Theoretical and numerical structure for reacting shock waves
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 methods for hyperbolic conservation laws with stiff relaxation I: spurious solutions
SIAM Journal on Applied Mathematics
The random projection method for hyperbolic conservation laws with stiff reaction terms
Journal of Computational Physics
Applied Numerical Mathematics
Applied Numerical Mathematics
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In this paper we extend the random projection method, recently proposed by the author and S. Jin [J. Comput. Phys. 163 (2000) 216] for under resolved numerical simulations of a qualitative model problem for combustion with stiff chemical reactions: ut + (f(u) - q0z)x = 0, zx = 1/εφ(u)z. In this problem, the reaction time ε is small, making the problem numerically stiff. A classic spurious numerical phenomenon - the incorrect shock speed - occurs when the reaction time scale is not properly resolved numerically. The random projection method is introduced recently to handle this kind of numerical difficulty. The key idea in this method is to randomize the ignition temperature in a suitable domain. Several numerical experiments demonstrate the reliability and robustness of this method.