New Formulation of Artificial Viscosity for Lagrangian Analysis of Shocks

ORAL

Abstract

We have developed a new artificial viscosity that satisfies a set of conditions set out by Caramana. \footnote{E. J. Caramana, M. J. Shashkov and P. P. Whalen, J. Comp. Physics, 144, 70-97, 1998.} This is based on Lew’s\footnote{A. Lew, R. Radovitzky and M. Ortiz, J. Computer-Aided Materials Design, 8, 213-231, 2001.} artificial viscosity. Due to the tensor nature of the new artificial viscosity, it reduces the dependence of the numerical solution on the grid. Central to this formulation is an eigenvalue viscosity limiter to control the magnitude of the artificial viscosity. This is effected in a simple and straightforward manner to obtain forms of artificial viscosity that are able to distinguish between adiabatic and shock compression. The formulation is applicable to any number of dimensions and for grids that are either logically rectangular or unstructured. The viscous stress is simply computed with respect to a given element of grid that always yields the compression condition and with limiter functions computed with respect to neighbor element.

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Authors

  • J.P. Escobedo

    Naval Research Enterprise Intern Program, Los Alamos National Laboratory, Los Alamos, USA, RFNC, All-Russia Research Institute of Experimental Physics, Sarov, Russia, University of Oxford, Lawrence Livermore National Laboratory, AWE, Department of Electrical and Electronic Engineering, National Defense Academy of Japan, Japan Synchrotron Radiation Research Institute / SPring-8, Division of Electrical, Electronic and Information Engineering, Osaka University, Division of Materials and Manufacturing Science, Osaka University, University of Illinois, RAFAEL, P. O. Box 2250, Haifa, Israel, Faculty of Mechanical Engineering, Technion - Israel Institute of Technology, 32000, Haifa, Israel, LANL, Fracture and Shock Physics, SMF Group, Cavendish Laboratory, JJ Thomson Ave., Cambridge, CB3 0HE, QinetiQ Ltd., Fort Halstead, Sevenoaks, Kent, TN14 7BP, UK, ILE, Osaka University, SPring-8, Lawrence Livermore National Lab., CEA, LULI, Ecole Polytechnique, Graduate School of Engineering, Osaka University, LLNL, Livermore, USA, LLE, Rocherster, USA, Graduate school of engineering, Osaka university, Suita, Osaka , Japan, LULI, Ecole polytechnique, Palaiseau, France, Georgia Institute of Technology, Shocks Unlimited, Los Alamos National Laboratory, Air Force Research Laboratory, Naval Surface Warfare Center, Institute for Shock Physics, Washington State University, Institute of Applied Physics and Computational Mathematics, Beijing, China, Institute of Applied Physics and Computational Mathematics, China, General Atomics, San Diego, CA, Fraunhofer Institute, Freiburg, Germany, LLNL, Harvard University, Corvid Technologies, IPCP RAS, Academy of Sciences of the Czech Republic, Institute of Physics of Materials and Los Alamos National Laboratory, Theoretical Division, QinetiQ, Department of Chemistry, University of Missouri-Columbia, Theoretical Division, Los Alamos National Laboratory, Theoretical Division, Los Alamos National Lab, Vanderbilt University, Laboratory for Shock Wave and Detonation Physics Research, Institute of Fluid Physics, Ioffe PTI RAS, Sandia National Laboratories, LCD-CNRS (UPR 9028), Institute for Shock Physics, Washington State University, Pullman, WA 99164-2816, CEA/DAM/DIF F91297 Arpajon, France, Russian Academy of Science, The First Aeronautic Institute of the Air Force, NSWC Dahlgren Division, ICMM UB RAS, Saitama Inst. Tech, Tohoku Univ., Sarov Laboratories, Carnegie Institution of Washington, National Institute of Standards and Technology, Universidad de Puerto Rico, National Institute for Materials Science, Japan, Shock Wave and Condensed Matter Research Center, Kumamoto University, Japan, Institute of Laser Engineering, Osaka University, Japan, Division of Electrical, Electronic and Information Engineering, Institute of Laser Engineering, Osaka University, Japan, Division of Electrical, Electronic and Information Engineering, Osaka University, Japan, Division of Materials and Manufacturing Science, Osaka University, Japan, LANL, USA, RFNC-VNIIEF, Cranfield University, LMPM ENSMA - CNRS, LCD ENSMA - CNRS, CEA Valduc, Laboratoire de Combustion et de Detonique (UPR 9028), ENSMA, Futuroscope, France, Laboratoire de Min\'eralogie (UMR 75-90), IMPMC, Paris, France, DPTA, CEA/DAM, Bruy\`eres-le-Ch\^atel, France, Centre for Astrophysics and Planetary Science, School of Physical Sciences, University of Kent, Canterbury, IARC, Dept. of Mineralogy, Natural History Museum, London, UK, Institute of Fluid Physics, CAEP, University of Missouri, Dept. of Mechanical and Aerospace Engineering, University of California at San Diego, La Jolla, CA 92093-0411, School of Materials Science and Engineering, Georgia Tech, Atlanta, GA 30332-0245, Lawrence Livermore National Laboratory, Physical Life Sciences, Livermore, California 94551, University of Cambridge, IHED RAS, ITT, Marquette University, Naval Surface Warfare Center, Carderock Division, Naval Surface Warfare Center, Dahlgren Division, Faculty of Science, Beijing University of Chemical Technology, Beijing 100029, China, ADAI, University of Coimbra, U.S. Army ARDEC, Naval Research Laboratory, Physics Department, USF, Ball Aerospace \& Technologies Corp., Joint Institute for High Temperatures RAS, Moscow, Russia, Institut fur Theoretische Physik und Astrophysik, Kiel, Germany, LALP, Sandia National Laboratories, New Mexico, PO Box 5800, Albuquerque, NM 87185-1454, Stanford University, Civil and Environmental Engineering Department, Palo Alto, California 94305, GEA Barr-Rosin Ltd., 48 Bell St., Maidenhead, SL6 1BR, UK, Russian Federal Nuclear Center,VNIIEF, Sarov, Russia, University of Maryland, College Park, Maryland 20742, University of Bayreuth, Germany, Royal Institute of Technology, Sweden, Energetic Materials Center, Lawrence Livermore National Laboratory, Livermore, CA 94550, IHDIV, NSWC, US Army Research Laboratory, beijing Institute of technology, University of Science \& Technology of China, Grad. Sch. Sci. and Engn., Tokyo Inst. Tech., ILE, Osaka Univ., Center for Quantum Science and Technology under Extreme Conditions, Osaka Univ., Inst. for Study of The Earth's Interior, Okayama Univ., Grad. Sch. Engn., Osaka Univ., National Key Laboratory for Shock Wave and Detonation Physics, Institute of Fluid Physics, People's Republic of China, Energetic Materials Center, Lawrence Livermore National Laboratory, AFRL/RXLMD Wright-Patterson AFB, OH, AFRL/RWME Eglin AFB, FL, AFRL/RWME, Institute of High Performance Computing, Singapore, School of Physical Sciences, University of Kent, Canterbury, UK, LZ Technology/ECSG, Johnson Space Centre, Houston, TX, USA, IARC, Dept. of Mineralogy, The Natural History Museum, London, UK, Mullard Space Science Laboratory, UK, Qiniteq, UK, JIHT RAS, Rutherford Appleton Laboratory, Science and Technology Facilities Council, AWE, Aldermaston, Reading, RG7 4PR, UK, CNRS-LALP, Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125 U.S.A., U.S. Army Research Office, RTP, NC 27709-2211, Institute of Problems of Chemical Physics, Chernogolovka, Russia, Department of Physics, Harvard University, Cambridge, MA 02138, AWE plc, CEA, DAM, CESTA, CEA, DAM, DIF, CEA, DAM, VALDUC, Leatherhead Foods International, Lawrence-Livermore Nat. Lab., Wash. State Univ., Institute of Applied Physics and Computational Mathematics, Beijing, 100094, China

  • J.P. Escobedo

    Naval Research Enterprise Intern Program, Los Alamos National Laboratory, Los Alamos, USA, RFNC, All-Russia Research Institute of Experimental Physics, Sarov, Russia, University of Oxford, Lawrence Livermore National Laboratory, AWE, Department of Electrical and Electronic Engineering, National Defense Academy of Japan, Japan Synchrotron Radiation Research Institute / SPring-8, Division of Electrical, Electronic and Information Engineering, Osaka University, Division of Materials and Manufacturing Science, Osaka University, University of Illinois, RAFAEL, P. O. Box 2250, Haifa, Israel, Faculty of Mechanical Engineering, Technion - Israel Institute of Technology, 32000, Haifa, Israel, LANL, Fracture and Shock Physics, SMF Group, Cavendish Laboratory, JJ Thomson Ave., Cambridge, CB3 0HE, QinetiQ Ltd., Fort Halstead, Sevenoaks, Kent, TN14 7BP, UK, ILE, Osaka University, SPring-8, Lawrence Livermore National Lab., CEA, LULI, Ecole Polytechnique, Graduate School of Engineering, Osaka University, LLNL, Livermore, USA, LLE, Rocherster, USA, Graduate school of engineering, Osaka university, Suita, Osaka , Japan, LULI, Ecole polytechnique, Palaiseau, France, Georgia Institute of Technology, Shocks Unlimited, Los Alamos National Laboratory, Air Force Research Laboratory, Naval Surface Warfare Center, Institute for Shock Physics, Washington State University, Institute of Applied Physics and Computational Mathematics, Beijing, China, Institute of Applied Physics and Computational Mathematics, China, General Atomics, San Diego, CA, Fraunhofer Institute, Freiburg, Germany, LLNL, Harvard University, Corvid Technologies, IPCP RAS, Academy of Sciences of the Czech Republic, Institute of Physics of Materials and Los Alamos National Laboratory, Theoretical Division, QinetiQ, Department of Chemistry, University of Missouri-Columbia, Theoretical Division, Los Alamos National Laboratory, Theoretical Division, Los Alamos National Lab, Vanderbilt University, Laboratory for Shock Wave and Detonation Physics Research, Institute of Fluid Physics, Ioffe PTI RAS, Sandia National Laboratories, LCD-CNRS (UPR 9028), Institute for Shock Physics, Washington State University, Pullman, WA 99164-2816, CEA/DAM/DIF F91297 Arpajon, France, Russian Academy of Science, The First Aeronautic Institute of the Air Force, NSWC Dahlgren Division, ICMM UB RAS, Saitama Inst. Tech, Tohoku Univ., Sarov Laboratories, Carnegie Institution of Washington, National Institute of Standards and Technology, Universidad de Puerto Rico, National Institute for Materials Science, Japan, Shock Wave and Condensed Matter Research Center, Kumamoto University, Japan, Institute of Laser Engineering, Osaka University, Japan, Division of Electrical, Electronic and Information Engineering, Institute of Laser Engineering, Osaka University, Japan, Division of Electrical, Electronic and Information Engineering, Osaka University, Japan, Division of Materials and Manufacturing Science, Osaka University, Japan, LANL, USA, RFNC-VNIIEF, Cranfield University, LMPM ENSMA - CNRS, LCD ENSMA - CNRS, CEA Valduc, Laboratoire de Combustion et de Detonique (UPR 9028), ENSMA, Futuroscope, France, Laboratoire de Min\'eralogie (UMR 75-90), IMPMC, Paris, France, DPTA, CEA/DAM, Bruy\`eres-le-Ch\^atel, France, Centre for Astrophysics and Planetary Science, School of Physical Sciences, University of Kent, Canterbury, IARC, Dept. of Mineralogy, Natural History Museum, London, UK, Institute of Fluid Physics, CAEP, University of Missouri, Dept. of Mechanical and Aerospace Engineering, University of California at San Diego, La Jolla, CA 92093-0411, School of Materials Science and Engineering, Georgia Tech, Atlanta, GA 30332-0245, Lawrence Livermore National Laboratory, Physical Life Sciences, Livermore, California 94551, University of Cambridge, IHED RAS, ITT, Marquette University, Naval Surface Warfare Center, Carderock Division, Naval Surface Warfare Center, Dahlgren Division, Faculty of Science, Beijing University of Chemical Technology, Beijing 100029, China, ADAI, University of Coimbra, U.S. Army ARDEC, Naval Research Laboratory, Physics Department, USF, Ball Aerospace \& Technologies Corp., Joint Institute for High Temperatures RAS, Moscow, Russia, Institut fur Theoretische Physik und Astrophysik, Kiel, Germany, LALP, Sandia National Laboratories, New Mexico, PO Box 5800, Albuquerque, NM 87185-1454, Stanford University, Civil and Environmental Engineering Department, Palo Alto, California 94305, GEA Barr-Rosin Ltd., 48 Bell St., Maidenhead, SL6 1BR, UK, Russian Federal Nuclear Center,VNIIEF, Sarov, Russia, University of Maryland, College Park, Maryland 20742, University of Bayreuth, Germany, Royal Institute of Technology, Sweden, Energetic Materials Center, Lawrence Livermore National Laboratory, Livermore, CA 94550, IHDIV, NSWC, US Army Research Laboratory, beijing Institute of technology, University of Science \& Technology of China, Grad. Sch. Sci. and Engn., Tokyo Inst. Tech., ILE, Osaka Univ., Center for Quantum Science and Technology under Extreme Conditions, Osaka Univ., Inst. for Study of The Earth's Interior, Okayama Univ., Grad. Sch. Engn., Osaka Univ., National Key Laboratory for Shock Wave and Detonation Physics, Institute of Fluid Physics, People's Republic of China, Energetic Materials Center, Lawrence Livermore National Laboratory, AFRL/RXLMD Wright-Patterson AFB, OH, AFRL/RWME Eglin AFB, FL, AFRL/RWME, Institute of High Performance Computing, Singapore, School of Physical Sciences, University of Kent, Canterbury, UK, LZ Technology/ECSG, Johnson Space Centre, Houston, TX, USA, IARC, Dept. of Mineralogy, The Natural History Museum, London, UK, Mullard Space Science Laboratory, UK, Qiniteq, UK, JIHT RAS, Rutherford Appleton Laboratory, Science and Technology Facilities Council, AWE, Aldermaston, Reading, RG7 4PR, UK, CNRS-LALP, Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125 U.S.A., U.S. Army Research Office, RTP, NC 27709-2211, Institute of Problems of Chemical Physics, Chernogolovka, Russia, Department of Physics, Harvard University, Cambridge, MA 02138, AWE plc, CEA, DAM, CESTA, CEA, DAM, DIF, CEA, DAM, VALDUC, Leatherhead Foods International, Lawrence-Livermore Nat. Lab., Wash. State Univ., Institute of Applied Physics and Computational Mathematics, Beijing, 100094, China

  • J.P. Escobedo

    Naval Research Enterprise Intern Program, Los Alamos National Laboratory, Los Alamos, USA, RFNC, All-Russia Research Institute of Experimental Physics, Sarov, Russia, University of Oxford, Lawrence Livermore National Laboratory, AWE, Department of Electrical and Electronic Engineering, National Defense Academy of Japan, Japan Synchrotron Radiation Research Institute / SPring-8, Division of Electrical, Electronic and Information Engineering, Osaka University, Division of Materials and Manufacturing Science, Osaka University, University of Illinois, RAFAEL, P. O. Box 2250, Haifa, Israel, Faculty of Mechanical Engineering, Technion - Israel Institute of Technology, 32000, Haifa, Israel, LANL, Fracture and Shock Physics, SMF Group, Cavendish Laboratory, JJ Thomson Ave., Cambridge, CB3 0HE, QinetiQ Ltd., Fort Halstead, Sevenoaks, Kent, TN14 7BP, UK, ILE, Osaka University, SPring-8, Lawrence Livermore National Lab., CEA, LULI, Ecole Polytechnique, Graduate School of Engineering, Osaka University, LLNL, Livermore, USA, LLE, Rocherster, USA, Graduate school of engineering, Osaka university, Suita, Osaka , Japan, LULI, Ecole polytechnique, Palaiseau, France, Georgia Institute of Technology, Shocks Unlimited, Los Alamos National Laboratory, Air Force Research Laboratory, Naval Surface Warfare Center, Institute for Shock Physics, Washington State University, Institute of Applied Physics and Computational Mathematics, Beijing, China, Institute of Applied Physics and Computational Mathematics, China, General Atomics, San Diego, CA, Fraunhofer Institute, Freiburg, Germany, LLNL, Harvard University, Corvid Technologies, IPCP RAS, Academy of Sciences of the Czech Republic, Institute of Physics of Materials and Los Alamos National Laboratory, Theoretical Division, QinetiQ, Department of Chemistry, University of Missouri-Columbia, Theoretical Division, Los Alamos National Laboratory, Theoretical Division, Los Alamos National Lab, Vanderbilt University, Laboratory for Shock Wave and Detonation Physics Research, Institute of Fluid Physics, Ioffe PTI RAS, Sandia National Laboratories, LCD-CNRS (UPR 9028), Institute for Shock Physics, Washington State University, Pullman, WA 99164-2816, CEA/DAM/DIF F91297 Arpajon, France, Russian Academy of Science, The First Aeronautic Institute of the Air Force, NSWC Dahlgren Division, ICMM UB RAS, Saitama Inst. Tech, Tohoku Univ., Sarov Laboratories, Carnegie Institution of Washington, National Institute of Standards and Technology, Universidad de Puerto Rico, National Institute for Materials Science, Japan, Shock Wave and Condensed Matter Research Center, Kumamoto University, Japan, Institute of Laser Engineering, Osaka University, Japan, Division of Electrical, Electronic and Information Engineering, Institute of Laser Engineering, Osaka University, Japan, Division of Electrical, Electronic and Information Engineering, Osaka University, Japan, Division of Materials and Manufacturing Science, Osaka University, Japan, LANL, USA, RFNC-VNIIEF, Cranfield University, LMPM ENSMA - CNRS, LCD ENSMA - CNRS, CEA Valduc, Laboratoire de Combustion et de Detonique (UPR 9028), ENSMA, Futuroscope, France, Laboratoire de Min\'eralogie (UMR 75-90), IMPMC, Paris, France, DPTA, CEA/DAM, Bruy\`eres-le-Ch\^atel, France, Centre for Astrophysics and Planetary Science, School of Physical Sciences, University of Kent, Canterbury, IARC, Dept. of Mineralogy, Natural History Museum, London, UK, Institute of Fluid Physics, CAEP, University of Missouri, Dept. of Mechanical and Aerospace Engineering, University of California at San Diego, La Jolla, CA 92093-0411, School of Materials Science and Engineering, Georgia Tech, Atlanta, GA 30332-0245, Lawrence Livermore National Laboratory, Physical Life Sciences, Livermore, California 94551, University of Cambridge, IHED RAS, ITT, Marquette University, Naval Surface Warfare Center, Carderock Division, Naval Surface Warfare Center, Dahlgren Division, Faculty of Science, Beijing University of Chemical Technology, Beijing 100029, China, ADAI, University of Coimbra, U.S. Army ARDEC, Naval Research Laboratory, Physics Department, USF, Ball Aerospace \& Technologies Corp., Joint Institute for High Temperatures RAS, Moscow, Russia, Institut fur Theoretische Physik und Astrophysik, Kiel, Germany, LALP, Sandia National Laboratories, New Mexico, PO Box 5800, Albuquerque, NM 87185-1454, Stanford University, Civil and Environmental Engineering Department, Palo Alto, California 94305, GEA Barr-Rosin Ltd., 48 Bell St., Maidenhead, SL6 1BR, UK, Russian Federal Nuclear Center,VNIIEF, Sarov, Russia, University of Maryland, College Park, Maryland 20742, University of Bayreuth, Germany, Royal Institute of Technology, Sweden, Energetic Materials Center, Lawrence Livermore National Laboratory, Livermore, CA 94550, IHDIV, NSWC, US Army Research Laboratory, beijing Institute of technology, University of Science \& Technology of China, Grad. Sch. Sci. and Engn., Tokyo Inst. Tech., ILE, Osaka Univ., Center for Quantum Science and Technology under Extreme Conditions, Osaka Univ., Inst. for Study of The Earth's Interior, Okayama Univ., Grad. Sch. Engn., Osaka Univ., National Key Laboratory for Shock Wave and Detonation Physics, Institute of Fluid Physics, People's Republic of China, Energetic Materials Center, Lawrence Livermore National Laboratory, AFRL/RXLMD Wright-Patterson AFB, OH, AFRL/RWME Eglin AFB, FL, AFRL/RWME, Institute of High Performance Computing, Singapore, School of Physical Sciences, University of Kent, Canterbury, UK, LZ Technology/ECSG, Johnson Space Centre, Houston, TX, USA, IARC, Dept. of Mineralogy, The Natural History Museum, London, UK, Mullard Space Science Laboratory, UK, Qiniteq, UK, JIHT RAS, Rutherford Appleton Laboratory, Science and Technology Facilities Council, AWE, Aldermaston, Reading, RG7 4PR, UK, CNRS-LALP, Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125 U.S.A., U.S. Army Research Office, RTP, NC 27709-2211, Institute of Problems of Chemical Physics, Chernogolovka, Russia, Department of Physics, Harvard University, Cambridge, MA 02138, AWE plc, CEA, DAM, CESTA, CEA, DAM, DIF, CEA, DAM, VALDUC, Leatherhead Foods International, Lawrence-Livermore Nat. Lab., Wash. State Univ., Institute of Applied Physics and Computational Mathematics, Beijing, 100094, China