Specific features of mathematical modeling of ceramic plates destruction under the influence of high-speed impactors

The paper examines the issues of mathematical modeling of ceramic armor panels’ penetration by high-speed cylindrical impactors. By means of the LS-DYNA software package, a corresponding numerical simulation methodology was developed by combining a chosen method, adjusted computational mesh cells size, appropriate Courant number, and values of linear and quadratic pseudo-viscosity coefficients. The results compared with experimental data show that Lagrangian and Eulerian numerical methods, unlike the SPH method (Smoothed Particle Hydrodynamics), improperly reproduce the process of the shock wave disintegration into an elastic precursor and a plastic wave. In addition, the common size of conical fractions dislodging from the ceramic plates was determined and the influence of the scale effect on the ceramics damage patterns was shown: an increase in the absolute value of the plate thickness leads to the increase in the dislodging cone semi-vertex angle.

Volume of Fluid Simulations of Copper Droplet Splat and Sensitivity to Modeling Methods

Liquid droplet interactions with solid surfaces are fundamental to a wide range of phenomena from novel manufacturing processes, ice accretion on surfaces, to ablation and fouling build-up when droplets are carried with fluid flow along a flow path. Computational fluid-dynamics based simulations offer a controlled environment in which to explore the details of the droplet motion, deformation, or break-up and solidification and melting as droplet impingement on a surface occurs. The operating, material, or geometric conditions can be altered and the resulting changes in the droplet related phenomena can be used to gain the information needed to control the droplet related processes for an intended purpose. The present work investigates the sensitivity of the predicted splat development as a single copper droplet impact upon a cool copper substrate to variations in a volume of fluid based computational modeling method. One liquid copper droplet is assigned an initial velocity and temperature and is set to impact a cold solid copper surface. The splat profile, as time progresses, is compared to the results in the literature. Among the computational modeling method changes investigated are the surface tension treatment, the solution method for the volume fraction equation, the volume fraction time sub-step calculation method, the volume fraction cut-off value and Courant number, the frequency of the volume fraction updates, the volume fraction discretization method, the mushy zone parameter, and mesh refinement. The study results can be used to provide information to aid in the generation of the models that can more accurately interrogate droplet-surface interactions.

The suite of Taylor–Galerkin class schemes for ice transport on sphere implemented by the INMOST package

Realizations of the numerical solution of the scalar transport equation on the sphere, written in divergent form, are presented. Various temporal discretizations are considered: the one-step Taylor–Galerkin method (TG2), the two-step Taylor–Galerkin method of the second (TTG2), third (TTG3), and fourth (TTG4) orders. The standard Finite-Element Galerkin method with linear basis functions on a triangle is applied as spatial discretization. The flux correction technique (FCT) is implemented. Test runs are carried out with different initial profiles: a function from C ∞ (Gaussian profile) and a discontinuous function (slotted cylinder). The profiles are advected by reversible, nondivergent velocity fields, therefore the initial distribution coincides with the final one. The case of a divergent velocity field is also considered to test the conservation and positivity properties of the schemes. It is demonstrated that TG2, TTG3, and TTG4 schemes with FCT applied give the best result for small Courant numbers, and TTG2, TTG4 are preferable in case of large Courant number. However, TTG2+FCT scheme has the worst stability. The use of FCT increases the integral errors, but ensures that the solution is positive with high accuracy. The implemented schemes are included in the dynamic core of a new sea ice model developed using the INMOST package. The acceleration of the parallel program and solution convergence with spatial resolution are demonstrated.

A Positivity-preserving Conservative Semi-Lagrangian Multi-moment Global Transport Model on the Cubed Sphere

A positivity-preserving conservative semi-Lagrangian transport model by multi-moment finite volume method has been developed on the cubed-sphere grid. Two kinds of moments (i.e., point values (PV moment) at cell interfaces and volume integrated average (VIA moment) value) are defined within a single cell. The PV moment is updated by a conventional semi-Lagrangian method, while the VIA moment is cast by the flux form formulation to assure the exact numerical conservation. Different from the spatial approximation used in the CSL2 (conservative semi-Lagrangian scheme with second order polynomial function) scheme, a monotonic rational function which can effectively remove non-physical oscillations is reconstructed within a single cell by the PV moments and VIA moment. To achieve exactly positive-definite preserving, two kinds of corrections are made on the original conservative semi-Lagrangian with rational function (CSLR) scheme. The resulting scheme is inherently conservative, non-negative, and allows a Courant number larger than one. Moreover, the spatial reconstruction can be performed within a single cell, which is very efficient and economical for practical implementation. In addition, a dimension-splitting approach coupled with multi-moment finite volume scheme is adopted on cubed-sphere geometry, which benefitsthe implementation of the 1D CSLR solver with large Courant number. The proposed model is evaluated by several widely used benchmark tests on cubed-sphere geometry. Numerical results show that the proposed transport model can effectively remove nonphysical oscillations and preserve the numerical non-negativity, and it has the potential to transport the tracers accurately in a real atmospheric model.

Three-Dimensional Effects on Slamming Loads

Three-dimensional effects on slamming loads predictions of a ship section are investigated numerically using the unsteady incompressible Reynolds-Average Navier-Stokes (RANS) equations and volume of fluid (VOF) method, which are implemented in interDyMFoam solver in open-source library OpenFoam. A convergence and uncertainty study is performed considering different resolutions and constant Courant number (CFL) following the ITTC guidelines. The numerical solutions are validated through comparisons of slamming loads and motions between the CFD simulations and the available experimental values. The total slamming force and slamming pressures on a 2D ship section and the 3D model are compared and discussed. Three-dimensional effects on the sectional force and the pressures are quantified both in transverse and longitudinal directions of the body considering various entry velocities. The non-dimensional pressure coefficient distribution on the 3D model is presented.

Numerical Assessment of Turbulence Effects on Water Entry of a Hemisphere

Water entry of a rigid hemisphere is simulated using the unsteady incompressible Reynolds-Average Navier-Stokes (RANS) equations and volume of fluid (VOF) method, which are implemented in the open-source library OpenFoam. The solver InterDyMFoam is applied and the algorithm PIMPLE which is a combination of PISO (Pressure Implicit with Splitting of Operators) and SIMPLE (Semi-Implicit Method for pressure-Linked Equations) algorithms are used in the simulations. A second-order backward difference scheme is applied for the temporal discretization. A convergence and uncertainty study is performed considering different resolutions and constant Courant number (CFL) using the procedures recommended by ITTC. The comparisons of slamming loads and motions between the CFD simulations are presented using both laminar and turbulence fluid models for the hemisphere entering the water at various speeds. Turbulence is modelled with a Reynolds averaged stress (RAS) k-ω two-equation model. The turbulence effects on the slamming loads will be assessed for the case with different entry velocities.

An accurate and efficient scheme involving unsteady friction for transient pipe flow

A robust prediction system should monitor all possible hydraulic transients, which is significant for appropriate and safe operations of pipe systems. A second-order finite volume method (FVM) Godunov-type scheme (GTS) considering unsteady friction factors is introduced to simulate hydraulic transients, which was rarely involved in previous work. One explicit-solution source item approach developed in this work is crucial for the proposed GTS to easily incorporate various forms of the existing unsteady friction models, including original convolution-based models (Zielke model and Vardy–Brown model), simplified convolution-based model (Trikha–Vardy–Brown (TVB) model), and Brunone instantaneous acceleration-based model. Results achieved by the proposed models are compared with experimental data as well as predictions by the classic Method of Characteristics (MOC). Results show that the MOC scheme may produce severe numerical attenuation in the case of a low Courant number. The proposed second-order GTS unsteady friction models are accurate, efficient, and stable even for Courant numbers less than one and sparse grid, and only need much less grid number and computation time to reach the same numerical accuracy. The TVB convolution-based model and Brunone model in the second-order GTS are suggested for further applications in hydraulic transients due to their high accuracy and efficiency.

Long Time Steps for Advection: MPDATA with implicit time stepping

<p>Semi-Lagrangian advection schemes are accurate and efficient and retain accuracy and stability even for large Courant numbers but are not conservative. Flux-form semi-Lagrangian is conservative and in principle can be used to achieve large Courant numbers. However this is complicated and would be prohibitively expensive on grids that are not logically rectangular. </p><p>Strong winds or updrafts can lead to localised violations of Courant number restrictions which can cause a model with explicit Eulerian advection to crash. Schemes are needed that remain stable in the presence of large Courant numbers. However accuracy in the presence of localised large Courant numbers may not be so crucial.</p><p>Implicit time stepping for advection is not popular in atmospheric science because of the cost of the global matrix solution and the phase errors for large Courant numbers. However implicit advection is simple to implement (once appropriate matrix solvers are available) and is conservative on any grid structure and can exploit improvements in solver efficiency and parallelisation. This talk will describe an implicit version of the MPDATA advection scheme and show results of linear advection test cases. To optimise accuracy and efficiency, implicit time stepping is only used locally where needed. This makes the matrix inversion problem local rather than global. With implicit time stepping MPDATA retains positivity, smooth solutions and accuracy in space and time.</p>

U-duct turbulent-flow computation with the ST-VMS method and isogeometric discretization

The U-duct turbulent flow is a known benchmark problem with the computational challenges of high Reynolds number, high curvature and strong flow dependence on the inflow profile. We use this benchmark problem to test and evaluate the Space–Time Variational Multiscale (ST-VMS) method with ST isogeometric discretization. A fully-developed flow field in a straight duct with periodicity condition is used as the inflow profile. The ST-VMS serves as the core method. The ST framework provides higher-order accuracy in general, and the VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the unsteady flow. The ST isogeometric discretization enables more accurate representation of the duct geometry and increased accuracy in the flow solution. In the straight-duct computations to obtain the inflow velocity, the periodicity condition is enforced with the ST Slip Interface method. All computations are carried out with quadratic NURBS meshes, which represent the circular arc of the duct exactly in the U-duct computations. We investigate how the results vary with the time-averaging range used in reporting the results, mesh refinement, and the Courant number. The results are compared to experimental data, showing that the ST-VMS with ST isogeometric discretization provides good accuracy in this class of flow problems.

ON A STUDY OF STAGGERED LEAPFROG SCHEME FOR LINEAR SHALLOW WATER EQUATIONS

In this paper, we present an analytical and numerical study of staggered leapfrog scheme for linear shallow water equation. It is shown that the scheme is stable when Courant number < 1, has second order accurate in both time and space, and there is no damping error in this scheme. We implement the scheme to simulate standing wave in a closed basin to show that the surface motions stay zero in a node and have constant amplitude at the antinode. For an external force given into the basin, it will induce a resonance, which cause the wave amplitude is getting bigger at the position of antinode. Moreover, we simulate a wave in a tidal basin, and show that the model has infinite spin up time. For a linear shallow water equation with linear friction, it is shown that the model has finite spin up time.