A 3D finite element ALE method using an approximate Riemann solution

Chiravalle, V. P.; Morgan, N. R.

doi:10.1002/fld.4284

Title: A 3D finite element ALE method using an approximate Riemann solution

Abstract

Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann-like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann-like problem. Here, two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well-known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problem results are presented.

Authors:

Chiravalle, V. P. ^[1]; Morgan, N. R. ^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:: 2016-08-09

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1304832

Report Number(s):: LA-UR-16-20312
Journal ID: ISSN 0271-2091

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: International Journal for Numerical Methods in Fluids

Additional Journal Information:: Journal Name: International Journal for Numerical Methods in Fluids; Journal ID: ISSN 0271-2091

Publisher:: Wiley

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING

Citation Formats


                    Chiravalle, V. P., and Morgan, N. R. A 3D finite element ALE method using an approximate Riemann solution.  United States: N. p., 2016. 
Web.  doi:10.1002/fld.4284.

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                    Chiravalle, V. P., & Morgan, N. R. A 3D finite element ALE method using an approximate Riemann solution.  United States.  https://doi.org/10.1002/fld.4284

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                    Chiravalle, V. P., and Morgan, N. R. Tue .  
"A 3D finite element ALE method using an approximate Riemann solution".  United States.  https://doi.org/10.1002/fld.4284.  https://www.osti.gov/servlets/purl/1304832.

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@article{osti_1304832,

  title        = {A 3D finite element ALE method using an approximate Riemann solution},

  author       = {Chiravalle, V. P. and Morgan, N. R.},

  abstractNote = {Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann-like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann-like problem. Here, two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well-known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problem results are presented.},

  doi          = {10.1002/fld.4284},

  journal      = {International Journal for Numerical Methods in Fluids},

  number       = ,

  volume       = ,

  place        = {United States},

  year         = {2016},

  month        = {8}

}

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https://doi.org/10.1002/fld.4284

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Title: A 3D finite element ALE method using an approximate Riemann solution

Abstract

Citation Formats

A second-order cell-centered Lagrangian scheme for two-dimensional compressible flow problems journal, January 2008

A compatible finite element multi-material ALE hydrodynamics algorithm journal, January 2008

Curvilinear finite elements for Lagrangian hydrodynamics journal, June 2010

3D staggered Lagrangian hydrodynamics scheme with cell-centered Riemann solver-based artificial viscosity: 3D LAGRANGIAN HYDRO SCHEME WITH RIEMANN SOLVER ARTIFICIAL VISCOSITY journal, September 2012

A Lagrangian Discontinuous Galerkin-type method on unstructured meshes to solve hydrodynamics problems journal, February 2004

A uniform strain hexahedron and quadrilateral with orthogonal hourglass control journal, May 1981

Reconstructing Volume Tracking journal, April 1998

Elimination of Artificial Grid Distortion and Hourglass-Type Motions by Means of Lagrangian Subzonal Masses and Pressures journal, May 1998

A Compatible, Energy and Symmetry Preserving Lagrangian Hydrodynamics Algorithm in Three-Dimensional Cartesian Geometry journal, January 2000

Lagrangian Gas Dynamics in Two Dimensions and Lagrangian systems journal, October 2005

A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws journal, April 1978

Use of artificial viscosity in multidimensional fluid dynamic calculations journal, July 1980

An efficient, accurate, simple ale method for nonlinear finite element programs journal, March 1989

A dissipation model for staggered grid Lagrangian hydrodynamics journal, August 2013

A cell-centered Lagrangian Godunov-like method for solid dynamics journal, August 2013

Verification of a three-dimensional unstructured finite element method using analytic and manufactured solutions journal, July 2013

A three-dimensional finite element arbitrary Lagrangian–Eulerian method for shock hydrodynamics on unstructured grids journal, March 2014

An arbitrary Lagrangian–Eulerian method with adaptive mesh refinement for the solution of the Euler equations journal, September 2004

A cell-centered Lagrangian hydrodynamics scheme on general unstructured meshes in arbitrary dimension journal, August 2009

A high-order cell-centered Lagrangian scheme for compressible fluid flows in two-dimensional cylindrical geometry journal, October 2009

A comparative study of interface reconstruction methods for multi-material ALE simulations journal, April 2010

ReALE: A reconnection-based arbitrary-Lagrangian–Eulerian method journal, June 2010

A two-dimensional unstructured cell-centered multi-material ALE scheme using VOF interface reconstruction journal, August 2010

An approach for treating contact surfaces in Lagrangian cell-centered hydrodynamics journal, October 2013

A Lagrangian staggered grid Godunov-like approach for hydrodynamics journal, February 2014

A Godunov-like point-centered essentially Lagrangian hydrodynamic approach journal, January 2015

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A second-order compatible staggered Lagrangian hydrodynamics scheme using a cell-centered multidimensional approximate Riemann solver journal, May 2010

A Method for the Numerical Calculation of Hydrodynamic Shocks journal, March 1950

A Cell-Centered Lagrangian Scheme for Two-Dimensional Compressible Flow Problems journal, January 2007

High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics journal, January 2012

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Staggered Lagrangian Discretization Based on Cell-Centered Riemann Solver and Associated Hydrodynamics Scheme journal, October 2011

Mesh Generation Using Unstructured Computational Meshes and Elliptic Partial Differential Equation Smoothing conference, June 2005

A second-order cell-centered Lagrangian scheme for two-dimensional compressible flow problems
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A compatible finite element multi-material ALE hydrodynamics algorithm
journal, January 2008

Curvilinear finite elements for Lagrangian hydrodynamics
journal, June 2010

3D staggered Lagrangian hydrodynamics scheme with cell-centered Riemann solver-based artificial viscosity: 3D LAGRANGIAN HYDRO SCHEME WITH RIEMANN SOLVER ARTIFICIAL VISCOSITY
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A Lagrangian Discontinuous Galerkin-type method on unstructured meshes to solve hydrodynamics problems
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A uniform strain hexahedron and quadrilateral with orthogonal hourglass control
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Reconstructing Volume Tracking
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Elimination of Artificial Grid Distortion and Hourglass-Type Motions by Means of Lagrangian Subzonal Masses and Pressures
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A Compatible, Energy and Symmetry Preserving Lagrangian Hydrodynamics Algorithm in Three-Dimensional Cartesian Geometry
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A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
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Use of artificial viscosity in multidimensional fluid dynamic calculations
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An efficient, accurate, simple ale method for nonlinear finite element programs
journal, March 1989

A dissipation model for staggered grid Lagrangian hydrodynamics
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