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 56 articles , 1 standard article )

Showing results 1 to 20 of 56.
Sorted by year (citations)

1 2 3 next

  1. Li, Zhilin; Qiao, Zhonghua; Tang, Tao: Numerical solution of differential equations. Introduction to finite difference and finite element methods (2018)
  2. Del Razo, M. J.; LeVeque, R. J.: Numerical methods for interface coupling of compressible and almost incompressible media (2017)
  3. Donna Calhoun, Carsten Burstedde: ForestClaw: A parallel algorithm for patch-based adaptive mesh refinement on a forest of quadtrees (2017) arXiv
  4. Liu, Cheng; Hu, Changhong: Adaptive THINC-GFM for compressible multi-medium flows (2017)
  5. Buchmüller, Pawel; Dreher, Jürgen; Helzel, Christiane: Finite volume WENO methods for hyperbolic conservation laws on Cartesian grids with adaptive mesh refinement (2016)
  6. Cravero, I.; Semplice, M.: On the accuracy of WENO and CWENO reconstructions of third order on nonuniform meshes (2016)
  7. 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)
  8. 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)
  9. Kolomenskiy, Dmitry; Nave, Jean-Christophe; Schneider, Kai: Adaptive gradient-augmented level set method with multiresolution error estimation (2016)
  10. Schreiber, Martin; Neckel, Tobias; Bungartz, Hans-Joachim: Evaluation of an efficient stack-RLE clustering concept for dynamically adaptive grids (2016)
  11. Semplice, M.; Coco, A.; Russo, G.: Adaptive mesh refinement for hyperbolic systems based on third-order compact WENO reconstruction (2016)
  12. Yuan, Xinpeng; Ning, Jianguo; Ma, Tianbao; Wang, Cheng: Stability of Newton TVD Runge-Kutta scheme for one-dimensional Euler equations with adaptive mesh (2016)
  13. Diaz, Julien; Grote, Marcus J.: Multi-level explicit local time-stepping methods for second-order wave equations (2015)
  14. Kostin, Victor; Lisitsa, Vadim; Reshetova, Galina; Tcheverda, Vladimir: Local time-space mesh refinement for simulation of elastic wave propagation in multi-scale media (2015)
  15. Sætra, Martin L.; Brodtkorb, André R.; Lie, Knut-Andreas: Efficient GPU-implementation of adaptive mesh refinement for the shallow-water equations (2015)
  16. Dumbser, Michael; Hidalgo, Arturo; Zanotti, Olindo: High order space-time adaptive ADER-WENO finite volume schemes for non-conservative hyperbolic systems (2014)
  17. Ricchiuto, M.; Filippini, A. G.: Upwind residual discretization of enhanced Boussinesq equations for wave propagation over complex bathymetries (2014)
  18. 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)
  19. Dumbser, Michael; Zanotti, Olindo; Hidalgo, Arturo; Balsara, Dinshaw S.: ADER-WENO finite volume schemes with space-time adaptive mesh refinement (2013)
  20. Li, Ruo; Wu, Shuonan: (H)-adaptive mesh method with double tolerance adaptive strategy for hyperbolic conservation laws (2013)

1 2 3 next