High-Order Multi-Material ALE Hydrodynamics

We present a new approach for multi-material arbitrary Lagrangian--Eulerian (ALE) hydrodynamics simulations based on high-order finite elements posed on high-order curvilinear meshes. The method builds on and extends our previous work in the Lagrangian [V. A. Dobrev, T. V. Kolev, and R. N. Rieben, SIAM J. Sci. Comput., 34 (2012), pp. B606--B641] and remap [R. W. Anderson et al., Internat. J. Numer. Methods Fluids, 77 (2015), pp. 249--273] phases of ALE, and depends critically on a functional perspective that enables subzonal physics and material modeling [V. A. Dobrev et al., Internat. J. Numer. Methods Fluids, 82 (2016), pp. 689--706]. Curvilinear mesh relaxation is based on node movement, which is determined through the solution of an elliptic equation. The remap phase is posed in terms of advecting state variables between two meshes over a fictitious time interval. The resulting advection equation is solved by a discontinuous Galerkin (DG) formulation, combined with a customized Flux Corrected Transpor...

[1]  Hyung Taek Ahn,et al.  Multi-material interface reconstruction on generalized polyhedral meshes , 2007, J. Comput. Phys..

[2]  J. Halleux,et al.  An arbitrary lagrangian-eulerian finite element method for transient dynamic fluid-structure interactions , 1982 .

[3]  David Bailey,et al.  Reduced-dissipation remapping of velocity in staggered arbitrary Lagrangian-Eulerian methods , 2010, J. Comput. Appl. Math..

[4]  R. N. Hill,et al.  Constrained optimization framework for interface-aware sub-scale dynamics closure model for multimaterial cells in Lagrangian and arbitrary Lagrangian-Eulerian hydrodynamics , 2014, J. Comput. Phys..

[5]  Pavel B. Bochev,et al.  Formulation, analysis and numerical study of an optimization-based conservative interpolation (remap) of scalar fields for arbitrary Lagrangian-Eulerian methods , 2011, J. Comput. Phys..

[6]  C. Schär,et al.  A Synchronous and Iterative Flux-Correction Formalism for Coupled Transport Equations , 1996 .

[7]  Jérôme Breil,et al.  Hybrid remap for multi-material ALE , 2011 .

[8]  D. Benson.  Computational methods in Lagrangian and Eulerian hydrocodes , 1992 .

[9]  Pavel Váchal,et al.  Synchronized flux corrected remapping for ALE methods , 2011 .

[10]  Chi-Wang Shu,et al.  A cell-centered Lagrangian scheme with the preservation of symmetry and conservation properties for compressible fluid flows in two-dimensional cylindrical geometry , 2010, J. Comput. Phys..

[11]  Veselin Dobrev,et al.  Curvilinear finite elements for Lagrangian hydrodynamics , 2011 .

[12]  Guglielmo Scovazzi,et al.  A geometrically-conservative, synchronized, flux-corrected remap for arbitrary Lagrangian-Eulerian computations with nodal finite elements , 2011, J. Comput. Phys..

[13]  S. Zalesak.  Introduction to “Flux-Corrected Transport. I. SHASTA, A Fluid Transport Algorithm That Works” , 1997 .

[14]  R. Garimella,et al.  Untangling of 2D meshes in ALE simulations , 2004 .

[15]  Mikhail Shashkov,et al.  Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/fld.1574 Closure models for multimaterial cells in arbitrary Lagrangian–Eulerian hydrocodes ‡ , 2022 .

[16]  J. Haas,et al.  Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities , 1987, Journal of Fluid Mechanics.

[17]  W. B. VanderHeyden,et al.  Compatible Fluxes for van Leer Advection , 1998 .

[18]  Tzanio V. Kolev,et al.  Multi‐material closure model for high‐order finite element Lagrangian hydrodynamics , 2016 .

[19]  Veselin Dobrev,et al.  Monotonicity in high‐order curvilinear finite element arbitrary Lagrangian–Eulerian remap , 2015 .

[20]  M. Shashkov,et al.  The Construction of Compatible Hydrodynamics Algorithms Utilizing Conservation of Total Energy , 1998 .

[21]  Donald E. Burton,et al.  Compatible, energy and symmetry preserving 2D lagrangian hydrodynamics in rz - cylindrical coordinates , 2010, ICCS.

[22]  Raphaël Loubère,et al.  ReALE: A reconnection-based arbitrary-Lagrangian-Eulerian method , 2010, J. Comput. Phys..

[23]  J. Thuburn.  Multidimensional Flux-Limited Advection Schemes , 1996 .

[24]  Rao V. Garimella,et al.  Polygonal surface mesh optimization , 2004, Engineering with Computers.

[25]  Jean-Luc Guermond,et al.  Entropy–viscosity method for the single material Euler equations in Lagrangian frame , 2016 .

[26]  Mikhail J. Shashkov,et al.  One-step hybrid remapping algorithm for multi-material arbitrary Lagrangian-Eulerian methods , 2012, J. Comput. Phys..

[27]  Xianyi Zeng,et al.  A frame-invariant vector limiter for flux corrected nodal remap in arbitrary Lagrangian-Eulerian flow computations , 2014, J. Comput. Phys..

[28]  Pavel Váchal,et al.  Optimization-based synchronized flux-corrected conservative interpolation (remapping) of mass and momentum for arbitrary Lagrangian-Eulerian methods , 2010, J. Comput. Phys..

[29]  David P. Starinshak,et al.  A multimaterial extension to subzonal reconstruction , 2016, J. Comput. Phys..

[30]  Jérôme Breil,et al.  Two-step hybrid conservative remapping for multimaterial arbitrary Lagrangian-Eulerian methods , 2011, J. Comput. Phys..

[31]  W. B. VanderHeyden,et al.  A general-purpose finite-volume advection scheme for continuous and discontinuous fields on unstructured grids , 2002 .

[32]  R. Abgrall,et al.  An Example of High Order Residual Distribution Scheme Using non-Lagrange Elements , 2010, J. Sci. Comput..

[33]  Nathaniel R. Morgan,et al.  A cell-centered Lagrangian Godunov-like method for solid dynamics , 2013 .

[34]  J. Brackbill,et al.  Adaptive zoning for singular problems in two dimensions , 1982 .

[35]  Jérôme Breil,et al.  A two-dimensional unstructured cell-centered multi-material ALE scheme using VOF interface reconstruction , 2010, J. Comput. Phys..

[36]  Tzanio V. Kolev,et al.  High-order curvilinear finite elements for axisymmetric Lagrangian hydrodynamics , 2013 .

[37]  Tzanio V. Kolev,et al.  High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics , 2012, SIAM J. Sci. Comput..

[38]  Mikhail J. Shashkov,et al.  Reconstruction of multi-material interfaces from moment data , 2008, J. Comput. Phys..

[39]  Jérôme Breil,et al.  A multi-material ReALE method with MOF interface reconstruction , 2013 .

[40]  W. Rider,et al.  Reconstructing Volume Tracking , 1998 .

[41]  Jeffrey Grandy.  Conservative Remapping and Region Overlays by Intersecting Arbitrary Polyhedra , 1999 .

[42]  Xianyi Zeng,et al.  A variational multiscale finite element method for monolithic ALE computations of shock hydrodynamics using nodal elements , 2016, J. Comput. Phys..

[43]  Mikhail J. Shashkov,et al.  Conservative multi-material remap for staggered multi-material Arbitrary Lagrangian-Eulerian methods , 2014, J. Comput. Phys..

[44]  Manuel Quezada de Luna,et al.  High-order local maximum principle preserving (MPP) discontinuous Galerkin finite element method for the transport equation , 2017, J. Comput. Phys..

[45]  Michael Dumbser,et al.  A direct Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3D , 2014, J. Comput. Phys..

[46]  David P. Starinshak,et al.  A subzone reconstruction algorithm for efficient staggered compatible remapping , 2014, J. Comput. Phys..

[47]  Mikhail Shashkov,et al.  A comparative study of multimaterial Lagrangian and Eulerian methods with pressure relaxation , 2013 .