EFFICIENT COMPUTATION OF COORDINATE-FREE MODELS OF FLAME FRONTS

DOI10.1017/S1446181121000079zbMath1484.65241MaRDI QIDQ5006006

David M. Ambrose, Benjamin F. Akers

Publication date: 12 August 2021

Published in: The ANZIAM Journal (Search for Journal in Brave)

zbMATH Keywords

flame frontscoordinate-free modelsoverturned interfaces

Mathematics Subject Classification ID

Stefan problems, phase changes, etc. (80A22) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Extrapolation to the limit, deferred corrections (65B05) Capillarity (surface tension) for incompressible viscous fluids (76D45) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Combustion (80A25) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) PDEs in connection with classical thermodynamics and heat transfer (35Q79)

Related Items (3)

Well-posedness of a two-dimensional coordinate-free model for the motion of flame fronts ⋮ Global solutions of the two-dimensional Kuramoto-Sivashinsky equation with a linearly growing mode in each direction ⋮ Well-Posedness and Asymptotics of a Coordinate-Free Model of Flame Fronts

Cites Work

• The route to chaos for the Kuramoto-Sivashinsky equation
• On the equation of a curved flame front
• On the \(\kappa\)-\(\theta\) model of cellular flames: existence in the large and asymptotics
• Removing the stiffness from interfacial flows with surface tension
• Overturned internal capillary-gravity waves
• A simple and fast numerical method for solving flame/smoldering evolution equations
• Predicting chaos for infinite dimensional dynamical systems: the Kuramoto-Sivashinsky equation, a case study.
• Implicit-Explicit Methods for Time-Dependent Partial Differential Equations
• A PseudoSpectral Procedure for the Solution of Nonlinear Wave Equations with Examples from Free-Surface Flows
• Fourth-Order Time-Stepping for Stiff PDEs
• Gravity perturbed Crapper waves
• An in-depth numerical study of the two-dimensional Kuramoto–Sivashinsky equation
• The long-time motion of vortex sheets with surface tension

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