An adaptive finite volume approach is presented to accurately simulate shockinduced combustion phenomena in gases, particularly detonation waves. The method uses a Cartesian mesh that is dynamically adapted to embedded geometries and flow features by using regular refinement patches. The discretisation is a reliable linearised Riemann solver for thermally perfect gas mixtures; detailed kinetics are considered in an operator splitting approach. Besides easily reproducible ignition problems, the capabilities of the method and its parallel implementation are quantified and demonstrated for fully resolved triple point structure investigations of Chapman-Jouguet detonations in low-pressure hydrogen-oxygen-argon mixtures in two and three space dimensions.

A virtual test facility (VTF) for studying the three-dimensional dynamic response of solid materials subject to strong shock and detonation waves has been constructed as part of the research program of the Center for Simulating the Dynamic Response of Materials at the California Institute of Technology. The compressible fluid flow is simulated with a Cartesian finite volume method and treating the solid as an embedded moving body, while a Lagrangian finite element scheme is employed to describe the structural response to the hydrodynamic pressure loading. A temporal splitting method is applied to update the position and velocity of the boundary between time steps. The boundary is represented implicitly in the fluid solver with a level set function that is constructed on-the-fly from the unstructured solid surface mesh. Block-structured mesh adaptation with time step refinement in the fluid allows for the efficient consideration of disparate fluid and solid time scales. We detail the design of the employed object-oriented mesh refinement framework AMROC and outline its effective extension for fluid-structure interaction problems. Further, we describe the parallelization of the most important algorithmic components for distributed memory machines and discuss the applied partitioning strategies. As computational examples for typical VTF applications, we present the dynamic deformation of a tantalum cylinder due to the detonation of an interior solid explosive and the impact of an explosion-induced shock wave on a multi-material soft tissue body.

Abstract.Structured adaptive mesh refinement (SAMR) techniques can enable cutting-edge simulations of problems governed by conservation laws. Focusing on the strictly hyperbolic case, these notes explain all algorithmic and mathematical details of a technically relevant implementation tailored for distributed memory computers. An overview of the background of commonly used finite volume discretizations for gas dynamics is included and typical benchmarks to quantify accuracy and performance of the dynamically adaptive code are discussed. Large-scale simulations of shock-induced realistic combustion in non-Cartesian geometry and shock-driven fluid-structure interaction with fully coupled dynamic boundary motion demonstrate the applicability of the discussed techniques for complex scenarios.

A hybrid weighted essentially non-oscillatory (WENO)/centered-difference numerical method, with low numerical dissipation, high-order shock-capturing, and structured adaptive mesh refinement (SAMR), has been developed for the direct numerical simulation of the multicomponent, compressive, reactive Navier-Stokes equations. The method enables accurate resolution of diffusive processes within reaction zones. The approach combines time-split reactive source terms with a high-order, shock-capturing scheme specifically designed for diffusive flows. A description of the orderoptimized, symmetric, finite difference, flux-based, hybrid WENO/centered-difference scheme is given, along with its implementation in a high-order SAMR framework. The implementation of new techniques for discontinuity flagging, scheme-switching, and high-order prolongation and restriction is described. In particular, the refined methodology does not require upwinded WENO at grid refinement interfaces for stability, allowing high-order prolongation and thereby eliminating a significant source of numerical diffusion within the overall code performance. A series of oneand two-dimensional test problems is used to verify the implementation, specifically the high-order accuracy of the diffusion terms. One-dimensional benchmarks include a viscous shock wave and a laminar flame. In two space dimensions, a Lamb-Oseen vortex and an unstable diffusive detonation are considered, for which quantitative convergence is demonstrated. Further, a two-dimensional high-resolution simulation of a reactive Mach reflection phenomenon with diffusive multi-species mixing is presented.

The problem of proximal bodies in hypersonic flow is encountered in several important situations, both natural and man-made. The present work seeks to investigate one aspect of this problem by exploring the forces experienced by a secondary body when some part of it is within the shocked region created by a primary body travelling at hypersonic speeds.An analytical methodology based on the blast wave analogy is developed and used to predict the secondary force coefficients for simple geometries in both two and three dimensions. When the secondary body is entirely inside the primary shocked region, the nature of the lateral coefficient is found to depend strongly on the relative size of the two bodies. For two spheres, the methodology predicts that the secondary body will experience an exclusively attractive lateral force if the secondary diameter is larger then one-sixth the primary diameter. The analytical results are compared with numerical simulations carried out using the AMROC software and good agreement is obtained if an appropriate normalization for the lateral displacement is used.Results from a series of experiments in the T5 hypervelocity shock tunnel are also presented and compared with perfect-gas numerical simulations, again with good agreement. In order to model this situation experimentally, a new force-measurement technique for short-duration hypersonic facilities has been developed, and results from the validation experiments are included.Finally, the analytical methodology is used to model two physical situations. First, the entry of a binary asteroid system into the Earth's atmosphere is simulated. Seciv ond, a model for a fragmenting meteoroid in a planetary atmosphere is developed, and simulations are carried out to determine whether the secondary scatter patterns in the Sikhote-Alin crater field may be attributed to aerodynamic interactions between fragments rather than to secondary fragmentation. It is found that while aerodynamic interactions lead to increased secondary crater grouping, these groups do not exhibit the typically elliptical shape that we would expect secondary fragmentation to produce.