A variational multiscale finite element method for monolithic ALE computations of shock hydrodynamics using nodal elements


Journal Article

© 2016 Elsevier Inc.. We present a monolithic arbitrary Lagrangian-Eulerian (ALE) finite element method for computing highly transient flows with strong shocks. We use a variational multiscale (VMS) approach to stabilize a piecewise-linear Galerkin formulation of the equations of compressible flows, and an entropy artificial viscosity to capture strong solution discontinuities. Our work demonstrates the feasibility of VMS methods for highly transient shock flows, an area of research for which the VMS literature is extremely scarce.In addition, the proposed monolithic ALE method is an alternative to the more commonly used Lagrangian+remap methods, in which, at each time step, a Lagrangian computation is followed by mesh smoothing and remap (conservative solution interpolation). Lagrangian+remap methods are the methods of choice in shock hydrodynamics computations because they provide nearly optimal mesh resolution in proximity of shock fronts. However, Lagrangian+remap methods are not well suited for imposing inflow and outflow boundary conditions. These issues offer an additional motivation for the proposed approach, in which we first perform the mesh motion, and then the flow computations using the monolithic ALE framework.The proposed method is second-order accurate and stable, as demonstrated by extensive numerical examples in two and three space dimensions.

Full Text

Duke Authors

Cited Authors

  • Zeng, X; Scovazzi, G

Published Date

  • June 15, 2016

Published In

Volume / Issue

  • 315 /

Start / End Page

  • 577 - 608

Electronic International Standard Serial Number (EISSN)

  • 1090-2716

International Standard Serial Number (ISSN)

  • 0021-9991

Digital Object Identifier (DOI)

  • 10.1016/j.jcp.2016.03.052

Citation Source

  • Scopus