Prediction of fragment distribution and trajectories of expolding shells

A semi-empirical model allowing for prediction of natural fragmentation of exploding shells is described. The initial velocity, projection angle, size and location, obtained for each fragment, are used by a point mass trajectory routine to determine the overall fragment distribution on the ground and to model fragments hitting a threedimensional object. Examples of validation against experimental data for 105mm shell and a mortar bomb are shown. The proposed model is useful for munition assessments, including a prediction of safety hazard in a credible accident

Burning surfaces evolution in solid propellants: a numerical model

A methodology for the solution of the internal physics of solid propellant rocket motors is described. The problem involves the simulation of a burning surface - a dynamically changing interface between the solid propellant and combustion gas phases. Burning surfaces can have complex shapes that change in time according to the solid chemistry and deformation, and according to gas parameters. The key element of the proposed model is the development of a new technique to conform the computational mesh to the interface. The paper documents mesh handling and solution procedures suitable for axisymmetric applications. The approach is to treat the problem in a uniform manner for solid and gas phases as a flow with moving sources. Unstructured, dynamically adjusting meshes are employed in the same way for both phases. This paper presents two specific test cases, with non-deforming solids, for which a comparison with theoretical results is possible

A multidimensional positive definite remapping for Lagrangian solutions of the Noh problem

A remapping based on the multidimensional positive definite advection transport algorithm (MPDATA), implemented for ALE methods, is used to model the Noh problem. Typical solutions in the Lagrangian reference frame contain heating errors which arise during the simulation of a shock reflection originating at a wall. The paper shows that the inherent properties of MPDATA can be exploited in the remapping to reduce wall heating errors. The resulting increase in accuracy and symmetry of solutions is demonstrated

A nonhydrostatic unstructured-mesh soundproof model for simulation of internal gravity waves

A semi-implicit edge-based unstructured-mesh model is developed that integrates nonhydrostatic soundproof equations, inclusive of anelastic and pseudo-incompressible systems of partial differential equations. The model builds on nonoscillatory forward-in-time MPDATA approach using finite-volume discretization and unstructured meshes with arbitrarily shaped cells. Implicit treatment of gravity waves benefits both accuracy and stability of the model. The unstructured-mesh solutions are compared to equivalent structured-grid results for intricate, multiscale internal-wave phenomenon of a non-Boussinesq amplification and breaking of deep stratospheric gravity waves. The departures of the anelastic and pseudo-incompressible results are quantified in reference to a recent asymptotic theory [Achatz et al. 2010, J. Fluid Mech., 663, 120-147)]

Iterated upwind schemes for gas dynamics

A class of high-resolution schemes established in integration of anelastic equations is extended to fully compressible flows, and documented for unsteady (and steady) problems through a span of Mach numbers from zero to supersonic. The schemes stem from iterated upwind technology of the multidimensional positive definite advection transport algorithm (MPDATA). The derived algorithms employ standard and modified forms of the equations of gas dynamics for conservation of mass, momentum and either total or internal energy as well as potential temperature. Numerical examples from elementary wave-propagation, through computational aerodynamics benchmarks, to atmospheric small- and large-amplitude acoustics with intricate wave-flow interactions verify the approach for both structured and unstructured meshes, and demonstrate its flexibility and robustness

An edge-based unstructured mesh framework for atmospheric flows

This paper describes an unstructured/hybrid mesh framework providing a robust environment for multiscale atmospheric modeling. The framework builds on nonoscillatory forward-in-time MPDATA solvers using finite volume edge-based discretization, and admits meshes with arbitrarily shaped cells. The numerical formulation is equally applicable to global and limited area models. Theoretical considerations are supported with canonical examples of slab-symmetric, nonhydrostatic orographic problems in weakly and strongly stratified flow regimes and three-dimensional hydrostatic analogues of the strongly stratified case on a slowly and rapidly rotating sphere

An edge-based unstructured mesh discretisation in geospherical framework

An arbitrary finite-volume approach is developed for discretising partial differential equations governing fluid flows on the sphere. Unconventionally for unstructured-mesh global models, the governing equations are cast in the anholonomic geospherical framework established in computational meteorology. The resulting discretisation retains proven properties of the geospherical formulation, while it offers the flexibility of unstructured meshes in enabling irregular spatial resolution. The latter allows for a global enhancement of the spatial resolution away from the polar regions as well as for a local mesh refinement. A class of non-oscillatory forward-in-time edge-based solvers is developed and applied to numerical examples of three-dimensional hydrostatic flows, including shallow-water benchmarks, on a rotating sphere

Numerical characterisation of stably stratified flows past spheres

A numerical study of stably stratified flows past spheres at moderate Reynolds numbers is presented. The resolved flows can adequately describe a wide class of geophysical, environmental, and engineering flows characterised by the density stratification of the terrestrial atmosphere and oceanic thermocline. The range of physical phenomena developing when stratified flows impact single and multiple spheres constitute a convenient benchmark for complex geometry applications, e.g. mountains, islands, wind turbines, and buildings. Solutions of Navier-Stokes equations, in the incompressible Boussinesq limit, are obtained by applying a semi-implicit finite volume (FV) non-oscillatory forward-in-time (NFT) integration scheme enhanced by MPI parallelization. The developed model is applied for a systematic investigation of stratified flow patterns arising for a range of Froude numbers Fr ∈ [0.1,∞] at Reynolds numbers Re = 200 and Re = 300, for which the neutrally stratified flows induces distinctly different near-wake features

Simulation of all-scale atmospheric dynamics on unstructured meshes

The advance of massively parallel computing in the nineteen nineties and beyond encouraged finer grid intervals in numerical weather-prediction models. This has improved resolution of weather systems and enhanced the accuracy of forecasts, while setting the trend for development of unified all-scale atmospheric models. This paper first outlines the historical background to a wide range of numerical methods advanced in the process. Next, the trend is illustrated with a technical review of a versatile nonoscillatory forward-in-time finite-volume (NFTFV) approach, proven effective in simulations of atmospheric flows from small-scale dynamics to global circulations and climate. The outlined approach exploits the synergy of two specific ingredients: the MPDATA methods for the simulation of fluid flows based on the sign-preserving properties of upstream differencing; and the flexible finite-volume median-dual unstructured-mesh discretisation of the spatial differential operators comprising PDEs of atmospheric dynamics. The paper consolidates the concepts leading to a family of generalised nonhydrostatic NFTFV flow solvers that include soundproof PDEs of incompressible Boussinesq, anelastic and pseudo-incompressible systems, common in large-eddy simulation of small- and meso-scale dynamics, as well as all-scale compressible Euler equations. Such a framework naturally extends predictive skills of large-eddy simulation to the global atmosphere, providing a bottom-up alternative to the reverse approach pursued in the weather-prediction models. Theoretical considerations are substantiated by calculations attesting to the versatility and efficacy of the NFTFV approach. Some prospective developments are also discussed

Simulation and measurement of fragment velocity in exploding shells

This paper presents simulations of initial velocity distribution of fragments for non-trivial shapes of casing in exploding shells, using a semi-empirical computational model. The key to the proposed approach is the use of transformation of a general geometrical shape to a hollow sphere followed by an application of Gurney principles in the transformed domain. The model is validated against an analytical model for a finite cylindrical charge bounded by a cylindrical shell and identical end-plates. A computation for 105-mm shell with steel casing and aluminium fuze illustrates aspects involved in reliable comparisons of fragmentation models against a standard trial data. Further, a simple and inexpensive experimental procedure based on a pin gauges measurement is described. Measurements obtained for short cylinders and an 81-mm mortar bomb are compared with numerical predictions. The described model responds to the need for an improved, fast assessment tool applicable to practical designs involving geometrically complex multi-material shells. The results highlight a requirement for quality experimental data obtained for complex shapes