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
The generalized Riemann problem for reactive flows
Journal of Computational Physics
A study of numerical methods for hyperbolic conservation laws with stiff source terms
Journal of Computational Physics
Numerical study of the mechanisms for initiation for reacting shock waves
SIAM Journal on Scientific and Statistical Computing
Theoretical and numerical structure for unstable one-dimensional detonations
SIAM Journal on Applied Mathematics
Numerical wave propagation in an advection equation with a nonlinear source term
SIAM Journal on Numerical Analysis
Numerical methods for hyperbolic conservation laws with stiff relaxation I: spurious solutions
SIAM Journal on Applied Mathematics
One-dimensional front tracking based on high resolution wave propagation methods
SIAM Journal on Scientific Computing
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Improved shock-capturing methods for multicomponent and reacting flows
Journal of Computational Physics
Multiresolution schemes for the reactive Euler equations
Journal of Computational Physics
The random projection method for hyperbolic conservation laws with stiff reaction terms
Journal of Computational Physics
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
The Random Projection Method for Stiff Detonation Capturing
SIAM Journal on Scientific Computing
Anti-diffusive flux corrections for high order finite difference WENO schemes
Journal of Computational Physics
A modified higher order Godunov's scheme for stiff source conservative hydrodynamics
Journal of Computational Physics
Numerical solution of under-resolved detonations
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
ENO schemes with subcell resolution
Journal of Computational Physics
Numerical and analytical solutions of new generalized fractional diffusion equation
Computers & Mathematics with Applications
The equilibrium state method for hyperbolic conservation laws with stiff reaction terms
Journal of Computational Physics
Hi-index | 31.45 |
A new high order finite-difference method utilizing the idea of Harten ENO subcell resolution method is proposed for chemical reactive flows and combustion. In reaction problems, when the reaction time scale is very small, e.g., orders of magnitude smaller than the fluid dynamics time scales, the governing equations will become very stiff. Wrong propagation speed of discontinuity may occur due to the underresolved numerical solution in both space and time. The present proposed method is a modified fractional step method which solves the convection step and reaction step separately. In the convection step, any high order shock-capturing method can be used. In the reaction step, an ODE solver is applied but with the computed flow variables in the shock region modified by the Harten subcell resolution idea. For numerical experiments, a fifth-order finite-difference WENO scheme and its anti-diffusion WENO variant are considered. A wide range of 1D and 2D scalar and Euler system test cases are investigated. Studies indicate that for the considered test cases, the new method maintains high order accuracy in space for smooth flows, and for stiff source terms with discontinuities, it can capture the correct propagation speed of discontinuities in very coarse meshes with reasonable CFL numbers.