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- Richard Liska, Mikhail Yu. Shashkov, Pavel Váchal, Burton Wendroff
- J. Comput. Physics
- 2010

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. Published by Elsevier Inc.

A procedure is presented to untangle unstructured 2D meshes containing inverted elements by node repositioning. The inverted elements may result from node movement in Arbitrary Lagrangian–Eulerian (ALE) simulations of continuum mechanics problems with large shear deformation such as fluid flow and metal forming. Meshes with inverted elements may also be… (More)

- Pavel Váchal, Burton Wendroff
- J. Comput. Physics
- 2014

Most efficient adaptive mesh methods employ only a few strategies, including local mesh refinement (h-adaptation), movement of mesh nodes (r-adaptation), and node reconnection (c-adaptation). Despite of its simplicity, node reconnection is the least popular of the three. However, using only node reconnection the discretization error can be significantly… (More)

The aim of the present work is the 3D extension of a general formalism to derive a staggered discretization for Lagrangian hydrodynamics on unstructured grids. The classical compatible discretization is used; namely, momentum equation is discretized using the fundamental concept of subcell forces. Specific internal energy equation is obtained using total… (More)

- Richard Liska, Pavel Váchal
- Applicable Algebra in Engineering, Communication…
- 2007

During the analysis of numerical methods for fluid flows some properties of numerical methods as stability or monotonicity can be stated as quantified problems and proved by quantifier elimination. A case study demonstrating such proofs is presented. The study shows that the stability region of the central scheme for advection-diffusion equation with… (More)

- Raphaël Loubère, Pierre-Henri Maire, Pavel Váchal
- ICCS
- 2010

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… (More)

- TRIANGULAR MESHES, PAVEL VÁCHAL, MARKUS BERNDT
- 2005

Most efficient adaptive mesh methods employ a few strategies, including local mesh refinement (h-adaptation), movement of mesh nodes (r-adaptation), and node reconnection (c-adaptation). Despite its simplicity, node reconnection methods are seldom analyzed apart from the other adaptation methods even in applications where severe restrictions are imposed on… (More)

Abstract. This work is focused on the issue of symmetry preservation, energy and volume conservation and other important properties of staggered Lagrangian hydrodynamic schemes in cylindrical geometry. Typical advantages and drawbacks of existing areaweighted (AW) and genuinely r-z schemes will be pointed out. With quadrilateral cells it is known that, in… (More)

- F Borgonovi, G L Celardo, A Musesti, R Trasarti-Battistoni, P Vachal
- Physical review. E, Statistical, nonlinear, and…
- 2006

We demonstrate the existence of a topological disconnection threshold, recently found by Borgonovi [J. Stat. Phys. 116, 1435 (2004)], for generic 1-d anisotropic Heisenberg models interacting with an interparticle potential R(-alpha) when 0<alpha<1(here R is the distance among spins). We also show that alpha if is greater than the embedding dimension then… (More)