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Title: Fully-Implicit Orthogonal Reconstructed Discontinuous Galerkin for Fluid Dynamics with Phase Change

Journal Article · · Journal of Computational Physics
 [1];  [2];  [3];  [1];  [1];  [1];  [3]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. North Carolina State Univ., Raleigh, NC (United States)
  3. Univ. of California, Davis, CA (United States)
+ Show Author Affiliations

A new reconstructed Discontinuous Galerkin (rDG) method, based on orthogonal basis/test functions, is developed for fluid flows on unstructured meshes. Orthogonality of basis functions is essential for enabling robust and efficient fully-implicit Newton-Krylov based time integration. The method is designed for generic partial differential equations, including transient, hyperbolic, parabolic or elliptic operators, which are attributed to many multiphysics problems. We demonstrate the method’s capabilities for solving compressible fluid-solid systems (in the low Mach number limit), with phase change (melting/solidification), as motivated by applications in Additive Manufacturing (AM). We focus on the method’s accuracy (in both space and time), as well as robustness and solvability of the system of linear equations involved in the linearization steps of Newton-based methods. The performance of the developed method is investigated for highly-stiff problems with melting/solidification, emphasizing the advantages from tight coupling of mass, momentum and energy conservation equations, as well as orthogonality of basis functions, which leads to better conditioning of the underlying (approximate) Jacobian matrices, and rapid convergence of the Krylov-based linear solver.

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC52-07NA27344; 13-SI-002
OSTI ID:
1241930
Alternate ID(s):
OSTI ID: 1359281
Report Number(s):
LLNL-JRNL-669889
Journal Information:
Journal of Computational Physics, Vol. 305; ISSN 0021-9991
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 15 works
Citation information provided by
Web of Science

References (35)

A second-order projection method for the incompressible navier-stokes equations journal December 1989
Implicit Time Integration Schemes for the Unsteady Compressible Navier–Stokes Equations: Laminar Flow journal June 2002
Numerical solution of the Navier-Stokes equations journal January 1968
Estimation of Sparse Jacobian Matrices and Graph Coloring Blems journal February 1983
Modelling liquid-solid phase changes with melt convection journal August 1989
Natural convection of air in a square cavity: A bench mark numerical solution journal May 1983
Arbitrary high order PNPM schemes on unstructured meshes for the compressible Navier–Stokes equations journal January 2010
A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes journal September 2008
Efficient implementation of high order unstructured WENO schemes for cavitating flows journal November 2013
Very high order PNPM schemes on unstructured meshes for the resistive relativistic MHD equations journal October 2009
High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method journal December 1982
On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. Part 1: Theory journal October 1990
Numerical calculation of almost incompressible flow journal August 1968
A numerical fluid dynamics calculation method for all flow speeds journal October 1971
SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems journal September 2005
Differencing of the diffusion equation in Lagrangian hydrodynamic codes journal February 1981
Mesoscopic simulation model of selective laser melting of stainless steel powder journal November 2014
Jacobian-free Newton–Krylov methods: a survey of approaches and applications journal January 2004
A p-multigrid discontinuous Galerkin method for the Euler equations on unstructured grids journal January 2006
A discontinuous Galerkin method based on a Taylor basis for the compressible flows on arbitrary grids journal October 2008
A Reconstructed Discontinuous Galerkin Method for the Euler Equations on Arbitrary Grids journal November 2012
A Parallel, Reconstructed Discontinuous Galerkin Method for the Compressible Flows on Arbitrary Grids journal February 2011
A reconstructed discontinuous Galerkin method for the compressible Navier–Stokes equations on arbitrary grids journal September 2010
A Parallel Reconstructed Discontinuous Galerkin Method for Compressible Flows on Arbitrary Grids
  • Luo, Hong; Ali, Amjad; Nourgaliev, Robert
  • 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition https://doi.org/10.2514/6.2010-366
conference June 2012
A Reconstructed Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations on Arbitrary Grids
  • Luo, Hong; Luo, Luqing; Nourgaliev, Robert
  • 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition https://doi.org/10.2514/6.2010-364
conference June 2012
A Hermite WENO reconstruction-based discontinuous Galerkin method for the Euler equations on tetrahedral grids journal June 2012
A reconstructed discontinuous Galerkin method based on a Hierarchical WENO reconstruction for compressible flows on tetrahedral grids journal March 2013
An Improved piso Algorithm for the Computation of Buoyancy-Driven Flows journal December 2001
On physics-based preconditioning of the Navier–Stokes equations journal December 2009
Elemental: A New Framework for Distributed Memory Dense Matrix Computations journal February 2013
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems journal July 1986
A fixed grid numerical modelling methodology for convection-diffusion mushy region phase-change problems journal August 1987
A third-order implicit discontinuous Galerkin method based on a Hermite WENO reconstruction for time-accurate solution of the compressible Navier-Stokes equations: A THIRD-ORDER IMPLICIT DISCONTINUOUS GALERKIN METHOD BASED ON A HERMITE WENO RECONSTRUCTION FOR TIME-ACCURATE SOLUTION OF THE COMPRESSIBLE NAVIER-STOK journal June 2015
An implicit Hermite WENO reconstruction-based discontinuous Galerkin method on tetrahedral grids journal June 2014
A set of parallel, implicit methods for a reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids journal July 2014

Cited By (3)

A reconstructed discontinuous Galerkin method for multi‐material hydrodynamics with sharp interfaces journal January 2020
High-order fully implicit solver for all-speed fluid dynamics: AUSM ride from nearly incompressible variable-density flows to shock dynamics journal November 2018
A trust region approach for numerical modeling of non-isothermal phase change journal July 2019

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Related Subjects

97 MATHEMATICS AND COMPUTING
Discontinuous Galerkin Method
High-Order Space-Time Discretization
Fully-Implicit Solvers
Newton-Krylov Algorithm
Fluid Dynamics
Phase-Change