VODE: a variable-coefficient ODE solver
SIAM Journal on Scientific and Statistical Computing
A note on splitting errors for advection-reaction equations
NUMDIFF-7 Selected papers of the seventh conference on Numerical treatment of differential equations
Explicit Runge-Kutta methods for parabolic partial differential equations
Applied Numerical Mathematics - Special issue celebrating the centenary of Runge-Kutta methods
RKC: an explicit solver for parabolic PDEs
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Journal of Computational Physics
A semi-implicit numerical scheme for reacting flow: I. stiff chemistry
Journal of Computational Physics
A numerical study for global atmospheric transport-chemistry problems
Mathematics and Computers in Simulation
A Second-Order Rosenbrock Method Applied to Photochemical Dispersion Problems
SIAM Journal on Scientific Computing
A semi-implicit numerical scheme for reacting flow: II. stiff, operator-split formulation
Journal of Computational Physics
An analysis of operator splitting techniques in the stiff case
Journal of Computational Physics
ACM Transactions on Mathematical Software (TOMS)
Accurate projection methods for the incompressible Navier—Stokes equations
Journal of Computational Physics
Algebraic splitting for incompressible Navier-Stokes equations
Journal of Computational Physics
Third Order Explicit Method for the Stiff Ordinary Differential Equations
WNAA '96 Proceedings of the First International Workshop on Numerical Analysis and Its Applications
On stabilized integration for time-dependent PDEs
Journal of Computational Physics
A high-order low-Mach number AMR construction for chemically reacting flows
Journal of Computational Physics
Journal of Computational Physics
Accelerating moderately stiff chemical kinetics in reactive-flow simulations using GPUs
Journal of Computational Physics
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An efficient projection scheme is developed for the simulation of reacting flow with detailed kinetics and transport. The scheme is based on a zero-Mach-number formulation of the compressible conservation equations for an ideal gas mixture. It relies on Strang splitting of the discrete evolution equations, where diffusion is integrated in two half steps that are symmetrically distributed around a single stiff step for the reaction source terms. The diffusive half-step is integrated using an explicit single-step, multistage, Runge---Kutta---Chebyshev (RKC) method. The resulting construction is second-order convergent, and has superior efficiency due to the extended real-stability region of the RKC scheme. Two additional efficiency-enhancements are also explored, based on an extrapolation procedure for the transport coefficients and on the use of approximate Jacobian data evaluated on a coarse mesh. We demonstrate the construction in 1D and 2D flames, and examine consequences of splitting errors. By including the above enhancements, performance tests using 2D computations with a detailed C1C2 methane-air mechanism and a mixture-averaged transport model indicate that speedup factors of about 15 are achieved over the starting split-stiff scheme