Lists of publications on preprint servers: arXiv, hal


  • Wasilij Barsukow, Raphaël Loubère, Pierre-Henri Maire:
    A node-conservative vorticity-preserving Finite Volume method for linear acoustics on unstructured grids, 2023 submitted
    • Abstract: Instead of ensuring that fluxes across edges add up to zero, we split the edge in two halves and also associate different fluxes to each of its sides. This is possible due to non-standard Riemann solvers with free parameters. We then enforce conservation by making sure that the fluxes around a node sum up to zero, which fixes the value of the free parameter. We demonstrate that for linear acoustics one of the non-standard Riemann solvers leads to a vorticity preserving method on unstructured meshes.

  • Remi Abgrall, Wasilij Barsukow, Christian Klingenberg:
    The Active Flux method for the Euler equations on Cartesian grids, 2023 submitted (pdf)
    • Abstract: Active Flux is an extension of the Finite Volume method and additionally incorporates point values located at cell boundaries. This gives rise to a globally continuous approximation of the solution. The method is third-order accurate. We demonstrate that a new semi-discrete Active Flux method (first described in Abgrall&Barsukow, 2022 for one space dimension) can easily be used to solve nonlinear hyperbolic systems in multiple dimensions, such as the compressible Euler equations of inviscid hydrodynamics. Originally, the Active Flux method emerged as a fully discrete method, and required an exact or approximate evolution operator for the point value update. For nonlinear problems such an operator is often difficult to obtain, in particular for multiple spatial dimensions. With the new approach it becomes possible to leave behind these difficulties. We introduce a multi-dimensional limiting strategy and demonstrate the performance of the new method on both Riemann problems and subsonic flows.

Refereed journal articles

  1. Wasilij Barsukow, Raul Borsche:
    Implicit Active Flux methods for linear advection, 2023 accepted (pdf)

  2. Wasilij Barsukow:
    All-speed numerical methods for the Euler equations via a sequential explicit time integration, J.Sci.Comp. (2023), 95 (pdf)

  3. Remi Abgrall, Wasilij Barsukow:
    Extensions of Active Flux to arbitrary order of accuracy, M2AN (2023) 57(2): 991-1027 (pdf, hal)

  4. Wasilij Barsukow, Jonas P. Berberich:
    A well-balanced Active Flux scheme for the shallow water equations with wetting and drying, CAMC (2023): 1-46 (pdf, hal)

  5. Wasilij Barsukow, Christian Klingenberg:
    Exact solution and a truly multidimensional Godunov scheme for the acoustic equations, M2AN (2022) 56(1): 317-347 (pdf, doi)

  6. Wasilij Barsukow, Jonas P. Berberich, Christian Klingenberg:
    On the active flux scheme for hyperbolic PDEs with source terms, SISC (2021) 43(6): A4015-A4042 (pdf, doi)

  7. Wasilij Barsukow:
    Truly multi-dimensional all-speed schemes for the Euler equations on Cartesian grids, J. Comp. Phys. 435 (2021), 110216, (pdf, doi)

  8. Wasilij Barsukow:
    The active flux scheme for nonlinear problems, J.Sci.Comp. (2021), 86 (pdf, doi)

  9. Wasilij Barsukow, Jonathan Hohm, Christian Klingenberg, Philip L. Roe:
    The active flux scheme on Cartesian grids and its low Mach number limit, J.Sci.Comp. (2019), 81(1): 594-622 (pdf, doi)

  10. Wasilij Barsukow:
    Stationarity preserving schemes for multi-dimensional linear systems, Math.Comp. (2019) 88(318): 1621-1645, (pdf, doi)

  11. Wasilij Barsukow, Philipp V. F. Edelmann, Christian Klingenberg, Fabian Miczek, Friedrich K. Roepke:
    A numerical scheme for the compressible low-Mach number regime of ideal fluid dynamics, J.Sci.Comp. (2017) 72(2): 623-646, (pdf, doi)

  12. Marcelo M. Miller Bertolami, Maxime Viallet, Vincent Prat, Wasilij Barsukow, Achim Weiss:
    On the relevance of bubbles and potential flows for stellar convection MNRAS (2016) 457 (4): 4441-4453, (pdf, doi)

Refereed conference proceedings

  1. Wasilij Barsukow:
    Truly multi-dimensional all-speed methods for the Euler equations, 2023 accepted as proceedings of FVCA10 (pdf)

  2. Remi Abgrall, Wasilij Barsukow:
    A hybrid finite element-finite volume method for conservation laws, Proc. of the NumHyp21 conference, AMC 447 (2023): 127846 (pdf, hal)

  3. Wasilij Barsukow:
    Stationarity preservation properties of the active flux scheme on Cartesian grids, Proc. of HONOM2019, Commun. Appl. Math. Comput., 2020 (doi, pdf)

  4. Wasilij Barsukow:
    Stationary states of finite volume discretizations of multi-dimensional linear hyperbolic systems, Proc. of the XVII International Conference on Hyperbolic Problems (HYP2018), A. Bressan et al. (eds), AIMS Series on Applied Mathematics Vol. 10, 2020 (pdf)

  5. Wasilij Barsukow:
    Stationarity and vorticity preservation for the linearized Euler equations in multiple spatial dimensions, Finite Volumes for Complex Applications VIII — Methods and Theoretical Aspects, C. Cancès and P. Omnes (eds.), Springer Proceedings in Mathematics & Statistics 199, 2017 (doi)

  6. Wasilij Barsukow, Philipp V. F. Edelmann, Christian Klingenberg, Friedrich K. Roepke:
    A low-Mach Roe-type solver for the Euler equations allowing for gravity source terms, Workshop on low velocity flows, Paris, 5-6 Nov. 2015, Dellacherie et al. (eds.), ESAIM: Proceedings and Surveys, Volume 56, 2017, (doi, pdf)

PhD Thesis

Other publications

  1. Wasilij Barsukow:
    Time integration of the semi-discrete Active Flux method, Oberwolfach Workshop Report 2022, 19

  2. Wasilij Barsukow:
    Approximate evolution operators for the Active Flux method, Oberwolfach Workshop Report 2021, 19 (doi, pdf)


Last modified: Thu Nov 23 10:59:03 CET 2023