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 40 articles , 1 standard article )

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  1. Cravero, I.; Semplice, M.: On the accuracy of WENO and CWENO reconstructions of third order on nonuniform meshes (2016)
  2. Kolomenskiy, Dmitry; Nave, Jean-Christophe; Schneider, Kai: Adaptive gradient-augmented level set method with multiresolution error estimation (2016)
  3. Semplice, M.; Coco, A.; Russo, G.: Adaptive mesh refinement for hyperbolic systems based on third-order compact WENO reconstruction (2016)
  4. Sætra, Martin L.; Brodtkorb, André R.; Lie, Knut-Andreas: Efficient GPU-implementation of adaptive mesh refinement for the shallow-water equations (2015)
  5. Dumbser, Michael; Hidalgo, Arturo; Zanotti, Olindo: High order space-time adaptive ADER-WENO finite volume schemes for non-conservative hyperbolic systems (2014)
  6. Dawson, Clint; Trahan, Corey Jason; Kubatko, Ethan J.; Westerink, Joannes J.: A parallel local timestepping Runge-Kutta discontinuous Galerkin method with applications to coastal Ocean modeling (2013)
  7. Li, Ruo; Wu, Shuonan: $H$-adaptive mesh method with double tolerance adaptive strategy for hyperbolic conservation laws (2013)
  8. Aymard, Benjamin; Clément, Frédérique; Coquel, Frédéric; Postel, Marie: Numerical simulation of the selection process of the ovarian follicles (2012)
  9. Lisitsa, Vadim; Reshetova, Galina; Tcheverda, Vladimir: Finite-difference algorithm with local time-space grid refinement for simulation of waves (2012)
  10. Trahan, Corey J.; Dawson, Clint: Local time-stepping in Runge-Kutta discontinuous Galerkin finite element methods applied to the shallow-water equations (2012)
  11. Chiavassa, Guillaume; Lombard, Bruno: Time domain numerical modeling of wave propagation in 2D heterogeneous porous media (2011)
  12. Deiterding, Ralf: Block-structured adaptive mesh refinement -- theory, implementation and application (2011)
  13. Domingues, Margarete O.; Gomes, S^onia M.; Roussel, Olivier; Schneider, Kai: Adaptive multiresolution methods (2011)
  14. Shen, Chaopeng; Qiu, Jing-Mei; Christlieb, Andrew: Adaptive mesh refinement based on high order finite difference WENO scheme for multi-scale simulations (2011)
  15. Chiavassa, Guillaume; Lombard, Bruno; Piraux, Joël: Numerical modeling of 1D transient poroelastic waves in the low-frequency range (2010)
  16. Bürger, Raimund; Ruiz, Ricardo; Schneider, Kai; Sepúlveda, Mauricio: Fully adaptive multiresolution schemes for strongly degenerate parabolic equations in one space dimension (2008)
  17. Cecil, Thomas C.; Osher, Stanley J.; Qian, Jianliang: Essentially non-oscillatory adaptive tree methods (2008)
  18. Domingues, Margarete O.; Gomes, S^onia M.; Roussel, Olivier; Schneider, Kai: An adaptive multiresolution scheme with local time stepping for evolutionary PDEs (2008)
  19. Zheng, H.W.; Shu, C.; Chew, Y.T.: An object-oriented and quadrilateral-mesh based solution adaptive algorithm for compressible multi-fluid flows (2008)
  20. Hay, A.; Visonneau, M.: Adaptive finite-volume solution of complex turbulent flows (2007)

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