Milan Kucharik

An efficient linearity-and-bound-preserving remapping method

In this paper we describe an efficient, local-bound-preserving conservative interpolation (remapping) algorithm, which is exact for a global linear function (linearity-preserving). The algorithm is based on reconstruction, approximate integration and mass re-distribution. We demonstrate our new algorithm on a series of numerical examples.

A comparative study of interface reconstruction methods for multi-material ALE simulations

In this paper we compare the performance of different methods for reconstructing interfaces in multi-material compressible flow simulations. The methods compared are a material-order-dependent Volume-of-Fluid (VOF) method, a material-order-independent VOF method based on power diagram partitioning of cells and the Moment-of-Fluid method (MOF). We demonstrate that the MOF method provides the most accurate tracking of interfaces, followed by the VOF method with the right material ordering. The material-order-independent VOF method performs somewhat worse than the above two while the solutions with VOF using the wrong material order are considerably worse.

Two-step hybrid conservative remapping for multimaterial arbitrary Lagrangian-Eulerian methods

We present a new hybrid conservative remapping algorithm for multimaterial Arbitrary Lagrangian-Eulerian (ALE) methods. The hybrid remapping is performed in two steps. In the first step, only nodes of the grid that lie inside subdomains occupied by single materials are moved. At this stage, computationally cheap swept-region remapping is used. In the second step, nodes that are vertices of mixed cells (cells containing several materials) and vertices of some cells in a buffer zone around mixed cells are moved. At this stage, intersection-based remapping is used. The hybrid algorithm results in computational expense that lies between swept-region and intersection-based remapping We demonstrate the performance of our new method for both structured and unstructured polygonal grids in two dimensions, as well as for cell-centered and staggered discretizations.

Conservative multi-material remap for staggered multi-material Arbitrary Lagrangian-Eulerian methods

Remapping is one of the essential parts of most multi-material Arbitrary Lagrangian-Eulerian (ALE) methods. In this paper, we present a new remapping approach in the framework of 2D staggered multi-material ALE on logically rectangular meshes. It is based on the computation of the second-order material mass fluxes (using intersections/overlays) to all neighboring cells, including the corner neighbors. Fluid mass is then remapped in a flux form as well as all other fluid quantities (internal energy, pressure). We pay a special attention to the remap of nodal quantities, performed also in a flux form. An optimization-based approach is used for the construction of the nodal mass fluxes. The flux-corrected remap (FCR) approach for flux limiting is employed for the nodal velocity remap, which enforces bound preservation of the remapped constructed velocity field. Several examples of numerical calculations are presented, which demonstrate properties of our remapping method in the context of a full ALE algorithm.

One-step hybrid remapping algorithm for multi-material arbitrary Lagrangian-Eulerian methods

In this paper, a new flux-based one-step hybrid remapping method for multi-material arbitrary Lagrangian-Eulerian (ALE) approach is introduced. In the vicinity of material interfaces, the swept region is intersected with pure material polygons in the Lagrangian mesh to construct the material fluxes. Far from interfaces, the fluxes are constructed in a standard swept-region manner without intersections. This method is conservative, second-order accurate and linearity-preserving (in case of straight material interfaces), and faster than method based on intersections, as shown on selected numerical examples.

Highly efficient accelerator of dense matter using laser-induced cavity pressure acceleration

Acceleration of dense matter to high velocities is of high importance for high energy density physics, inertial confinement fusion, or space research. The acceleration schemes employed so far are capable of accelerating dense microprojectiles to velocities approaching 1000 km/s; however, the energetic efficiency of acceleration is low. Here, we propose and demonstrate a highly efficient scheme of acceleration of dense matter in which a projectile placed in a cavity is irradiated by a laser beam introduced into the cavity through a hole and then accelerated in a guiding channel by the pressure of a hot plasma produced in the cavity by the laser beam or by the photon pressure of the ultra-intense laser radiation trapped in the cavity. We show that the acceleration efficiency in this scheme can be much higher than that achieved so far and that sub-relativisitic projectile velocities are feasible in the radiation pressure regime.

Recent results from experimental studies on laser?plasma coupling in a shock ignition relevant regime

Shock ignition (SI) is an appealing approach in the inertial confinement scenario for the ignition and burn of a pre-compressed fusion pellet. In this scheme, a strong converging shock is launched by laser irradiation at an intensity Iλ 2 >10 15 Wc m −2 µm 2 at the end of the compression phase. In this intensity regime, laser–plasma interactions are characterized by the onset of a variety of instabilities, including stimulated Raman scattering, Brillouin scattering and the two plasmon decay, accompanied by the generation of a population of fast electrons. The effect of the fast electrons on the efficiency of the shock wave production is investigated in a series of dedicated experiments at the Prague Asterix Laser Facility (PALS). We study the laser–plasma coupling in a SI relevant regime in a planar geometry by creating an extended preformed plasma with a laser beam at ∼7 × 10 13 Wc m −2 (250 ps, 1315 nm). A strong shock is launched by irradiation with a second laser beam at intensities in the range 10 15 –10 16 Wc m −2 (250 ps, 438 nm) at various delays with respect to the first beam. The pre-plasma is characterized using x-ray spectroscopy, ion diagnostics and interferometry. Spectroscopy and calorimetry of the backscattered radiation is performed in the spectral range 250–850 nm, including (3/2)ω, ω and ω/2 emission. The fast electron production is characterized through spectroscopy and imaging of the Kα emission. Information on the shock pressure is obtained using shock breakout chronometry and measurements of the craters produced by the shock in a massive target. Preliminary results show that the backscattered energy is in the range 3–15%, mainly due to backscattered light at the laser wavelength (438 nm), which increases with increasing the delay between the two laser beams. The values of the peak shock pressures inferred from the shock breakout times are lower than expected from 2D numerical simulations. The same simulations reveal that the 2D effects play a major role in these experiments, with the laser spot size comparable with the distance between critical and ablation layers.

Advanced scheme for high-yield laser driven nuclear reactions

The use of a low contrast nanosecond laser pulse with a relatively low intensity (3?????1016?W?cm?2) allowed the enhancing of the yield of induced nuclear reactions in advanced solid targets. In particular the ?ultraclean? proton?boron fusion reaction, producing energetic alpha particles without neutron generation, was chosen. A spatially well-defined layer of boron dopants in a hydrogen-enriched silicon substrate was used as a target. A combination of the specific target composition and the laser pulse temporal shape allowed the enhancing of the yield of alpha particles up to 109 per steradian. This result can be ascribed to the interaction of the long-laser pre-pulse with the target and to the optimal target geometry and composition.

Enhanced efficiency of plasma acceleration in the laser-induced cavity pressure acceleration scheme

Among various methods for the acceleration of dense plasmas the mechanism called laser-induced cavity pressure acceleration (LICPA) is capable of achieving the highest energetic efficiency. In the LICPA scheme, a projectile placed in a cavity is accelerated along a guiding channel by the laser-induced thermal plasma pressure or by the radiation pressure of an intense laser radiation trapped in the cavity. This arrangement leads to a significant enhancement of the hydrodynamic or electromagnetic forces driving the projectile, relative to standard laser acceleration schemes. The aim of this paper is to review recent experimental and numerical works on LICPA with the emphasis on the acceleration of heavy plasma macroparticles and dense ion beams. The main experimental part concerns the research carried out at the kilojoule sub-nanosecond PALS laser facility in Prague. Our measurements performed at this facility, supported by advanced two-dimensional hydrodynamic simulations, have demonstrated that the LICPA accelerator working in the long-pulse hydrodynamic regime can be a highly efficient tool for the acceleration of heavy plasma macroparticles to hyper-velocities and the generation of ultra-high-pressure (>100 Mbar) shocks through the collision of the macroparticle with a solid target. The energetic efficiency of the macroparticle acceleration and the shock generation has been found to be significantly higher than that for other laser-based methods used so far. Using particle-in-cell simulations it is shown that the LICPA scheme is highly efficient also in the short-pulse high-intensity regime and, in particular, may be used for production of intense ion beams of multi-MeV to GeV ion energies with the energetic efficiency of tens of per cent, much higher than for conventional laser acceleration schemes.

Using the feasible set method for rezoning in ALE

One of the steps in the Arbitrary Lagrangian Eulerian (ALE) algorithm is the improvement of the quality of the computational mesh. This step, commonly referred to as rezoning, is essential for maintaining a mesh that does not become invalid during a simulation. In this paper, we present a new robust and computationally efficient 2D mesh relaxation method. This feasible set method is a geometric method for finding the convex polygon that represents the region of coordinates that a vertex in a mesh can occupy while the mesh around it remains valid. After the feasible set has been computed for a vertex in a mesh, a new vertex location can be chosen that lies inside this feasible set. As a result, the mesh after relaxation is guaranteed to be valid. We present an example ALE simulation, that highlights the robustness of the feasible set method when used as a rezoning method in ALE.