Pavel Váchal

Optimization-based synchronized flux-corrected conservative interpolation (remapping) of mass and momentum for arbitrary Lagrangian-Eulerian methods

A new optimization-based synchronized flux-corrected conservative interpolation (remapping) of mass and momentum for arbitrary Lagrangian-Eulerian hydro methods is described. Fluxes of conserved variables - mass and momentum - are limited in a synchronous way to preserve local bounds of primitive variables - density and velocity.

A second-order compatible staggered Lagrangian hydrodynamics scheme using a cell-centered multidimensional approximate Riemann solver

We develop a general framework to derive and analyze staggered numerical schemes devoted to solve hydrodynamics equations in 2D. In this framework a cell-centered multi-dimensional approximate Riemann solver is used to build a form of artificial viscosity that leads to a conservative, compatible and thermodynamically consistent scheme. A second order extension in space and time for this scheme is proposed in this work and we prove on numerical examples the validity of this approach.

Symmetry- and essentially-bound-preserving flux-corrected remapping of momentum in staggered ALE hydrodynamics

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.

ALE simulations of high-velocity impact problem

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.

A symmetry preserving dissipative artificial viscosity in an r-z staggered Lagrangian discretization

We present an artificial viscous force for two-dimensional axi-symmetric r-z geometry and logically rectangular grids that is dissipative, conserves the z-component of momentum and preserves spherical symmetry on an equi-angular polar grid. The method turns out to be robust and performs well for spherically symmetric problems on various grid types, without any need for problem- or grid-dependent parameters.

On preservation of symmetry in r-z staggered Lagrangian schemes

In the focus of this work are symmetry preservation, conservation of energy and volume, and other important properties of staggered Lagrangian hydrodynamic schemes in cylindrical (r-z) geometry. It is well known that on quadrilateral cells in r-z, preservation of spherical symmetry, perfect satisfaction of the Geometrical Conservation Law (GCL), and total energy conservation are incompatible even on conforming grids.This paper suggests a novel staggered grid approach that preserves symmetry, conserves total energy by construction and tries to do its best by diminishing the GCL error to the order of entropy error. In particular, the forces from an existing volume consistent scheme are corrected so that spherical symmetry is preserved.The incorporation of subcell pressure mechanism to reduce spurious grid deformations is described and the relation of the new scheme to popular area-weighted and control volume approaches studied.

ALE Method for Simulations of Laser-Produced Plasmas

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.

Modeling of annular-laser-beam-driven plasma jets from massive planar targets

Production of sharply collimated high velocity outflows – plasma jets from massive planar targets by a single laser beam at PALS facility is clarified via numerical simulations. Since only a few experimental data on the intensity distribution in the interaction beam near the focus are available for the PALS facility, the laser beam profile was calculated by a numerical model of the laser system and the interaction optics. The obtained intensity profiles are used as the input for plasma dynamic simulations by our cylindrical two-dimensional fluid code PALE. Jet formation due to laser intensity profile with a minimum on the axis is demonstrated. The outflow collimation improves significantly for heavier elements, even when radiative cooling is omitted. Using an optimized interaction beam profile, a homogeneous jet with a length exceeding its diameter by several times may be reliably generated for applications in laboratory astrophysics and impact ignition studies.

Formulation of a staggered two-dimensional Lagrangian scheme by means of cell-centered approximate Riemann solver

In this work we develop a general framework to derive and analyze staggered numerical scheme devoted to solve hydrodynamics equations.

Volume change and energy exchange: How they affect symmetry in the Noh problem

Abstract The edge viscosity of Caramana, Shashkov and Whalen is known to fail on the Noh problem in an initially rectangular grid. We present a simple change that significantly improves the behavior in that case. We also show that added energy exchange between cells improves the symmetry of both edge viscosity and the tensor viscosity of Campbell and Shashkov. As suggested by Noh, this addition also reduces the wall heating effect.