Localization effects and measure source terms in numerical schemes for balance laws
Mathematics of Computation
An adaptive numerical scheme for high-speed reactive flow on overlapping grids
Journal of Computational Physics
Conservative multi-implicit spectral deferred correction methods for reacting gas dynamics
Journal of Computational Physics
A wave propagation algorithm for hyperbolic systems on curved manifolds
Journal of Computational Physics
Second-order Godunov-type scheme for reactive flow calculations on moving meshes
Journal of Computational Physics
A wave propagation method for hyperbolic systems on the sphere
Journal of Computational Physics
On a practical implementation of particle methods
Applied Numerical Mathematics - Selected papers from the first Chilean workshop on numerical analysis of partial differential equations (WONAPDE 2004)
An artificial nonlinear diffusivity method for supersonic reacting flows with shocks
Journal of Computational Physics
Numerical solution of under-resolved detonations
Journal of Computational Physics
Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws
Journal of Computational Physics
Implicit-explicit schemes for flow equations with stiff source terms
Journal of Computational and Applied Mathematics
ADER Schemes for Nonlinear Systems of Stiff Advection---Diffusion---Reaction Equations
Journal of Scientific Computing
Journal of Computational Physics
The equilibrium state method for hyperbolic conservation laws with stiff reaction terms
Journal of Computational Physics
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The numerical approximation of combustion processes may lead to numerical difficulties, which are caused by different time scales of the transport part and the reactive part of the model equations. Here we consider a modified fractional step method that overcomes this difficulty on standard test problems and allows the use of a mesh width and time step determined by the nonreactive part, without precisely resolving the very small reaction zone. High-resolution Godunov methods are employed and the structure of the Riemann solution is used to determine where burning should occur in each time step. The modification is implemented in the software package CLAWPACK. Numerical results for 1D and 2D detonation waves are shown, including a detonation wave diffracting around a corner.