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• Numerical algorithms for propagating interfaces: Hamilton-Jacobi equations and conservation laws
• The piecewise parabolic method (PPM) for gas-dynamical simulations
• A generalized Riemann problem for quasi-one-dimensional gas flows
• The validity of nonlinear geometric optics for weak solutions of conservation laws
• Hyperbolic conservation laws with relaxation
• Uniformly high order accurate essentially non-oscillatory schemes. III
• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• The generalized Riemann problem for reactive flows
• Quasilinear hyperbolic systems
• Approximate Riemann solvers, parameter vectors, and difference schemes
• An adaptive Lagrangian method for computing 1D reacting and non-reacting flows
• Towards the ultimate conservative difference scheme. IV: A new approach to numerical convection
• Convergence of MUSCL and filtered schemes for scalar conservation laws and Hamilton-Jacobi equations
• A study of numerical methods for hyperbolic conservation laws with stiff source terms
• Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
• Numerical Methods for Hyperbolic Conservation Laws with Stiff Relaxation II. Higher-Order Godunov Methods
• Hyperbolic systems of conservation laws II
• On the Relation Between the Upwind-Differencing Schemes of Godunov, Engquist–Osher and Roe
• Theoretical and Numerical Structure for Unstable One-Dimensional Detonations
• Calculation of linear detonation instability: one-dimensional instability of plane detonation
• Numerical Study of the Mechanisms for Initiation of Reacting Shock Waves
• An Asymptotic Theory of Deflagrations and Detonations I. The Steady Solutions
• Resonantly Interacting Weakly Nonlinear Hyperbolic Waves. I. A Single Space Variable
• An Upwind Second-Order Scheme for Compressible Duct Flows
• Theoretical and Numerical Structure for Reacting Shock Waves
• Nonlinear Mean Field-High Frequency Wave Interactions in the Induction Zone
• Amplification of Small-Amplitude High-Frequency Waves in a Reactive Mixture
• Monotone Difference Approximations for Scalar Conservation Laws
• Stable upwind schemes for hyperbolic conservation laws with source terms
• Numerical Wave Propagation in an Advection Equation with a Nonlinear Source Term
• Numerical Methods for Hyperbolic Conservation Laws With Stiff Relaxation I. Spurious Solutions
• Hyperbolic conservation laws with stiff relaxation terms and entropy
• Error Bounds for Fractional Step Methods for Conservation Laws with Source Terms
• The dynamical limit of one-dimensional detonations
• One-Dimensional Front Tracking Based on High Resolution Wave Propagation Methods
• On the Construction and Comparison of Difference Schemes
• FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES
• Stability of Idealized One-Reaction Detonations