Methods and Algorithms for Scientific Computing

High-Order Wave Propagation Algorithms for Hyperbolic Systems


We present a finite volume method that is applicable to hyperbolic PDEs including spatially varying and semilinear nonconservative systems. The spatial discretization, like that of the well-known Clawpack software, is based on solving Riemann problems and calculating fluctuations (not fluxes). The implementation employs weighted essentially nonoscillatory reconstruction in space and strong stability preserving Runge--Kutta integration in time. The method can be extended to arbitrarily high order of accuracy and allows a well-balanced implementation for capturing solutions of balance laws near steady state. This well-balancing is achieved through the $f$-wave Riemann solver and a novel wave-slope WENO reconstruction procedure. The wide applicability and advantageous properties of the method are demonstrated through numerical examples, including problems in nonconservative form, problems with spatially varying fluxes, and problems involving near-equilibrium solutions of balance laws.


  1. hyperbolic PDEs
  2. high-order methods
  3. wave propagation
  4. Godunov-type methods
  5. WENO

MSC codes

  1. 65M20
  2. 65M08
  3. 35L50

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Information & Authors


Published In

cover image SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Pages: A351 - A377
ISSN (online): 1095-7197


Submitted: 11 April 2011
Accepted: 28 August 2012
Published online: 22 January 2013


  1. hyperbolic PDEs
  2. high-order methods
  3. wave propagation
  4. Godunov-type methods
  5. WENO

MSC codes

  1. 65M20
  2. 65M08
  3. 35L50



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