A General Well-Balanced Finite Volume Scheme for Euler Equations with Gravity

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 236)


We present a second-order well-balanced Godunov-type finite volume scheme for compressible Euler equations with a gravitational source term. The scheme is designed to work for any hydrostatic equilibrium, which must be known á priori. It can be combined with any numerical flux function, time-stepping method, and grid topology. The scheme is based on the reconstruction of a special set of variables and a special source term discretization. We show the well-balanced property numerically for isothermal and polytropic equilibria in one and two dimensions using the Roe flux function and an explicit three-stage Runge–Kutta scheme. We demonstrate the superior resolution of small pressure perturbations of hydrostatic equilibria, down to an order \(10^{-10}\) and below compared to the hydrostatic background.


Euler equations with gravity Finite volume method Well-balancing 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WürzburgWürzburgGermany
  2. 2.TIFR Center for Applicable MathematicsBangaloreIndia

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