Anil Kapahi

A three-dimensional sharp interface Cartesian grid method for solving high speed multi-material impact, penetration and fragmentation problems

This work presents a three-dimensional, Eulerian, sharp interface, Cartesian grid technique for simulating the response of elasto-plastic solid materials to hypervelocity impact, shocks and detonations. The mass, momentum and energy equations are solved along with evolution equations for deviatoric stress and plastic strain using a third-order finite difference scheme. Material deformation occurs with accompanying nonlinear stress wave propagation; in the Eulerian framework the boundaries of the deforming material are tracked in a sharp fashion using level-sets and the conditions on the immersed boundaries are applied by suitable modifications of a ghost fluid approach. The dilatational response of the material is modeled using the Mie-Gruneisen equation of state and the Johnson-Cook model is employed to characterize the material response due to rate-dependent plastic deformation. Details are provided on the treatment of the deviatoric stress ghost state so that physically correct boundary conditions can be applied at the material interfaces. An efficient parallel algorithm is used to handle computationally intensive three-dimensional problems. The results demonstrate the ability of the method to simulate high-speed impact, penetration and fragmentation phenomena in three dimensions.

Simulation of high speed impact, penetration and fragmentation problems on locally refined Cartesian grids

Techniques are presented to solve problems involving high speed material interactions that can lead to large deformations followed by fragmentation. To simulate such problems in an Eulerian framework on a fixed Cartesian mesh, interfaces (free surfaces as well as interacting material interfaces) are tracked as levelsets; to resolve shocks and interfaces, a quadtree adaptive mesh is employed. This paper addresses issues associated with the treatment of all interfaces as sharp entities by defining ghost fields on each side of the interface. Collisions between embedded objects are resolved using an efficient collision detection algorithm and appropriate interfacial conditions are supplied. Key issues of supplying interfacial conditions at the precise location of the sharp interface and populating the ghost cells with physically consistent values during and beyond fragmentation events are addressed. Numerous examples pertaining to impact, penetration, void collapse and fragmentation phenomena are presented along with careful benchmarking to establish the validity, accuracy and versatility of the approach.

Tree-Based Local Mesh Refinement for Compressible Multiphase Flows

Shock waves interacting with multi-material interfaces in compressible flows result in complex shock diffraction patterns involving total or partial reflection, refraction and transmission of the impinging shock wave. To simulate such complicated interfacial dynamics problems, a fixed Cartesian grid approach in conjunction with level set interface tracking is attractive. In this regard, a unified Riemann solver based Ghost Fluid Method (GFM) was developed to accurately resolve and represent the embedded solid and fluid object(s) in high speed compressible multiphase flows. While the GFM-based Cartesian grid approach significantly alleviates the complexity associated with mesh management, the method lacks flexibility in effective grid point placement in regions with rich structures in the flow field. Thus for higher-order and highly accurate sharp interface Cartesian grid based calculations with optimal computational effort, it is imperative to supplement the solution with adaptive mesh refinement technique. Hence in this work, a simple procedure is presented to complement the Riemann solver based GFM approach with quadtree (octree in three dimensions) based Local Mesh Refinement (LMR) technique for efficient and high fidelity computations involving strong shock interactions in multiphase compressible flows. The paper reports on a simple, conservative formulation for accurate calculation of ENO-based numerical fluxes at the fine-coarse mesh boundary. The numerical examples displayed in this paper clearly demonstrate that the methodology is consistent in generating satisfactory solutions, and effectively capturing fine structures in the flow.

Three Dimensional Compressible Multi-Material Flows

Shock Waves and Detonation waves have been topic of cutting edge research for decades. The interaction of these waves with multi materials can result in complex wave structures in two and three dimensions. Large-scale computations are required to simulate physical phenomena involving detonation and shock waves like supernova formation, explosions and hypervelocity impact and penetration. In this paper we describe the parallel implementation of fixed Cartesian grid flow solver with moving boundaries. A higher order conservation scheme such as ENO is used for calculating the numerical fluxes and level sets are used to define the objects immersed in flow field. A Riemann solver based Ghost fluid method is used for interface treatment of embedded objects. This paper describes the methodology for parallelization with emphasis on efficient storage and retrieval of data, handling moving boundaries in multi-processor environment and definition and treatment of ghost layer in three dimensions. All the features, which have been observed in serial computation, are reproduced with capturing of additional finer structures.

Shock wave interaction with voids in heterogeneous energetic materials

Shock waves interacting with heterogeneous materials are important in studies related to impact, penetration and detonation in condensed media, with applications in propulsive devices, munitions and explosive-target interactions. The study of release of energy is a crucial requirement in these systems. Traditional models for these applications are based on continuum theories where the microstructural heterogeneities of the material is ignored or homogenized. These simulations based on a continuum mechanics approach at the macro scale miss the key aspect of modeling energy release at a scale corresponding to particle size. Designing propulsion devices and munitions for precise operational performances demands comprehensive understanding and manipulation of the spatial and temporal distribution of energy release in activated energetic materials. Localized events, such as void collapse and inter-particle friction must be accounted for in detailed study of these materials. The proposed work seeks to develop a computational tool to conduct realistic modeling of the multi scale dynamics of shocked heterogeneous media.

Shock wave interaction with microstructures and heterogeneous media

Shock waves interacting with heterogeneous energetic materials are important in studies related to detonation and deflagration in condensed media. They have plethora of applications in propulsive devices, munitions and explosive targets. The study of release of energy is crucial requirement in these systems. Traditional models for these applications are based on continuum theories where the inherent microstructure of material is ignored. These simulations based on continuum mechanic approach on macro scale miss the key aspect of modeling energy release at a scale corresponding to particle size. Designing propulsion devices and munitions for precise operational performances demands comprehensive understanding and manipulation of the spatial and temporal distribution of energy release in activated energetic materials. The localized events like void collapse and inter-particle friction must account for in detailed study of these materials. The proposed work seeks to develop a computational tool to conduct a realistic modeling of the multi scale dynamics of heterogeneous media.

Three Dimensional Parallel Compressible Multi-material Flows

*** § Shock Waves and Detonation waves have been topic of cutting edge research for decades. The interaction of these waves with multi materials can result in complex wave structures in two and three dimensions. Large-scale computations are required to simulate physical phenomena involving detonation and shock waves like supernova formation, explosions and hypervelocity impact and penetration. In this paper we describe the parallel implementation of fixed Cartesian grid flow solver with moving boundaries. A higher order conservation scheme such as ENO is used for calculating the numerical fluxes and level sets are used to define the objects immersed in flow field. A Riemann solver based Ghost fluid method is used for interface treatment of embedded objects. This paper describes the methodology for parallelization with emphasis on strong shocks interacting with embedded interfaces (solid-fluid, solid-solid and fluidfluid) in three-dimensional compressible flow framework. It also explains the handling of moving boundaries in multi-processor environment and definition and treatment of ghost layer in three dimensions.

A Three-Dimensional Sharp Interface Cartesian Grid Method for Solving High Speed Multi-Material Impact Problems

*** § Large-scale computations are required to simulate physical phenomena involving detonation and shock waves in supernova formation, explosions and hypervelocity impact and penetration. The interaction of these waves with multi materials can result in complex wave structures in two and three dimensions. In addition, the embedded materials may experience large motions and deformation under the influence of the high-speed flows. In this paper, the main focus is on parallel implementation of a fixed Cartesian grid flow solver with moving boundaries. A higher order conservation scheme such as ENO is used for calculating the numerical fluxes and level sets are used to define the objects immersed in flow field. A Riemann solver based Ghost fluid method is used for interface treatment of embedded objects. The issues involved in parallelization of the moving boundary solver are presented with emphasis on strong shocks interacting with embedded interfaces (solid-solid) in three-dimensional compressible flow framework. The handling of moving boundaries, tracked using narrow-band levelsets leads to issues peculiar to the multi-processor environment; the solution to object passage between subdomains and treatment of ghost regions for inter-processor communication are also addressed. Example calculations for three-dimensional impact/penetration problems are presented. I. INTRODUCTION The levelset[22] based sharp interface methods have been developed for solution of moving boundary problems on fixed Cartesian grids. This treatment reduces the complexity involved in grid generation while defining complicate shapes implicitly using level set fields. In previous papers, a simple and a unified Cartesian grid approach were developed for accurate representation of embedded solid and fluid objects in high-speed compressible multiphase flows[20, 21].