Explicit Time Marching Methods for the Time-Dependent Euler Computations

Blast Wave Simulations with a Runge-Kutta Discontinuous Galerkin Method

“…In order to solve the resulting system of equations, an in-house computational fluid dynamics code which was able to solve Euler equations using a finite volume technique was further modified to include an RKDG method. The code was first tested with a Sod's shock tube problem with the so-called moderate extremely strong discontinuities [23]. Predictions were compared with the predictions obtained using a finite volume technique and to the exact solutions [24].…”

“…These were the same conditions studied in [23] as an extremely strong discontinuity case. This case was selected because it more closely resembled a blast wave simulation problem and it constituted an extremely difficult case for numerical methods because of large gradients in the flowfield.…”

“…On the other hand, Superbee limiter [30] is the least dissipative and is suitable for flows with very strong shocks like a blast wave [23]. In this study minmod and Superbee limiters along with the Sweby limiter [37], which is between Superbee and minmod limiters, were used for numerical solutions.…”

“…Simulations were performed for one-dimensional moving rectangular and spherical shock waves (blast waves). Planar shock waves were simulated by solving planar shock tube problem with moderate and extremely strong discontinuities [23]. These two cases were compared in order to display the difficulties numerical methods may experience when the discontinuities in the flowfield are strong, as in the case of blast waves due to explosions.…”

A Three-Dimensional Numerical Investigation into the Interaction of Blast Waves with Bomb Shelters

“…The upwind scheme has a natural dissipation property, based on characteristic theory, and has no artificial viscosity term to describe the physical phenomena (15) . The temporal integer is calculated using the explicit multi-step standard Runge-Kutta method combined with the Hancock predictor-corrector method (16) .…”