Conservative multi-implicit spectral deferred correction methods for reacting gas dynamics.

DOI10.1016/j.jcp.2003.09.010zbMath1100.76048OpenAlexW2161077841MaRDI QIDQ1427845

Anita T. Layton, Michael L. Minion

Publication date: 14 March 2004

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

Full work available at URL: https://doi.org/10.1016/j.jcp.2003.09.010

zbMATH Keywords

Operator splittingReactive flowsSemi-implicit methodsConservative methodsSpectral deferred correction methods

Mathematics Subject Classification ID

Gas dynamics (general theory) (76N15) Spectral methods applied to problems in fluid mechanics (76M22) Reaction effects in flows (76V05) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

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Uses Software

• RODAS
• CHEMKIN

Cites Work

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• The piecewise parabolic method (PPM) for gas-dynamical simulations
• Multidimensional upwind methods for hyperbolic conservation laws
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• Efficient implementation of essentially nonoscillatory shock-capturing schemes. II
• High-order multi-implicit spectral deferred correction methods for problems of reactive flow.
• Spectral deferred correction methods for ordinary differential equations
• The random projection method for stiff multispecies detonation capturing
• Additive Runge-Kutta schemes for convection-diffusion-reaction equations
• Semi-implicit extension of a Godunov-type scheme based on low Mach number asymptotics. I: One-dimensional flow
• Two-dimensional front tracking based on high resolution wave propagation methods
• Analysis of operator splitting for advection-diffusion-reaction problems from air pollution modelling
• Semi-implicit spectral deferred correction methods for ordinary differential equations
• A Modified Fractional Step Method for the Accurate Approximation of Detonation Waves
• High Resolution Schemes and the Entropy Condition
• Theoretical and Numerical Structure for Reacting Shock Waves
• Comparison of Several Difference Schemes on 1D and 2D Test Problems for the Euler Equations
• An Adaptive Finite Element Method for Unsteady Convection-Dominated Flows with Stiff Source Terms
• One-Dimensional Front Tracking Based on High Resolution Wave Propagation Methods
• The Theoretical Accuracy of Runge–Kutta Time Discretizations for the Initial Boundary Value Problem: A Study of the Boundary Error
• On the Removal of Boundary Errors Caused by Runge–Kutta Integration of Nonlinear Partial Differential Equations
• On the Construction and Comparison of Difference Schemes
• Integration of Stiff Equations