An Approach to Obtain the Correct Shock Speed for Euler Equations with Stiff Detonation (Communications in Computational Physics, 2019)
Incorrect propagation speed of discontinuities may occur by straightforward application of standard dissipative schemes for problems that contain stiff sourceterms for underresolved grids even for time steps within the CFL condition. By examining the dissipative discretized counterpart of the Euler equations for a detonationproblem that consists of a single reaction, detailed analysis on the spurious wave pattern is presented employing the fractional step method, which utilizes the Strang splitting. With the help of physical arguments, a threshold values method (TVM), whichcan be extended to more complicated stiff problems, is developed to eliminate thewrong shock speed phenomena. Several single reaction detonations as well as multi-species and multi-reaction detonation test cases with strong stiffness are examined toillustrate the performance of the TVM approach.
Keywords: Detonation; spurious behavior; reactive Euler equations; threshold values method; stiffness.