Coarse graining, dynamic renormalization and the kinetic theory of shock clustering

We demonstrate the utility of the equation-free methodology developed by one of the authors (I.G.K) for the study of scalar conservation laws with disordered initial conditions. The numerical scheme is benchmarked on exact solutions in Burgers turbulence corresponding to Lévy process initial data. For these initial data, the kinetics of shock clustering is described by Smoluchowski’s coagulation equation with additive kernel. The equation-free methodology is used to develop a particle scheme that computes self-similar solutions to the coagulation equation, including those with fat tails. Work completed at Division of Applied Mathematics, Brown University, 182 George St., Providence, RI 02912, USA. Current address: Department of Mathematics and Statistics, University of North Carolina, Charlotte, NC 28223. Email: [email protected]. Work completed at Program for Applied and Computational Mathematics and Department of Chemical and Biological Engineering, Princeton University, 6 Olden St., Princeton, NJ 08544, USA. Current address: United Technologies Research Center, 411 Silver Lane, East Hartford, CT 06118, USA. Email: [email protected]. Program for Applied and Computational Mathematics and Department of Chemical and Biological Engineering, Princeton University, 6 Olden St., Princeton, NJ 08544, USA. Email: [email protected]. Division of Applied Mathematics, Brown University, 182 George St., Providence, RI 02912, USA, Email: govind [email protected].