Skip to main content
Log in

Large Time Step Finite Volume Evolution Galerkin Methods

  • Published:
Journal of Scientific Computing Aims and scope Submit manuscript


We present two new large time step methods within the framework of the well-balanced finite volume evolution Galerkin (FVEG) schemes. The methodology will be illustrated for low Froude number shallow water flows with source terms modeling the bottom topography and Coriolis forces, but results can be generalized to more complex systems of balance laws. The FVEG methods couple a finite volume formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of multidimensional hyperbolic systems, such that all of the infinitely many directions of wave propagation are taken into account explicitly. We present two variants of large time step FVEG method: a semi-implicit time approximation and an explicit time approximation using several evolution steps along bicharacteristic cones.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others


  1. Algorithm 832: Davis T.A. UMFPACK, an unsymmetric-pattern multifrontal method. ACM Trans. Math. Softw. 30(2), 196–199 (2004)

    Article  Google Scholar 

  2. Bollermann, A., Lukáčová-Medvid’ová, M., Noelle, S.: Well-balanced finite volume Evolution Galerkin methods for the 2D shallow water equations on adaptive grids. In: Proceedings of ALGORITMY, pp. 81–90 (2009)

    Google Scholar 

  3. Lukáčová-Medvid’ová, M., Morton, K.W., Warnecke, G.: Evolution Galerkin methods for hyperbolic systems in two space dimensions. Math. Comput. 69, 1355–1384 (2000)

    Article  MATH  Google Scholar 

  4. Lukáčová-Medvid’ová, M., Noelle, S., Kraft, M.: Well-balanced finite volume evolution Galerkin methods for the shallow water equations. J. Comput. Phys. 221, 122–147 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. Meister, A.: Asymptotic based preconditioning technique for low Mach number flows. Z. Angew. Math. Mech. 83(1), 3–25 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  6. Ricchiuto, M., Bollermann, A.: Stabilized residual distribution for shallow water simulations,. J. Comput. Phys. 228, 1071–1115 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  7. SACADO:

  8. Sun, Y., Ren, Y.-X.: The finite volume local evolution Galerkin method for solving the hyperbolic conservation laws. J. Comput. Phys. 228(13), 4945–4960 (2009)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to M. Lukáčová-Medvid’ová.

Additional information

This research has been supported by the German Research Foundation DFG under the grant LU 1470/2-1.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hundertmark-Zaušková, A., Lukáčová-Medvid’ová, M. & Prill, F. Large Time Step Finite Volume Evolution Galerkin Methods. J Sci Comput 48, 227–240 (2011).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: