CELL-CENTERED LAGRANGIAN LAX-WENDROFF HLL HYBRID SCHEME ON UNSTRUCTURED MESHES

We have recently introduced a new cell-centered Lax-Wendroff HLL hybrid scheme for Lagrangian hydrodynamics [Fridrich et al. J. Comp. Phys. 326 (2016) 878-892] with results presented only on logical rectangular quadrilateral meshes. In this study we present an improved version on unstructured meshes, including uniform triangular and hexagonal meshes and non-uniform triangular and polygonal meshes. The performance of the scheme is verified on Noh and Sedov problems and its second-order convergence is verified on a smooth expansion test.Finally the choice of the scalar parameter controlling the amount of added artificial dissipation is studied.

The Lagrangian hydrodynamics code magma2

ABSTRACT We present the methodology and performance of the new Lagrangian hydrodynamics code magma2, a smoothed particle hydrodynamics (SPH) code that benefits from a number of non-standard enhancements. By default it uses high-order smoothing kernels and wherever gradients are needed, they are calculated via accurate matrix inversion techniques, but a more conventional formulation with kernel gradients has also been implemented for comparison purposes. We also explore a matrix inversion formulation of SPH with a symmetrization in the particle indices that is not frequently used. We find interesting advantages of this formulation in some of the tests, for example, a substantial reduction of surface tension effects for non-ideal particle setups and more accurate peak densities in Sedov blast waves. magma2 uses artificial viscosity, but enhanced by techniques that are commonly used in finite-volume schemes such as reconstruction and slope limiting. While simple to implement, this approach efficiently suppresses particle noise, but at the same time drastically reduces dissipation in locations where it is not needed and actually unwanted. We demonstrate the performance of the new code in a number of challenging benchmark tests including, for example, multidimensional vorticity creating Schulz–Rinne-type Riemann problems and more astrophysical tests such as a collision between two stars to demonstrate its robustness and excellent conservation properties.