Fambri, F.; Zampa, E.; Busto, S.; Río-Martín, L.; Hindenlang, F.; Sonnendrücker, E.; Dumbser, M. A well-balanced and exactly divergence-free staggered semi-implicit hybrid finite volume / finite element scheme for the incompressible MHD equations. (English) Zbl 07748072 J. Comput. Phys. 493, Article ID 112493, 48 p. (2023). MSC: 76Mxx 65Mxx 76Wxx PDFBibTeX XMLCite \textit{F. Fambri} et al., J. Comput. Phys. 493, Article ID 112493, 48 p. (2023; Zbl 07748072) Full Text: DOI arXiv
Dumbser, Michael (ed.); Busto, Saray (ed.); Vázquez-Cendón, M. Elena (ed.); Peshkov, Ilya (ed.) Preface for the special issue “Hyperbolic PDE in computational physics: advanced mathematical models and structure-preserving numerics”. (English) Zbl 07701078 Appl. Math. Comput. 450, Article ID 127994, 3 p. (2023). MSC: 00B15 PDFBibTeX XMLCite \textit{M. Dumbser} (ed.) et al., Appl. Math. Comput. 450, Article ID 127994, 3 p. (2023; Zbl 07701078) Full Text: DOI
Chiocchetti, Simone; Dumbser, Michael An exactly curl-free staggered semi-implicit finite volume scheme for a first order hyperbolic model of viscous two-phase flows with surface tension. (English) Zbl 07682799 J. Sci. Comput. 94, No. 1, Paper No. 24, 62 p. (2023). MSC: 65Mxx 76Mxx 35Lxx PDFBibTeX XMLCite \textit{S. Chiocchetti} and \textit{M. Dumbser}, J. Sci. Comput. 94, No. 1, Paper No. 24, 62 p. (2023; Zbl 07682799) Full Text: DOI arXiv
Balsara, Dinshaw S.; Käppeli, Roger; Boscheri, Walter; Dumbser, Michael Curl constraint-preserving reconstruction and the guidance it gives for mimetic scheme design. (English) Zbl 1524.35142 Commun. Appl. Math. Comput. 5, No. 1, 235-294 (2023). MSC: 35Fxx 35Lxx 35Qxx PDFBibTeX XMLCite \textit{D. S. Balsara} et al., Commun. Appl. Math. Comput. 5, No. 1, 235--294 (2023; Zbl 1524.35142) Full Text: DOI arXiv
Abgrall, Rémi; Busto, Saray; Dumbser, Michael A simple and general framework for the construction of thermodynamically compatible schemes for computational fluid and solid mechanics. (English) Zbl 1510.76098 Appl. Math. Comput. 440, Article ID 127629, 40 p. (2023). MSC: 76M12 76M10 65M08 65M12 65M60 76B15 PDFBibTeX XMLCite \textit{R. Abgrall} et al., Appl. Math. Comput. 440, Article ID 127629, 40 p. (2023; Zbl 1510.76098) Full Text: DOI
Busto, S.; Dumbser, M.; Río-Martín, L. An arbitrary-Lagrangian-Eulerian hybrid finite volume/finite element method on moving unstructured meshes for the Navier-Stokes equations. (English) Zbl 1510.76081 Appl. Math. Comput. 437, Article ID 127539, 29 p. (2023). MSC: 76M10 76M12 PDFBibTeX XMLCite \textit{S. Busto} et al., Appl. Math. Comput. 437, Article ID 127539, 29 p. (2023; Zbl 1510.76081) Full Text: DOI arXiv
Castro Díaz, Manuel J. (ed.); Després, Bruno (ed.); Dumbser, Michael (ed.); Klingenberg, Christian (ed.) Structure-preserving discretizations for nonlinear systems of hyperbolic, involution-constrained partial differential equations on manifolds. Abstracts from the workshop held April 10–16, 2022. (English) Zbl 1519.00016 Oberwolfach Rep. 19, No. 2, 979-1037 (2022). MSC: 00B05 00B25 35-06 35L45 35L65 58J45 65M06 65M08 65M12 65M25 65M60 74C20 76W05 76M12 78M10 78M12 83C05 83C22 PDFBibTeX XMLCite \textit{M. J. Castro Díaz} (ed.) et al., Oberwolfach Rep. 19, No. 2, 979--1037 (2022; Zbl 1519.00016) Full Text: DOI
Busto, Saray; Dumbser, Michael A new family of thermodynamically compatible discontinuous Galerkin methods for continuum mechanics and turbulent shallow water flows. (English) Zbl 1503.65223 J. Sci. Comput. 93, No. 2, Paper No. 56, 40 p. (2022). MSC: 65M60 65L06 65N30 65M12 76F10 76B15 76D05 76N06 76M10 74B20 74S05 80A19 35L02 35Q31 35Q30 35Q79 PDFBibTeX XMLCite \textit{S. Busto} and \textit{M. Dumbser}, J. Sci. Comput. 93, No. 2, Paper No. 56, 40 p. (2022; Zbl 1503.65223) Full Text: DOI
Dhaouadi, Firas; Dumbser, Michael A first order hyperbolic reformulation of the Navier-Stokes-Korteweg system based on the GPR model and an augmented Lagrangian approach. (English) Zbl 07599597 J. Comput. Phys. 470, Article ID 111544, 30 p. (2022). MSC: 65Mxx 76Mxx 35Lxx PDFBibTeX XMLCite \textit{F. Dhaouadi} and \textit{M. Dumbser}, J. Comput. Phys. 470, Article ID 111544, 30 p. (2022; Zbl 07599597) Full Text: DOI
Boscheri, Walter; Dumbser, Michael; Gaburro, Elena Continuous finite element subgrid basis functions for discontinuous Galerkin schemes on unstructured polygonal Voronoi meshes. (English) Zbl 1492.65261 Commun. Comput. Phys. 32, No. 1, 259-298 (2022). MSC: 65M60 65M50 PDFBibTeX XMLCite \textit{W. Boscheri} et al., Commun. Comput. Phys. 32, No. 1, 259--298 (2022; Zbl 1492.65261) Full Text: DOI arXiv
Chiocchetti, Simone; Peshkov, Ilya; Gavrilyuk, Sergey; Dumbser, Michael High order ADER schemes and GLM curl cleaning for a first order hyperbolic formulation of compressible flow with surface tension. (English) Zbl 07510040 J. Comput. Phys. 426, Article ID 109898, 45 p. (2021). MSC: 76-XX 35-XX PDFBibTeX XMLCite \textit{S. Chiocchetti} et al., J. Comput. Phys. 426, Article ID 109898, 45 p. (2021; Zbl 07510040) Full Text: DOI arXiv
Boscheri, W.; Dumbser, M.; Ioriatti, M.; Peshkov, I.; Romenski, E. A structure-preserving staggered semi-implicit finite volume scheme for continuum mechanics. (English) Zbl 07508471 J. Comput. Phys. 424, Article ID 109866, 40 p. (2021). MSC: 80-XX 35-XX PDFBibTeX XMLCite \textit{W. Boscheri} et al., J. Comput. Phys. 424, Article ID 109866, 40 p. (2021; Zbl 07508471) Full Text: DOI arXiv
Gaburro, Elena; Castro, Manuel J.; Dumbser, Michael A well balanced finite volume scheme for general relativity. (English) Zbl 07456293 SIAM J. Sci. Comput. 43, No. 6, B1226-B1251 (2021). MSC: 65-XX 35L40 65M08 83C05 83C10 85-08 85-10 85A30 PDFBibTeX XMLCite \textit{E. Gaburro} et al., SIAM J. Sci. Comput. 43, No. 6, B1226--B1251 (2021; Zbl 07456293) Full Text: DOI arXiv
Tsoutsanis, Panagiotis; Dumbser, Michael Arbitrary high order central non-oscillatory schemes on mixed-element unstructured meshes. (English) Zbl 1521.76372 Comput. Fluids 225, Article ID 104961, 20 p. (2021). MSC: 76M10 65M60 76L05 76N06 PDFBibTeX XMLCite \textit{P. Tsoutsanis} and \textit{M. Dumbser}, Comput. Fluids 225, Article ID 104961, 20 p. (2021; Zbl 1521.76372) Full Text: DOI Link
Peshkov, Ilya; Dumbser, Michael; Boscheri, Walter; Romenski, Evgeniy; Chiocchetti, Simone; Ioriatti, Matteo Simulation of non-Newtonian viscoplastic flows with a unified first order hyperbolic model and a structure-preserving semi-implicit scheme. (English) Zbl 1521.76573 Comput. Fluids 224, Article ID 104963, 17 p. (2021). MSC: 76M20 65M06 76A10 PDFBibTeX XMLCite \textit{I. Peshkov} et al., Comput. Fluids 224, Article ID 104963, 17 p. (2021; Zbl 1521.76573) Full Text: DOI arXiv
Busto, S.; Río-Martín, L.; Vázquez-Cendón, M. E.; Dumbser, M. A semi-implicit hybrid finite volume/finite element scheme for all Mach number flows on staggered unstructured meshes. (English) Zbl 1510.76082 Appl. Math. Comput. 402, Article ID 126117, 29 p. (2021). MSC: 76M10 65M60 76M20 65M08 35Q35 PDFBibTeX XMLCite \textit{S. Busto} et al., Appl. Math. Comput. 402, Article ID 126117, 29 p. (2021; Zbl 1510.76082) Full Text: DOI arXiv
Avesani, Diego; Dumbser, Michael; Vacondio, Renato; Righetti, Maurizio An alternative SPH formulation: ADER-WENO-SPH. (English) Zbl 1506.76123 Comput. Methods Appl. Mech. Eng. 382, Article ID 113871, 25 p. (2021). MSC: 76M28 65M75 PDFBibTeX XMLCite \textit{D. Avesani} et al., Comput. Methods Appl. Mech. Eng. 382, Article ID 113871, 25 p. (2021; Zbl 1506.76123) Full Text: DOI
Gaburro, Elena; Dumbser, Michael A posteriori subcell finite volume limiter for general \(P_NP_M\) schemes: applications from gasdynamics to relativistic magnetohydrodynamics. (English) Zbl 1475.65091 J. Sci. Comput. 86, No. 3, Paper No. 37, 41 p. (2021). Reviewer: Abdallah Bradji (Annaba) MSC: 65M08 65M60 65M50 76N15 76W05 76Y05 PDFBibTeX XMLCite \textit{E. Gaburro} and \textit{M. Dumbser}, J. Sci. Comput. 86, No. 3, Paper No. 37, 41 p. (2021; Zbl 1475.65091) Full Text: DOI arXiv
Busto, Saray; Dumbser, Michael; Escalante, Cipriano; Favrie, Nicolas; Gavrilyuk, Sergey On high order ADER discontinuous Galerkin schemes for first order hyperbolic reformulations of nonlinear dispersive systems. (English) Zbl 1465.76060 J. Sci. Comput. 87, No. 2, Paper No. 48, 47 p. (2021). MSC: 76M12 76B15 PDFBibTeX XMLCite \textit{S. Busto} et al., J. Sci. Comput. 87, No. 2, Paper No. 48, 47 p. (2021; Zbl 1465.76060) Full Text: DOI
Reinarz, Anne; Charrier, Dominic E.; Bader, Michael; Bovard, Luke; Dumbser, Michael; Duru, Kenneth; Fambri, Francesco; Gabriel, Alice-Agnes; Gallard, Jean-Matthieu; Köppel, Sven; Krenz, Lukas; Rannabauer, Leonhard; Rezzolla, Luciano; Samfass, Philipp; Tavelli, Maurizio; Weinzierl, Tobias ExaHyPE: an engine for parallel dynamically adaptive simulations of wave problems. (English) Zbl 07687570 Comput. Phys. Commun. 254, Article ID 107251, 16 p. (2020). MSC: 76-XX 65-XX PDFBibTeX XMLCite \textit{A. Reinarz} et al., Comput. Phys. Commun. 254, Article ID 107251, 16 p. (2020; Zbl 07687570) Full Text: DOI arXiv
Gaburro, Elena; Boscheri, Walter; Chiocchetti, Simone; Klingenberg, Christian; Springel, Volker; Dumbser, Michael High order direct arbitrary-Lagrangian-Eulerian schemes on moving Voronoi meshes with topology changes. (English) Zbl 07504692 J. Comput. Phys. 407, Article ID 109167, 44 p. (2020). MSC: 65-XX 76-XX PDFBibTeX XMLCite \textit{E. Gaburro} et al., J. Comput. Phys. 407, Article ID 109167, 44 p. (2020; Zbl 07504692) Full Text: DOI arXiv
Dumbser, Michael; Fambri, Francesco; Gaburro, Elena; Reinarz, Anne On GLM curl cleaning for a first order reduction of the CCZ4 formulation of the Einstein field equations. (English) Zbl 1453.85002 J. Comput. Phys. 404, Article ID 109088, 15 p. (2020). MSC: 85A05 83C55 83-08 65M60 PDFBibTeX XMLCite \textit{M. Dumbser} et al., J. Comput. Phys. 404, Article ID 109088, 15 p. (2020; Zbl 1453.85002) Full Text: DOI arXiv
Bassi, C.; Busto, S.; Dumbser, M. High order ADER-DG schemes for the simulation of linear seismic waves induced by nonlinear dispersive free-surface water waves. (English) Zbl 1447.74042 Appl. Numer. Math. 158, 236-263 (2020). MSC: 74S05 74S20 74L05 74J05 74F10 76B15 86A15 PDFBibTeX XMLCite \textit{C. Bassi} et al., Appl. Numer. Math. 158, 236--263 (2020; Zbl 1447.74042) Full Text: DOI arXiv
Kemm, Friedemann; Gaburro, Elena; Thein, Ferdinand; Dumbser, Michael A simple diffuse interface approach for compressible flows around moving solids of arbitrary shape based on a reduced Baer-Nunziato model. (English) Zbl 1519.76176 Comput. Fluids 204, Article ID 104536, 15 p. (2020). MSC: 76M12 65M08 74F10 76Nxx PDFBibTeX XMLCite \textit{F. Kemm} et al., Comput. Fluids 204, Article ID 104536, 15 p. (2020; Zbl 1519.76176) Full Text: DOI arXiv
Boscheri, Walter; Semplice, Matteo; Dumbser, Michael Central WENO subcell finite volume limiters for ADER discontinuous Galerkin schemes on fixed and moving unstructured meshes. (English) Zbl 1474.65307 Commun. Comput. Phys. 25, No. 2, 311-346 (2019). MSC: 65M08 65M60 PDFBibTeX XMLCite \textit{W. Boscheri} et al., Commun. Comput. Phys. 25, No. 2, 311--346 (2019; Zbl 1474.65307) Full Text: DOI
Escalante, C.; Dumbser, M.; Castro, M. J. An efficient hyperbolic relaxation system for dispersive non-hydrostatic water waves and its solution with high order discontinuous Galerkin schemes. (English) Zbl 1452.65188 J. Comput. Phys. 394, 385-416 (2019). MSC: 65M08 65M60 65Y05 35L40 76M12 65Z05 PDFBibTeX XMLCite \textit{C. Escalante} et al., J. Comput. Phys. 394, 385--416 (2019; Zbl 1452.65188) Full Text: DOI
Tavelli, Maurizio; Dumbser, Michael; Charrier, Dominic Etienne; Rannabauer, Leonhard; Weinzierl, Tobias; Bader, Michael A simple diffuse interface approach on adaptive Cartesian grids for the linear elastic wave equations with complex topography. (English) Zbl 1452.74113 J. Comput. Phys. 386, 158-189 (2019). MSC: 74S05 74S10 74J05 65M50 65M60 86A15 86-08 65Z05 PDFBibTeX XMLCite \textit{M. Tavelli} et al., J. Comput. Phys. 386, 158--189 (2019; Zbl 1452.74113) Full Text: DOI arXiv
Dumbser, Michael; Fambri, Francesco; Tavelli, Maurizio; Bader, Michael; Weinzierl, Tobias Efficient implementation of ADER discontinuous Galerkin schemes for a scalable hyperbolic PDE engine. (English) Zbl 1434.65179 Axioms 7, No. 3, Paper No. 63, 26 p. (2018). MSC: 65M60 65M06 35L65 76M12 PDFBibTeX XMLCite \textit{M. Dumbser} et al., Axioms 7, No. 3, Paper No. 63, 26 p. (2018; Zbl 1434.65179) Full Text: DOI arXiv
Gaburro, Elena; Castro, Manuel J.; Dumbser, Michael A well balanced diffuse interface method for complex nonhydrostatic free surface flows. (English) Zbl 1410.76224 Comput. Fluids 175, 180-198 (2018). MSC: 76M12 65M08 65Y10 76Nxx 76T10 PDFBibTeX XMLCite \textit{E. Gaburro} et al., Comput. Fluids 175, 180--198 (2018; Zbl 1410.76224) Full Text: DOI arXiv
Dumbser, Michael (ed.); Titarev, Vladimir (ed.); Saurel, Richard (ed.) Preface to the special issue “Recent progress in numerical methods for nonlinear time-dependent flow & transport problems”. (English) Zbl 1391.00051 Comput. Fluids 169, 1-2 (2018). MSC: 00B15 76-06 76Mxx 35L60 PDFBibTeX XMLCite \textit{M. Dumbser} (ed.) et al., Comput. Fluids 169, 1--2 (2018; Zbl 1391.00051) Full Text: DOI