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Summary A typical Arbitrary Lagrangian-Eulerian (ALE) algorithm consists of a Lagrangian step, where the computational mesh moves with the fluid flow, a rezoning step, where the computational mesh is smoothed and repaired in case it gets too distorted, and a remapping step, where all fluid quantities are conservatively interpolated on this new mesh. In single-material simulations, the remapping process can be represented in a flux form, with fluxes approximated by integrating a reconstructed function over intersections of neighboring computational cells on the original and rezoned computational mesh. This algorithm is complex and computationally demanding – therefore a simpler approach, which utilizes regions swept by the cell edges during rezoning, is often used in practice. However, it has been observed that such simplification can lead to distortion of the solution symmetry, especially when the mesh movement is not bound by such symmetry. For this reason, we propose an algorithm combining both approaches in a similar way that was proposed for multi-material remapping (two-step hybrid remap). Intersections and exact integration are employed only in certain parts of the computational mesh, marked by a switching function – various different criteria are presented in this paper. The swept-based method is used elsewhere in areas that are not marked. This way our algorithm can retain the beneficial symmetry-preserving capabilities of intersection-based remapping while keeping the overall computational cost moderate. This article is protected by copyright. All rights reserved.

Remapping is an essential part of most Arbitrary Lagrangian–Eulerian (ALE) methods. In this paper, we focus on the part of the remapping algorithm that performs the interpolation of the fluid velocity field from the Lagrangian to the rezoned computational mesh in the context of a staggered discretization. Standard remapping algorithms generate a discrepancy between the remapped kinetic energy, and the kinetic energy that is obtained from the remapped nodal velocities which conserves momentum. In most ALE codes, this discrepancy is redistributed to the internal energy of adjacent computational cells which allows for the conservation of total energy. This approach can introduce oscillations in the internal energy field, which may not be acceptable. We analyze the approach introduced in Bailey (1984) [11] which is not supposed to introduce dissipation. On a simple example, we demonstrate a situation in which this approach fails. A modification of this approach is described, which eliminates (when it is possible) or reduces the energy discrepancy.

We propose an algebraic basis for symmetric Strang splitting for first and second order accurate schemes for hyperbolic systems in N dimensions. Examples are given for two and three dimensions. Optimal stability is shown for symmetric systems. Lack of strong stability is shown for a non-symmetric example. Some numerical examples are presented for some Euler-like constant coefficient problems.

Remapping is one of the essential parts of most arbitrary Lagrangian-Eulerian methods. Here, we extend the idea of swept integration introduced in (J. Comput. Phys. 2003; 184(1):266-298) to meshes with connectivity changing in Voronoi-like manner. To demonstrate properties of the developed method, we present several numerical examples.

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.

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.

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.

Production of high dynamic pressure using a strong shock wave is a topic of high relevance for high energy density physics, inertial confinement fusion and materials science. Although the pressures in the multi-megabar range can be produced by the shocks generated with a large variety of methods, the higher pressures, in the sub-gigabar or gigabar range, are achievable only with nuclear explosions or laser-driven shocks. However, the laser-to-shock energy conversion efficiency in the laser-based methods currently applied is low and, as a result, multi-kilojoule multi-beam lasers have to be used to produce such extremely high pressures. In this paper, the generation of high-pressure shocks in the newly proposed collider in which the projectile impacting a solid target is driven by the laser-induced cavity pressure acceleration (LICPA) mechanism is investigated using two-dimensional hydrodynamic simulations. A special attention is paid to the dependence of shock parameters and the laser-to-shock energy conversion efficiency on the impacted target material and the laser driver energy. It has been found that both in case of low-density and high-density solid targets the shock pressures in the sub-gigabar range can be produced in the LICPA-based collider with the laser energy of only a few hundred of joules, and the laser-to-shock energy conversion efficiency can reach values of 10 to 20 percent, by an order of magnitude higher than the conversion efficiencies achieved with other laser-based methods used so far., Comment: 18 pages, 12 figures

A novel, efficient method of generating ultra-high-pressure shocks is proposed and investigated. In this method, the shock is generated by collision of a fast plasma projectile (a macro-particle) driven by laser-induced cavity pressure acceleration (LICPA) with a solid target placed at the LICPA accelerator channel exit. Using the measurements performed at the kilojoule PALS laser facility and two-dimensional hydrodynamic simulations, it is shown that the shock pressure ∼ Gbar can be produced with this method at the laser driver energy of only a few hundred joules, by an order of magnitude lower than the energy needed for production of such pressure with other laser-based methods known so far.