Theoretical and numerical structure for reacting shock waves
SIAM Journal on Scientific and Statistical Computing
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Multidimensional upwind methods for hyperbolic conservation laws
Journal of Computational Physics
One-dimensional front tracking based on high resolution wave propagation methods
SIAM Journal on Scientific Computing
Journal of Computational Physics
SIAM Journal on Scientific Computing
Two-dimensional front tracking based on high resolution wave propagation methods
Journal of Computational Physics
SIAM Journal on Scientific Computing
Proceedings of the on Numerical methods for differential equations
An Adaptive Finite Element Method for Unsteady Convection-Dominated Flows with Stiff Source Terms
SIAM Journal on Scientific Computing
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
The random projection method for stiff multispecies detonation capturing
Journal of Computational Physics
A Modified Fractional Step Method for the Accurate Approximation of Detonation Waves
SIAM Journal on Scientific Computing
Additive Runge-Kutta schemes for convection-diffusion-reaction equations
Applied Numerical Mathematics
High-order multi-implicit spectral deferred correction methods for problems of reactive flow
Journal of Computational Physics
High-order multi-implicit spectral deferred correction methods for problems of reactive flow
Journal of Computational Physics
An integral equation method for epitaxial step-flow growth simulations
Journal of Computational Physics
Arbitrary order Krylov deferred correction methods for differential algebraic equations
Journal of Computational Physics
Numerical methods for solving moment equations in kinetic theory of neuronal network dynamics
Journal of Computational Physics
Error estimates for deferred correction methods in time
Applied Numerical Mathematics
A fourth-order auxiliary variable projection method for zero-Mach number gas dynamics
Journal of Computational Physics
On the choice of correctors for semi-implicit Picard deferred correction methods
Applied Numerical Mathematics
Applied Numerical Mathematics
A multirate time integrator for regularized Stokeslets
Journal of Computational Physics
On the order of deferred correction
Applied Numerical Mathematics
A Hybrid Implicit-Explicit Adaptive Multirate Numerical Scheme for Time-Dependent Equations
Journal of Scientific Computing
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In most models of reacting gas dynamics, the characteristic time scales of chemical reactions are much shorter than the hydrodynamic and diffusive time scales, rendering the reaction part of the model equations stiff. Moreover, non-linear forcings may introduce into the solutions sharp gradients or shocks, the robust behavior and correct propagation of which require the use of specialized spatial discretization procedures. This study presents high-order conservative methods for the temporal integration of model equations of reacting flows. By means of a method of lines discretization on the flux difference form of the equations, these methods compute approximations to the cell-averaged or finite-volume solution. The temporal discretization is based on a multi-implicit generalization of spectral deferred correction methods. The advection term is integrated explicitly, and the diffusion and reaction terms are treated implicitly but independently, with the splitting errors reduced via the spectral deferred correction procedure. To reduce computational cost, different time steps may be used to integrate processes with widely-differing time scales. Numerical results show that the conservative nature of the methods allows a robust representation of discontinuities and sharp gradients; the results also demonstrate the expected convergence rates for the methods of orders three, four, and five for smooth problems.