caa a22 4500 445331712 CHVBK 20180317142739.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s10208-010-9076-y doi (NATIONALLICENCE)springer-10.1007/s10208-010-9076-y Discrete Lie Advection of Differential Forms [Elektronische Daten] [P. Mullen, A. McKenzie, D. Pavlov, L. Durant, Y. Tong, E. Kanso, J. Marsden, M. Desbrun] In this paper, we present a numerical technique for performing Lie advection of arbitrary differential forms. Leveraging advances in high-resolution finite-volume methods for scalar hyperbolic conservation laws, we first discretize the interior product (also calledcontraction) through integrals over Eulerian approximations of extrusions. This, along with Cartan's homotopy formula and a discrete exterior derivative, can then be used to derive a discrete Lie derivative. The usefulness of this operator is demonstrated through the numerical advection of scalar fields and 1-forms on regular grids. SFoCM, 2010 Discrete contraction nationallicence Discrete Lie derivative nationallicence Discrete differential forms nationallicence Finite-volume methods nationallicence Hyperbolic PDEs nationallicence Mullen P. Computing + Mathematical Sciences, California Institute of Technology, 91125, Pasadena, CA, USA aut McKenzie A. Computing + Mathematical Sciences, California Institute of Technology, 91125, Pasadena, CA, USA aut Pavlov D. Computing + Mathematical Sciences, California Institute of Technology, 91125, Pasadena, CA, USA aut Durant L. Computing + Mathematical Sciences, California Institute of Technology, 91125, Pasadena, CA, USA aut Tong Y. Computer Science & Engineering, Michigan State University, 48824, East Lansing, MI, USA aut Kanso E. Aerospace and Mechanical Engineering, University of Southern California, 90089, Los Angeles, CA, USA aut Marsden J. Computing + Mathematical Sciences, California Institute of Technology, 91125, Pasadena, CA, USA aut Desbrun M. Computing + Mathematical Sciences, California Institute of Technology, 91125, Pasadena, CA, USA aut Foundations of Computational Mathematics Springer-Verlag 11/2(2011-04-01), 131-149 1615-3375 11:2<131 2011 11 10208 https://doi.org/10.1007/s10208-010-9076-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10208-010-9076-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Mullen P. Computing + Mathematical Sciences, California Institute of Technology, 91125, Pasadena, CA, USA aut NATIONALLICENCE 700 1- McKenzie A. Computing + Mathematical Sciences, California Institute of Technology, 91125, Pasadena, CA, USA aut NATIONALLICENCE 700 1- Pavlov D. Computing + Mathematical Sciences, California Institute of Technology, 91125, Pasadena, CA, USA aut NATIONALLICENCE 700 1- Durant L. Computing + Mathematical Sciences, California Institute of Technology, 91125, Pasadena, CA, USA aut NATIONALLICENCE 700 1- Tong Y. Computer Science & Engineering, Michigan State University, 48824, East Lansing, MI, USA aut NATIONALLICENCE 700 1- Kanso E. Aerospace and Mechanical Engineering, University of Southern California, 90089, Los Angeles, CA, USA aut NATIONALLICENCE 700 1- Marsden J. Computing + Mathematical Sciences, California Institute of Technology, 91125, Pasadena, CA, USA aut NATIONALLICENCE 700 1- Desbrun M. Computing + Mathematical Sciences, California Institute of Technology, 91125, Pasadena, CA, USA aut NATIONALLICENCE 773 0- Foundations of Computational Mathematics Springer-Verlag 11/2(2011-04-01), 131-149 1615-3375 11:2<131 2011 11 10208 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer