Adaptive mesh refinement using wave-propagation algorithms for hyperbolic systems. The authors present a generalisation of an adaptive mesh refinement algorithm developed for the Euler equations of gas dynamics to employ high-resolution wave-propagation algorithms in a more general framework. This extension can be used on a variety of new problems, including hyperbolic equations, which are not in a conservation form, problems with source terms of capacity functions, and logically rectangular curvilinear grids. The developed framework requires a modified approach to maintaining consistency and conservation at grid interfaces, which is described in detail. The algorithm is implemented in the software package AMRCLAW, which is freely available.

References in zbMATH (referenced in 65 articles , 1 standard article )

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  1. Lundquist, Tomas; Nordström, Jan; Malan, Arnaud: Stable dynamical adaptive mesh refinement (2021)
  2. Ma, Wenhua; Zhao, Zhongshu; Ni, Guoxi: A multi-resolution method for two-phase fluids with complex equations of state by binomial solvers in three space dimensions (2021)
  3. Berezovski, Mihhail; Berezovski, Arkadi: Discontinuity-driven mesh alignment for evolving discontinuities in elastic solids (2020)
  4. Charrier, Dominic Etienne; Hazelwood, Benjamin; Weinzierl, Tobias: Enclave tasking for DG methods on dynamically adaptive meshes (2020)
  5. Dunning, D.; Marts, W.; Robey, R. W.; Bridges, P.: Adaptive mesh refinement in the fast lane (2020)
  6. Hoang, Thi-Thao-Phuong; Ju, Lili; Leng, Wei; Wang, Zhu: High order explicit local time stepping methods for hyperbolic conservation laws (2020)
  7. Giuliani, Andrew; Krivodonova, Lilia: Adaptive mesh refinement on graphics processing units for applications in gas dynamics (2019)
  8. Hoang, Thi-Thao-Phuong; Leng, Wei; Ju, Lili; Wang, Zhu; Pieper, Konstantin: Conservative explicit local time-stepping schemes for the shallow water equations (2019)
  9. Dumbser, Michael; Fambri, Francesco; Tavelli, Maurizio; Bader, Michael; Weinzierl, Tobias: Efficient implementation of ADER discontinuous Galerkin schemes for a scalable hyperbolic PDE engine (2018)
  10. Li, Zhilin; Qiao, Zhonghua; Tang, Tao: Numerical solution of differential equations. Introduction to finite difference and finite element methods (2018)
  11. Del Razo, M. J.; LeVeque, R. J.: Numerical methods for interface coupling of compressible and almost incompressible media (2017)
  12. Donna Calhoun, Carsten Burstedde: ForestClaw: A parallel algorithm for patch-based adaptive mesh refinement on a forest of quadtrees (2017) arXiv
  13. Liu, Cheng; Hu, Changhong: Adaptive THINC-GFM for compressible multi-medium flows (2017)
  14. Buchmüller, Pawel; Dreher, Jürgen; Helzel, Christiane: Finite volume WENO methods for hyperbolic conservation laws on Cartesian grids with adaptive mesh refinement (2016)
  15. Cravero, I.; Semplice, M.: On the accuracy of WENO and CWENO reconstructions of third order on nonuniform meshes (2016)
  16. Deiterding, Ralf; Domingues, Margarete O.; Gomes, Sônia M.; Schneider, Kai: Comparison of adaptive multiresolution and adaptive mesh refinement applied to simulations of the compressible Euler equations (2016)
  17. Greene, Patrick T.; Eldredge, Jeff D.; Zhong, Xiaolin; Kim, John: A high-order multi-zone cut-stencil method for numerical simulations of high-speed flows over complex geometries (2016)
  18. Kolomenskiy, Dmitry; Nave, Jean-Christophe; Schneider, Kai: Adaptive gradient-augmented level set method with multiresolution error estimation (2016)
  19. Schreiber, Martin; Neckel, Tobias; Bungartz, Hans-Joachim: Evaluation of an efficient stack-RLE clustering concept for dynamically adaptive grids (2016)
  20. Semplice, M.; Coco, A.; Russo, G.: Adaptive mesh refinement for hyperbolic systems based on third-order compact WENO reconstruction (2016)

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