Theoretical and numerical structure for reacting shock waves
SIAM Journal on Scientific and Statistical Computing
Total-variation-diminishing time discretizations
SIAM Journal on Scientific and Statistical Computing
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
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
Summation by parts, projections, and stability. I
Mathematics of Computation
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Improved shock-capturing methods for multicomponent and reacting flows
Journal of Computational Physics
Correction of conservative Euler solvers for gas mixtures
Journal of Computational Physics
Journal of Computational Physics
Entropy splitting and numerical dissipation
Journal of Computational Physics
The random projection method for hyperbolic conservation laws with stiff reaction terms
Journal of Computational Physics
A Modified Fractional Step Method for the Accurate Approximation of Detonation Waves
SIAM Journal on Scientific Computing
Multiresolution Wavelet Based Adaptive Numerical Dissipation Control for High Order Methods
Journal of Scientific Computing
Development of low dissipative high order filter schemes for multiscale Navier-Stokes/MHD systems
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
Positivity-preserving high order finite difference WENO schemes for compressible Euler equations
Journal of Computational Physics
The equilibrium state method for hyperbolic conservation laws with stiff reaction terms
Journal of Computational Physics
Hi-index | 31.45 |
The goal of this paper is to relate numerical dissipations that are inherited in high order shock-capturing schemes with the onset of wrong propagation speed of discontinuities. For pointwise evaluation of the source term, previous studies indicated that the phenomenon of wrong propagation speed of discontinuities is connected with the smearing of the discontinuity caused by the discretization of the advection term. The present study focuses only on solving the reactive system by the fractional step method using the Strang splitting. Studies shows that the degree of wrong propagation speed of discontinuities is highly dependent on the accuracy of the numerical method. The manner in which the smearing of discontinuities is contained by the numerical method and the overall amount of numerical dissipation being employed play major roles. Depending on the numerical method, time step and grid spacing, the numerical simulation may lead to (a) the correct solution (within the truncation error of the scheme), (b) a divergent solution, (c) a wrong propagation speed of discontinuities solution or (d) other spurious solutions that are solutions of the discretized counterparts but are not solutions of the governing equations. The findings might shed some light on the reported difficulties in numerical combustion and problems with stiff nonlinear (homogeneous) source terms and discontinuities in general.