Ralf Deiterding

A low numerical dissipation patch-based adaptive mesh refinement method for large-eddy simulation of compressible flows

We present a methodology for the large-eddy simulation of compressible flows with a low-numerical dissipation scheme and structured adaptive mesh refinement (SAMR). A description of a conservative, flux-based hybrid numerical method that uses both centered finite-difference and a weighted essentially non-oscillatory (WENO) scheme is given, encompassing the cases of scheme alternation and internal mesh interfaces resulting from SAMR. In this method, the centered scheme is used in turbulent flow regions while WENO is employed to capture shocks. One-, two- and three-dimensional numerical experiments and example simulations are presented including homogeneous shock-free turbulence, a turbulent jet and the strongly shock-driven mixing of a Richtmyer-Meshkov instability.

A virtual test facility for the efficient simulation of solid material response under strong shock and detonation wave loading

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.

An adaptive high-order hybrid scheme for compressive, viscous flows with detailed chemistry

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, compressible, 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 order-optimized, 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 one-and 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.

Construction and Application of an AMR Algorithm for Distributed Memory Computers

While the parallelization of blockstructured adaptive mesh refinement techniques is relatively straight-forward on shared memory architectures, appropriate distribution strategies for the emerging generation of distributed memory machines are a topic of on-going research. In this paper, a localitypreserving domain decomposition is proposed that partitions the entire AMR hierarchy from the base level on. It is shown that the approach reduces the communication costs and simplifies the implementation. Emphasis is put on the effective parallelization of the flux correction procedure at coarse-fine boundaries, which is indispensable for conservative finite volume schemes. An easily reproducible standard benchmark and a highly resolved parallel AMR simulation of a diffracting hydrogen-oxygen detonation demonstrate the proposed strategy in practice.

Detonation structure simulation with AMROC

Numerical simulations can be the key to the thorough understanding of the multi-dimensional nature of transient detonation waves. But the accurate approximation of realistic detonations is extremely demanding, because a wide range of different scales needs to be resolved. In this paper, we summarize our successful efforts in simulating multi-dimensional detonations with detailed and highly stiff chemical kinetics on recent parallel machines with distributed memory, especially on clusters of standard personal computers. We explain the design of AMROC, a freely available dimension-independent mesh adaptation framework for time-explicit Cartesian finite volume methods on distributed memory machines, and discuss the locality-preserving rigorous domain decomposition technique it employs. The framework provides a generic implementation of the blockstructured adaptive mesh refinement algorithm after Berger and Collela designed especially for the solution of hyperbolic fluid flow problems on logically rectangular grids. The ghost fluid approach is integrated into the refinement algorithm to allow for embedded non-Cartesian boundaries represented implicitly by additional level-set variables. Two- and three-dimensional simulations of regular cellular detonation structure in purely Cartesian geometry and a two-dimensional detonation propagating through a smooth 60 degree pipe bend are presented. Briefly, the employed upwind scheme and the treatment of the non-equilibrium reaction terms are sketched.

Adaptive Mesh Refinement-Based Numerical Simulation of Detonation Initiation in Supersonic Combustible Mixtures Using a Hot Jet

An open-source program implementing a block-structured adaptive mesh refinement method was adopted for the fine structure numerical simulation of detonation initiation in supersonic combustible mixtures. Simulations were conducted on a nested parallel computing system. The initiation process was specified as three stages, and their respective flow field characteristics were analyzed. Results indicate that a hot jet under specific conditions can have a similar effect as a pneumatic oblique bevel for inducing periodical shock-induced detonative combustion by a bow shock. The interaction of bow shock–induced combustion with the local detonation wave, produced by the reflection shock on the upper wall, can create a structure with two triple-wave points. The hot jet not only plays a role in the detonation initiation but also acts as a stabilizing control mechanism for detonation propagation. In the simulations in this study, the detonation wave propagates in an overdriven state initially and achieves self-sustaining motion after the shutdown of the hot jet. Subsequently, the final pisiform structure of typical stable Chapman-Jouguet detonation cells is formed.

High-Resolution Numerical Simulation and Analysis of Mach Reflection Structures in Detonation Waves in Low-Pressure H2–O2–Ar Mixtures: A Summary of Results Obtained with the Adaptive Mesh Refinement Framework AMROC

Numerical simulation can be key to the understanding of the multidimensional nature of transient detonation waves. However, the accurate approximation of realistic detonations is demanding as a wide range of scales needs to be resolved. This paper describes a successful solution strategy that utilizes logically rectangular dynamically adaptive meshes. The hydrodynamic transport scheme and the treatment of the nonequilibrium reaction terms are sketched. A ghost fluid approach is integrated into the method to allow for embedded geometrically complex boundaries. Large-scale parallel simulations of unstable detonation structures of Chapman-Jouguet detonations in low-pressure hydrogen-oxygen-argon mixtures demonstrate the efficiency of the described techniques in practice. In particular, computations of regular cellular structures in two and three space dimensions and their development under transient conditions, that is, under diffraction and for propagation through bends are presented. Some of the observed patterns are classified by shock polar analysis, and a diagram of the transition boundaries between possible Mach reflection structures is constructed.

High-resolution Simulation of Detonations with Detailed Chemistry

Numerical simulations can be the key to the thorough understanding of the multi-dimensional nature of transient detonation waves. But the accurate approximation of realistic detonations is extremely demanding, because a wide range of different scales need to be resolved. This paper describes an entire solution strategy for the Euler equations of thermally perfect gas-mixtures with detailed chemical kinetics that is based on a highly adaptive finite volume method for blockstructured Cartesian meshes. Large-scale simulations of unstable detonation structures of hydrogen-oxygen detonations demonstrate the efficiency of the approach in practice.

Eulerian adaptive finite-difference method for high-velocity impact and penetration problems

Owing to the complex processes involved, faithful prediction of high-velocity impact events demands a simulation method delivering efficient calculations based on comprehensively formulated constitutive models. Such an approach is presented herein, employing a weighted essentially non-oscillatory (WENO) method within an adaptive mesh refinement (AMR) framework for the numerical solution of hyperbolic partial differential equations. Applied widely in computational fluid dynamics, these methods are well suited to the involved locally non-smooth finite deformations, circumventing any requirement for artificial viscosity functions for shock capturing. Application of the methods is facilitated through using a model of solid dynamics based upon hyper-elastic theory comprising kinematic evolution equations for the elastic distortion tensor. The model for finite inelastic deformations is phenomenologically equivalent to Maxwells model of tangential stress relaxation. Closure relations tailored to the expected high-pressure states are proposed and calibrated for the materials of interest. Sharp interface resolution is achieved by employing level-set functions to track boundary motion, along with a ghost material method to capture the necessary internal boundary conditions for material interactions and stress-free surfaces. The approach is demonstrated for the simulation of high velocity impacts of steel projectiles on aluminium target plates in two and three dimensions.

Hydrodynamic Instabilities in Gaseous Detonations: Comparison of Euler, Navier–Stokes, and Large-Eddy Simulation

A large-eddy simulation is conducted to investigate the transient structure of an unstable detonation wave in two dimensions and the evolution of intrinsic hydrodynamic instabilities. The dependency of the detonation structure on the grid resolution is investigated, and the structures obtained by large-eddy simulation are compared with the predictions from solving the Euler and Navier–Stokes equations directly. The results indicate that to predict irregular detonation structures in agreement with experimental observations the vorticity generation and dissipation in small scale structures should be taken into account. Thus, large-eddy simulation with high grid resolution is required. In a low grid resolution scenario, in which numerical diffusion dominates, the structures obtained by solving the Euler or Navier–Stokes equations and large-eddy simulation are qualitatively similar. When high grid resolution is employed, the detonation structures obtained by solving the Euler or Navier–Stokes equations directly are roughly similar yet equally in disagreement with the experimental results. For high grid resolution, only the large-eddy simulation predicts detonation substructures correctly, a fact that is attributed to the increased dissipation provided by the subgrid scale model. Specific to the investigated configuration, major differences are observed in the occurrence of unreacted gas pockets in the high-resolution Euler and Navier–Stokes computations, which appear to be fully combusted when large-eddy simulation is employed.