Time-dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation |
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| Institution: | 1. School of Computer Science and Engineering, The Hebrew University, Jerusalem 91904, Israel;2. Institute of Mathematics, The Hebrew University, Jerusalem 91904, Israel;1. Departamento de Matemática e Computação, Faculdade de Ciências e Tecnologia, Universidade Estadual Paulista “Júlio de Mesquita Filho”, 19060-900 Presidente Prudente, SP, Brazil;2. Departamento de Engenharia Química, CEFT, Faculdade de Engenharia da Universidade do Porto, Porto, Portugal;1. Institute for Polymers and Composites/I3N, University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal;2. Departamento de Engenharia Química, CEFT, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias s/n, 4200-465 Porto, Portugal;3. Centro de Estudos de Fenómenos de Transporte, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias s/n, 4200-465 Porto, Portugal;1. Department of Mechanical Engineering, Technical University of Denmark, Produktionstorvet, 2800 Kgs. Lyngby, Denmark;2. Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ 08544, USA |
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| Abstract: | We present a second-order finite-difference scheme for viscoelastic flows based on a recent reformulation of the constitutive laws as equations for the matrix logarithm of the conformation tensor. We present a simple analysis that clarifies how the passage to logarithmic variables remedies the high-Weissenberg numerical instability. As a stringent test, we simulate an Oldroyd-B fluid in a lid-driven cavity. The scheme is found to be stable at large values of the Weissenberg number. These results support our claim that the high Weissenberg numerical instability may be overcome by the use of logarithmic variables. Remaining issues are rather concerned with accuracy, which degrades with insufficient resolution. |
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