Adaptive multiresolution WENO schemes for multi-species kinematic flow models

  • Authors:

  • Raimund Bürger;Alice Kozakevicius

  • Affiliations:

  • Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160-C, Concepción, Chile;Departamento de Matemática-CCNE, Universidade Federal de Santa Maria, Faixa de Camobi, km 9, Campus Universitário, Santa Maria, RS, CEP 97105-900, Brazil

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2007

Quantified Score

Hi-index 31.46

Visualization

Abstract

Multi-species kinematic flow models lead to strongly coupled, nonlinear systems of first-order, spatially one-dimensional conservation laws. The number of unknowns (the concentrations of the species) may be arbitrarily high. Models of this class include a multi-species generalization of the Lighthill-Whitham-Richards traffic model and a model for the sedimentation of polydisperse suspensions. Their solutions typically involve kinematic shocks separating areas of constancy, and should be approximated by high resolution schemes. A fifth-order weighted essentially non-oscillatory (WENO) scheme is combined with a multiresolution technique that adaptively generates a sparse point representation (SPR) of the evolving numerical solution. Thus, computational effort is concentrated on zones of strong variation near shocks. Numerical examples from the traffic and sedimentation models demonstrate the effectiveness of the resulting WENO multiresolution (WENO-MRS) scheme.