High-order hybrid numerical simulations of two-dimensional detonation waves

Abstract

In order to study multi-dimensional unstable detonation waves, we have developed a high order numerical scheme suitable for calculating the detailed transverse wave structures of multidimensional detonation waves. The numericai aigorit hm uses a multi-domain approach so different numerical techniques can be applied for different components of detonation waves.

On high-order shock-fitting and front-tracking schemes for numerical simulation of shock–disturbance interactions

“…Kopriva [54,55] used the Chebyshev spectral collocation method in conjunction with shock-fitting and extended it to multidomain [56]. Cai [57] used a shock-fitting algorithm to compute two-dimensional detonation waves. Zhong [58] developed new high-order finite-difference schemes and coupled them with the shock-fitting algorithm for studying hypersonic boundary layers.…”

High-Order Finite-Difference Schemes for Numerical Simulation of Hypersonic Boundary-Layer Transition

“…Hussaini et al [40] used the shock-fitting spectral method to simulate shock /turbulent interaction. Cai [41] used a shock-fitting method to compute two-dimensional detonation waves. The interactions between the bow shocks and disturbance waves are resolved by the shock-fitting method without generating numerical spurious oscillations.…”

“…They are numerically evaluated using a sixth-order compact central scheme shown in Eqs. (37) to (41). The spatially discretized equations are advanced in time using an explicit Runge-Kutta scheme [42] for the perfect gas flow.…”

A Conservative Staggered-Grid Chebyshev Multidomain Method for Compressible Flows

“…Derivativesarechosenfrom appropriate subdomainsso that wave componentsare "upwinded". The other approachuses a correction procedure( [25], [26], [1], [4]). To implement the correction method, the interior point approximationis integratedeverywhere, including at the boundaries.As a result, multiple solution valuesare available at eachinterfacepoint.…”

“…The maindifferencesbetweenthe Lobattogrid methodsarewhethertheequations are written in conservativeor non-conservativeform, and the manner in which the interfacesare treated.The conservativeform of the equationswasused,for example,in the methodspresented by [18] and [4]. Non-conservativeforms wereconsideredin [33], [26] and [1].…”