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For numerical simulations of impact problems or fluid–solid interactions, the ALE (Arbitrary Lagrangian–Eulerian) approach is a useful tool due to its ability to keep the computational mesh smooth and moving with the fluid. The elastic–plastic extension of the compressible fluid model requires tensor variables for the description of non-volumetric (deviatoric) mechanical stress. While Lagrangian numerical schemes based on the evolution equation of the stress tensor are well developed, tensor remap is still a relatively unexplored territory. We propose a new approach to deviatoric stress remapping, where the second invariant J 2 (a conservative scalar quantity related to the strain energy) is remapped independently of the tensor components. These are re-scaled to match the remapped invariant value, effectively using only the principal directions and eigenvalue ratio from the component-wise remap. This approach is frame invariant, preserves J 2 invariant bounds and conserves the total invariant. We compare our method with component-based remapping using a simple synchronized limiter or a specialized stress tensor limiter described in the literature.

The magneto-hydrodynamic model is widely used for description of magnetized fluids in plasma dynamics, microfluidics, astrophysics and many other applications. In terms of modelling, the Lagrangian formulation is favourable for the rapid expansion during laser­target interaction for example. This is the case for inertial fusion and laboratory astrophysics applications, which are our primary interest. However, the proposed numerical method remains general and can be applied elsewhere. The conservation properties and divergence-free magnetic field are crucial aspects, which are not satisfied by the traditional numerical schemes. Here, the Lagrangian hydrodynamics using curvilinear finite elements is extended to the resistive magneto-hydrodynamics. An energy-conserving numerical scheme is formulated maintaining divergence-free magnetic field. The mixed finite element formulation provides theoretically arbitrary order of the spatial convergence and application on unstructured Lagrangian grids in multiple dimensions. An example of a physically relevant numerical simulation is presented.

Archaeogenetic time transect in Europe unravels genetic and social changes before and after the arrival of “steppe” ancestry., Europe’s prehistory oversaw dynamic and complex interactions of diverse societies, hitherto unexplored at detailed regional scales. Studying 271 human genomes dated ~4900 to 1600 BCE from the European heartland, Bohemia, we reveal unprecedented genetic changes and social processes. Major migrations preceded the arrival of “steppe” ancestry, and at ~2800 BCE, three genetically and culturally differentiated groups coexisted. Corded Ware appeared by 2900 BCE, were initially genetically diverse, did not derive all steppe ancestry from known Yamnaya, and assimilated females of diverse backgrounds. Both Corded Ware and Bell Beaker groups underwent dynamic changes, involving sharp reductions and complete replacements of Y-chromosomal diversity at ~2600 and ~2400 BCE, respectively, the latter accompanied by increased Neolithic-like ancestry. The Bronze Age saw new social organization emerge amid a ≥40% population turnover.

Detailed description of the transport processes in plasma is crucial for many disciplines. When the mean-free-path of the electrons is comparable or exceeds a characteristic length scale of the plasma profile, non-local behavior can be observed. Predictions of the diffusion theory are not valid and non-local electric and magnetic fields are generated. Kinetic modeling of these phenomena on time scales several orders of magnitude longer than the electron–electron collision time has proven to be cumbersome due to prohibitive requirements on the time step and violation of the conservation laws in the classical explicit Vlasov–Fokker–Planck methods. Therefore, a multi-dimensional conservative implicit Vlasov–Fokker–Planck–Maxwell method is proposed, where the distribution function is approximated by a truncated Cartesian tensor expansion. The electric and magnetic fields are modeled self-consistently, describing the generation process and emergence of non-locality in detail. Mixed finite elements are employed in space and the velocity dimension is discretized by staggered finite differences. Conservation properties are proved theoretically and the overall features are benchmarked on a series of physically representative problems. The second order convergence in velocity and the spatial order proportional to the polynomial order of the finite elements is shown. Further possible extensions of the method are discussed.

Magneto-hydrodynamics is one of the foremost models in plasma physics with applications in inertial confinement fusion, astrophysics and elsewhere. Advanced numerical methods are needed to get an insight into the complex physical phenomena. The classical Lagrangian methods are typically limited to the low orders of convergence and suffer from violation of the divergence-free condition for magnetic field or conservation of the invariants. This paper is the first part of a new series about high-order non-ideal magneto-hydrodynamics, where a multi-dimensional conservative Lagrangian method based on curvilinear finite elements is presented. The condition on zero divergence of magnetic field and conservation of mass, momentum, magnetic flux and the total energy are satisfied exactly. The curvilinear elements prevent entangling of the computational mesh and its imprinting into the solution. A high-order conservative time integration is applied, where an arbitrary order of convergence is attained for problems of ideal magneto-hydrodynamics. The resistive magnetic field diffusion is solved by an implicit scheme. Description of the method is given and multiple test problems demonstrating properties of the scheme are performed. The construction of the method and possible future directions of development are discussed.

Reliable simulations of laser–target interaction on the macroscopic scale are burdened by the fact that the energy transport is very often non-local. This means that the mean-free-path of the transported species is larger than the local gradient scale lengths and transport can be no longer considered diffusive. Kinetic simulations are not a feasible option due to tremendous computational demands, limited validity of the collisional operators and inaccurate treatment of thermal radiation. This is the point where hydrodynamic codes with non-local radiation and electron heat transport based on first principles emerge. The simulation code PETE (Plasma Euler and Transport Equations) combines both of them with a laser absorption method based on the Helmholtz equation and a radiation diffusion scheme presented in this article. In the case of modelling ablation processes it can be observed that both, thermal and radiative, transport processes are strongly non-local for laser intensities of 1013W/cm2 and above. In this paper simulations for various laser intensities and different ablator materials are presented, where the non-local and diffusive treatments of radiation transport are compared. Significant discrepancies are observed, supporting importance of non-local transport for inertial confinement fusion related studies as well as for pre-pulse generated plasma in ultra-high intensity laser–target interaction. Keywords: Inertial confinement fusion, Laser–plasma interaction, Radiation hydrodynamics, Transport theory, PACS Codes: 52.65.Kj, 52.57.-z, 52.50.Jm, 52.35.Tc, 52.25.Dg, 52.25.Fi, 44.40.+a, 47.70.Mc, 52.38.Dx, 52.38.Mf, 42.25.Bs, 52.25.Os

Models of the laser propagation and absorption are a crucial part of the laser–plasma interaction models. Hydrodynamic codes are afflicted by usage of the simplified, not self-consistent, models of the geometrical optics, limiting their physical accuracy. A robust and efficient method is presented for computing the stationary wave solution, not restricted to this field of application exclusively. The method combines the semi-analytic and high-order differential approaches to benefit from both. Flexibility of the discretization is maintained, including the discontinuous methods. Performance of the model is evaluated for the problem of a transition layer by comparison with the analytic solution. Reliable results on coarse computational meshes and high convergence rates on fine meshes are obtained. The relevance to the current fusion research and non-local energy transport is pointed out.

We present a new flux-corrected approach for remapping of velocity in the framework of staggered arbitrary Lagrangian-Eulerian methods. The main focus of the paper is the definition and preservation of coordinate invariant local bounds for velocity vector and development of momentum remapping method such that the radial symmetry of the radially symmetric flows is preserved when remapping from one equiangular polar mesh to another. The properties of this new method are demonstrated on a set of selected numerical cyclic remapping tests and a full hydrodynamic example.

Bell Beaker pottery spread across western and central Europe beginning around 2750 BCE before disappearing between 2200–1800 BCE. The mechanism of its expansion is a topic of long-standing debate, with support for both cultural diffusion and human migration. We present new genome-wide ancient DNA data from 170 Neolithic, Copper Age and Bronze Age Europeans, including 100 Beaker-associated individuals. In contrast to the Corded Ware Complex, which has previously been identified as arriving in central Europe following migration from the east, we observe limited genetic affinity between Iberian and central European Beaker Complex-associated individuals, and thus exclude migration as a significant mechanism of spread between these two regions. However, human migration did have an important role in the further dissemination of the Beaker Complex, which we document most clearly in Britain using data from 80 newly reported individuals dating to 3900–1200 BCE. British Neolithic farmers were genetically similar to contemporary populations in continental Europe and in particular to Neolithic Iberians, suggesting that a portion of the farmer ancestry in Britain came from the Mediterranean rather than the Danubian route of farming expansion. Beginning with the Beaker period, and continuing through the Bronze Age, all British individuals harboured high proportions of Steppe ancestry and were genetically closely related to Beaker-associated individuals from the Lower Rhine area. We use these observations to show that the spread of the Beaker Complex to Britain was mediated by migration from the continent that replaced >90% of Britain’s Neolithic gene pool within a few hundred years, continuing the process that brought Steppe ancestry into central and northern Europe 400 years earlier.

Low-density foam layers may be utilized in inertial fusion targets for smoothing of transverse inhomogeneities in ablation pressure. Alternatively, transparent underdense foam may serve as a dynamic phase plate for spatiotemporal smoothing of inhomogeneity patterns inside laser beams. We present here results of one-and two-dimensional fluid simulations of laser interactions with foams. For foams with submicron pores and wall thicknesses of order 10 nm, laser tunneling through overdense ionized walls is observed and laser penetration into the foam is accelerated. Qualitative comparison with recent experimental results is performed.

In one and two spatial dimensions, Lax-Wendroff schemes provide second-order accurate optimally-stable dispersive conservation-form approximations to non-linear conservation laws. These approximations are an important ingredient in sophisticated simulation algorithms for conservation laws whose solutions are discontinuous. Straightforward generalization of these Lax-Wendroff schemes to three dimensions produces an approximation that is unconditionally unstable. However, some dimensionally-split schemes do provide second-order accurate optimally-stable approximations in 3D (and 2D), and there are sub-optimally-stable non-split Lax-Wendroff-type schemes in 3D. The main result of this paper is the creation of new Lax-Wendroff-type second-order accurate optimally-stable dispersive non-split scheme that is in conservation form. The scheme is created by using linear equivalence to transform a symmetrized dimensionally-split scheme (based on a one-dimensional Lax-Wendroff scheme) to conservation form. We then create both composite and hybrid schemes by combining the new scheme with the diffusive first-order accurate Lax-Friedrichs scheme. Codes based on these schemes perform well on difficult fluid flow problems.

We describe here our newly developed ALE code on 2D quadrilaterals. The code is employed here in the numerical simulations of the erater formation during impact of small accelerated object on bulk target. The simulation of the high-velocity impact problem by the Lagrangian hydrodynamical codes leads in later stages to severe distortion of the Lagrangian grid which prevents continuation of computation. Such situations can however be treated by the Arbitrary Lagrangian Eulerian (ALE) method. In order to maintain the grid quality, the ALE method applies grid smoothing regularly after several time steps of Lagrangian computation. After changing the grid, the conservative quantities have to be conservatively remapped from the old grid to the new, better one. After remapping, Lagrangian computation can continue.

Simulations of laser-produced plasmas are essential for laser-plasma interaction studies and for inertial confinement fusion (ICF) technology. Dynamics of such plasmas typically involves regions of large scale expansion or compression, which requires to use the moving Lagrangian coordinates. For some kind of flows such as shear or vortex the moving Lagrangian mesh however tangles and such flows require the use of arbitrary Lagrangian Eulerian (ALE) method. We have developed code PALE (Prague ALE) for simulations of laser-produced plasmas which includes Lagrangian and ALE hydrodynamics complemented by heat conductivity and laser absorption. Here we briefly review the numerical methods used in PALE code and present its selected applications to modeling of laser interaction with targets.

The remapping algorithm is an essential part of the ALE (Arbitrary Lagrangian-Eulerian) method. In this talk we present such an algorithm based on linear function reconstruction, approximate integration and mass redistribution.

In this paper, a symmetry-preserving remapping algorithm for vectors respecting their local bounds by components and in magnitude is presented. First, description of the Vector Image Polygon (VIP) limiter for a piece-wise linear velocity reconstruction is presented. Numerical fluxes obtained from this reconstruction lead to symmetry- and bounds- preserving remap of momentum for staggered Arbitrary Lagrangian-Eulerian (ALE) hydrodynamical methods. A novel bounds definition for vectors and corresponding modification of the VIP limiter is introduced, which fixes undershoots in a radial velocity component for polar meshes. Comparison with standard scalar-based limiters is given. Cyclic remapping is performed to numerically verify properties of the methods.