WENO Schemes for Mixed-Element Unstructured Meshes

WENO Schemes for Mixed-Element Unstructured Meshes

Year:    2010

Communications in Computational Physics, Vol. 8 (2010), Iss. 3 : pp. 585–609

Abstract

The paper extends weighted essentially non-oscillatory (WENO) schemes to two-dimensional quadrilateral and mixed-element unstructured meshes. The key element of the proposed methods is a reconstruction procedure suitable for arbitrarily-shaped cells. The resulting schemes achieve the designed uniformly high-order of accuracy and compute discontinuous solutions without spurious oscillations at interfaces between cells of two different types.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.040909.080110a

Communications in Computational Physics, Vol. 8 (2010), Iss. 3 : pp. 585–609

Published online:    2010-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:   

  1. Stencil selection algorithms for WENO schemes on unstructured meshes

    Tsoutsanis, Panagiotis

    Journal of Computational Physics, Vol. 475 (2023), Iss. P.108840

    https://doi.org/10.1016/j.jcp.2019.07.039 [Citations: 5]
  2. Robust Conservative Level Set Method for 3D Mixed-Element Meshes — Application to LES of Primary Liquid-Sheet Breakup

    Pringuey, Thibault | Cant, R. Stewart

    Communications in Computational Physics, Vol. 16 (2014), Iss. 2 P.403

    https://doi.org/10.4208/cicp.140213.210214a [Citations: 7]
  3. An Efficient Quadrature-Free Formulation for High Order Arbitrary-Lagrangian–Eulerian ADER-WENO Finite Volume Schemes on Unstructured Meshes

    Boscheri, W. | Dumbser, M.

    Journal of Scientific Computing, Vol. 66 (2016), Iss. 1 P.240

    https://doi.org/10.1007/s10915-015-0019-2 [Citations: 15]
  4. CWENO Finite-Volume Interface Capturing Schemes for Multicomponent Flows Using Unstructured Meshes

    Tsoutsanis, Panagiotis | Adebayo, Ebenezer Mayowa | Merino, Adrian Carriba | Arjona, Agustin Perez | Skote, Martin

    Journal of Scientific Computing, Vol. 89 (2021), Iss. 3

    https://doi.org/10.1007/s10915-021-01673-y [Citations: 23]
  5. Review of the High-Order TENO Schemes for Compressible Gas Dynamics and Turbulence

    Fu, Lin

    Archives of Computational Methods in Engineering, Vol. 30 (2023), Iss. 4 P.2493

    https://doi.org/10.1007/s11831-022-09877-7 [Citations: 27]
  6. A simple WENO-AO method for solving hyperbolic conservation laws

    Huang, Cong | Chen, Li Li

    Applied Mathematics and Computation, Vol. 395 (2021), Iss. P.125856

    https://doi.org/10.1016/j.amc.2020.125856 [Citations: 1]
  7. High Order Schemes on Three-Dimensional General Polyhedral Meshes — Application to the Level Set Method

    Pringuey, Thibault | Cant, R. Stewart

    Communications in Computational Physics, Vol. 12 (2012), Iss. 1 P.1

    https://doi.org/10.4208/cicp.260511.050811a [Citations: 9]
  8. Central Weighted ENO Schemes for Hyperbolic Conservation Laws on Fixed and Moving Unstructured Meshes

    Dumbser, Michael | Boscheri, Walter | Semplice, Matteo | Russo, Giovanni

    SIAM Journal on Scientific Computing, Vol. 39 (2017), Iss. 6 P.A2564

    https://doi.org/10.1137/17M1111036 [Citations: 75]
  9. High-Order Methods for Hypersonic Shock Wave Turbulent Boundary Layer Interaction Flow

    Antoniadis, Antonios F. | Drikakis, Dimitris | Kokkinakis, Ioannis W. | Tsoutsanis, Panagiotis | Rana, Zeeshan A.

    20th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, (2015),

    https://doi.org/10.2514/6.2015-3524 [Citations: 2]
  10. High Order Direct Arbitrary-Lagrangian–Eulerian (ALE) Finite Volume Schemes for Hyperbolic Systems on Unstructured Meshes

    Boscheri, Walter

    Archives of Computational Methods in Engineering, Vol. 24 (2017), Iss. 4 P.751

    https://doi.org/10.1007/s11831-016-9188-x [Citations: 15]
  11. Cell centered direct Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume schemes for nonlinear hyperelasticity

    Boscheri, Walter | Dumbser, Michael | Loubère, Raphaël

    Computers & Fluids, Vol. 134-135 (2016), Iss. P.111

    https://doi.org/10.1016/j.compfluid.2016.05.004 [Citations: 32]
  12. Finite volume WENO schemes for nonlinear parabolic problems with degenerate diffusion on non-uniform meshes

    Arbogast, Todd | Huang, Chieh-Sen | Zhao, Xikai

    Journal of Computational Physics, Vol. 399 (2019), Iss. P.108921

    https://doi.org/10.1016/j.jcp.2019.108921 [Citations: 25]
  13. A Class of Hybrid DG/FV Methods for Conservation Laws III: Two-Dimensional Euler Equations

    Zhang, Laiping | Liu, Wei | He, Lixin | Deng, Xiaogang

    Communications in Computational Physics, Vol. 12 (2012), Iss. 1 P.284

    https://doi.org/10.4208/cicp.210111.140711a [Citations: 11]
  14. UCNS3D: An open-source high-order finite-volume unstructured CFD solver

    Antoniadis, Antonis F. | Drikakis, Dimitris | Farmakis, Pericles S. | Fu, Lin | Kokkinakis, Ioannis | Nogueira, Xesús | Silva, Paulo A.S.F. | Skote, Martin | Titarev, Vladimir | Tsoutsanis, Panagiotis

    Computer Physics Communications, Vol. 279 (2022), Iss. P.108453

    https://doi.org/10.1016/j.cpc.2022.108453 [Citations: 28]
  15. A High-Order Unstaggered Constrained-Transport Method for the Three-Dimensional Ideal Magnetohydrodynamic Equations Based on the Method of Lines

    Helzel, Christiane | Rossmanith, James A. | Taetz, Bertram

    SIAM Journal on Scientific Computing, Vol. 35 (2013), Iss. 2 P.A623

    https://doi.org/10.1137/120870323 [Citations: 15]
  16. Finite difference and finite volume ghost multi-resolution WENO schemes with increasingly higher order of accuracy

    Zhang, Yan | Zhu, Jun

    Journal of Computational Physics, Vol. 504 (2024), Iss. P.112890

    https://doi.org/10.1016/j.jcp.2024.112890 [Citations: 2]
  17. Three-dimensional high-order finite-volume method based on compact WENO reconstruction with hybrid unstructured grids

    Zhan, Ningyu | Chen, Rongqian | You, Yancheng

    Journal of Computational Physics, Vol. 490 (2023), Iss. P.112300

    https://doi.org/10.1016/j.jcp.2023.112300 [Citations: 4]
  18. Improvement of the computational performance of a parallel unstructured WENO finite volume CFD code for Implicit Large Eddy Simulation

    Tsoutsanis, Panagiotis | Antoniadis, Antonis F. | Jenkins, Karl W.

    Computers & Fluids, Vol. 173 (2018), Iss. P.157

    https://doi.org/10.1016/j.compfluid.2018.03.012 [Citations: 30]
  19. Three-dimensional third-order gas-kinetic scheme on hybrid unstructured meshes for Euler and Navier–Stokes equations

    Yang, Yaqing | Pan, Liang | Xu, Kun

    Computers & Fluids, Vol. 255 (2023), Iss. P.105834

    https://doi.org/10.1016/j.compfluid.2023.105834 [Citations: 10]
  20. Extended bounds limiter for high-order finite-volume schemes on unstructured meshes

    Tsoutsanis, Panagiotis

    Journal of Computational Physics, Vol. 362 (2018), Iss. P.69

    https://doi.org/10.1016/j.jcp.2018.02.009 [Citations: 33]
  21. A New Family of High Order Unstructured MOOD and ADER Finite Volume Schemes for Multidimensional Systems of Hyperbolic Conservation Laws

    Loubère, Raphaël | Dumbser, Michael | Diot, Steven

    Communications in Computational Physics, Vol. 16 (2014), Iss. 3 P.718

    https://doi.org/10.4208/cicp.181113.140314a [Citations: 90]
  22. A relaxed a posteriori MOOD algorithm for multicomponent compressible flows using high-order finite-volume methods on unstructured meshes

    Tsoutsanis, Panagiotis | Pavan Kumar, Machavolu Sai Santosh | Farmakis, Pericles S.

    Applied Mathematics and Computation, Vol. 437 (2023), Iss. P.127544

    https://doi.org/10.1016/j.amc.2022.127544 [Citations: 3]
  23. High order cell-centered Lagrangian-type finite volume schemes with time-accurate local time stepping on unstructured triangular meshes

    Boscheri, Walter | Dumbser, Michael | Zanotti, Olindo

    Journal of Computational Physics, Vol. 291 (2015), Iss. P.120

    https://doi.org/10.1016/j.jcp.2015.02.052 [Citations: 26]
  24. Efficient implementation of high order unstructured WENO schemes for cavitating flows

    Dumbser, Michael | Iben, Uwe | Munz, Claus-Dieter

    Computers & Fluids, Vol. 86 (2013), Iss. P.141

    https://doi.org/10.1016/j.compfluid.2013.07.011 [Citations: 52]
  25. Reprint of: EBR-WENO scheme for solving gas dynamics problems with discontinuities on unstructured meshes

    Bakhvalov, Pavel | Kozubskaya, Tatiana

    Computers & Fluids, Vol. 169 (2018), Iss. P.98

    https://doi.org/10.1016/j.compfluid.2018.03.050 [Citations: 3]
  26. EBR-WENO scheme for solving gas dynamics problems with discontinuities on unstructured meshes

    Bakhvalov, Pavel | Kozubskaya, Tatiana

    Computers & Fluids, Vol. 157 (2017), Iss. P.312

    https://doi.org/10.1016/j.compfluid.2017.09.004 [Citations: 46]
  27. An accurate and practical numerical solver for simulations of shock, vortices and turbulence interaction problems

    Cheng, Lidong | Deng, Xi | Xie, Bin

    Acta Astronautica, Vol. 210 (2023), Iss. P.1

    https://doi.org/10.1016/j.actaastro.2023.04.049 [Citations: 7]
  28. A new type of multi-resolution WENO schemes with increasingly higher order of accuracy on triangular meshes

    Zhu, Jun | Shu, Chi-Wang

    Journal of Computational Physics, Vol. 392 (2019), Iss. P.19

    https://doi.org/10.1016/j.jcp.2019.04.027 [Citations: 54]
  29. An efficient unstructured WENO method for supersonic reactive flows

    Zhao, Wen-Geng | Zheng, Hong-Wei | Liu, Feng-Jun | Shi, Xiao-Tian | Gao, Jun | Hu, Ning | Lv, Meng | Chen, Si-Cong | Zhao, Hong-Da

    Acta Mechanica Sinica, Vol. 34 (2018), Iss. 4 P.623

    https://doi.org/10.1007/s10409-018-0756-1 [Citations: 7]
  30. A direct Arbitrary-Lagrangian–Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3D

    Boscheri, Walter | Dumbser, Michael

    Journal of Computational Physics, Vol. 275 (2014), Iss. P.484

    https://doi.org/10.1016/j.jcp.2014.06.059 [Citations: 106]
  31. High order accurate direct Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume schemes on moving curvilinear unstructured meshes

    Boscheri, Walter | Dumbser, Michael

    Computers & Fluids, Vol. 136 (2016), Iss. P.48

    https://doi.org/10.1016/j.compfluid.2016.05.020 [Citations: 28]
  32. A new open-source library based on novel high-resolution structure-preserving convection schemes

    Deng, Xi

    Journal of Computational Science, Vol. 74 (2023), Iss. P.102150

    https://doi.org/10.1016/j.jocs.2023.102150 [Citations: 6]
  33. Von Neumann Stable, Implicit, High Order, Finite Volume WENO Schemes

    Arbogast, Todd | Huang, Chieh-Sen | Zhao, Xikai

    Day 1 Wed, April 10, 2019, (2019),

    https://doi.org/10.2118/193817-MS [Citations: 5]
  34. An absolutely convergent fixed-point fast sweeping WENO method on triangular meshes for steady state of hyperbolic conservation laws

    Li, Liang | Zhu, Jun | Zhang, Yong-Tao

    Journal of Computational Physics, Vol. 514 (2024), Iss. P.113215

    https://doi.org/10.1016/j.jcp.2024.113215 [Citations: 0]
  35. Uniformly high-order schemes on arbitrary unstructured meshes for advection–diffusion equations

    Titarev, V.A. | Drikakis, D.

    Computers & Fluids, Vol. 46 (2011), Iss. 1 P.467

    https://doi.org/10.1016/j.compfluid.2010.10.008 [Citations: 11]
  36. Low-dissipation BVD schemes for single and multi-phase compressible flows on unstructured grids

    Cheng, Lidong | Deng, Xi | Xie, Bin | Jiang, Yi | Xiao, Feng

    Journal of Computational Physics, Vol. 428 (2021), Iss. P.110088

    https://doi.org/10.1016/j.jcp.2020.110088 [Citations: 18]
  37. Third-order accurate conservative method on unstructured meshes for gasdynamic simulations

    Shirobokov, D. A.

    Computational Mathematics and Mathematical Physics, Vol. 57 (2017), Iss. 4 P.661

    https://doi.org/10.1134/S0965542517040091 [Citations: 1]
  38. High-order unstructured Lagrangian one-step WENO finite volume schemes for non-conservative hyperbolic systems: Applications to compressible multi-phase flows

    Dumbser, Michael | Boscheri, Walter

    Computers & Fluids, Vol. 86 (2013), Iss. P.405

    https://doi.org/10.1016/j.compfluid.2013.07.024 [Citations: 60]
  39. A new 3D OpenFoam solver with improved resolution for hyperbolic systems on hybrid unstructured grids

    Cheng, Lidong | Deng, Xi | Xie, Bin | Jiang, Yi | Xiao, Feng

    Applied Mathematical Modelling, Vol. 108 (2022), Iss. P.142

    https://doi.org/10.1016/j.apm.2022.03.022 [Citations: 1]
  40. Fifth-Order Hermite Targeted Essentially Non-oscillatory Schemes for Hyperbolic Conservation Laws

    Wibisono, Indra | Kosasih, Engkos A.

    Journal of Scientific Computing, Vol. 87 (2021), Iss. 3

    https://doi.org/10.1007/s10915-021-01485-0 [Citations: 16]
  41. An iterative near-boundary reconstruction strategy for unstructured finite volume method

    Chen, Zedong | Zhang, Fan | Liu, Jun | Chen, Biaosong

    Journal of Computational Physics, Vol. 418 (2020), Iss. P.109621

    https://doi.org/10.1016/j.jcp.2020.109621 [Citations: 3]
  42. Numerical study on the convergence to steady-state solutions of a new class of finite volume WENO schemes: triangular meshes

    Zhu, J. | Shu, C.-W.

    Shock Waves, Vol. 29 (2019), Iss. 1 P.3

    https://doi.org/10.1007/s00193-018-0833-1 [Citations: 20]
  43. Stencil selection algorithms for WENO schemes on unstructured meshes

    Tsoutsanis, Panagiotis

    Journal of Computational Physics: X, Vol. 4 (2019), Iss. P.100037

    https://doi.org/10.1016/j.jcpx.2019.100037 [Citations: 6]
  44. High resolution multi-moment finite volume method for supersonic combustion on unstructured grids

    Deng, Xi | Xie, Bin | Teng, Honghui | Xiao, Feng

    Applied Mathematical Modelling, Vol. 66 (2019), Iss. P.404

    https://doi.org/10.1016/j.apm.2018.08.010 [Citations: 13]
  45. An efficient modified WENO scheme based on the identification of inflection points

    Chai, Delin | Xi, Guang | Sun, Zhongguo | Wang, Zhiheng | Huang, Zhu

    Computers & Fluids, Vol. 170 (2018), Iss. P.176

    https://doi.org/10.1016/j.compfluid.2018.04.036 [Citations: 5]
  46. A new type of third-order finite volume multi-resolution WENO schemes on tetrahedral meshes

    Zhu, Jun | Shu, Chi-Wang

    Journal of Computational Physics, Vol. 406 (2020), Iss. P.109212

    https://doi.org/10.1016/j.jcp.2019.109212 [Citations: 27]
  47. On numerical modeling of the contaminant transport equations of the wetland hydrology and water quality model WETSAND

    Kazezyılmaz-Alhan, Cevza Melek | Medina, Miguel A.

    Applied Mathematical Modelling, Vol. 40 (2016), Iss. 5-6 P.4260

    https://doi.org/10.1016/j.apm.2015.10.034 [Citations: 2]
  48. High order direct Arbitrary-Lagrangian-Eulerian (ALE) PP schemes with WENO Adaptive-Order reconstruction on unstructured meshes

    Boscheri, Walter | Balsara, Dinshaw S.

    Journal of Computational Physics, Vol. 398 (2019), Iss. P.108899

    https://doi.org/10.1016/j.jcp.2019.108899 [Citations: 24]
  49. WENO schemes on arbitrary unstructured meshes for laminar, transitional and turbulent flows

    Tsoutsanis, Panagiotis | Antoniadis, Antonios Foivos | Drikakis, Dimitris

    Journal of Computational Physics, Vol. 256 (2014), Iss. P.254

    https://doi.org/10.1016/j.jcp.2013.09.002 [Citations: 82]
  50. High order space–time adaptive ADER-WENO finite volume schemes for non-conservative hyperbolic systems

    Dumbser, Michael | Hidalgo, Arturo | Zanotti, Olindo

    Computer Methods in Applied Mechanics and Engineering, Vol. 268 (2014), Iss. P.359

    https://doi.org/10.1016/j.cma.2013.09.022 [Citations: 78]
  51. High-order Schemes on Mixed-element Unstructured Grids for Aerodynamic Flows

    Antoniadis, Antonios | Tsoutsanis, Panagiotis | Drikakis, Dimitrios

    42nd AIAA Fluid Dynamics Conference and Exhibit, (2012),

    https://doi.org/10.2514/6.2012-2833 [Citations: 6]
  52. Hybrid discontinuous Galerkin-finite volume techniques for compressible flows on unstructured meshes

    Maltsev, Vadim | Yuan, Dean | Jenkins, Karl W. | Skote, Martin | Tsoutsanis, Panagiotis

    Journal of Computational Physics, Vol. 473 (2023), Iss. P.111755

    https://doi.org/10.1016/j.jcp.2022.111755 [Citations: 11]
  53. Arbitrary high order central non-oscillatory schemes on mixed-element unstructured meshes

    Tsoutsanis, Panagiotis | Dumbser, Michael

    Computers & Fluids, Vol. 225 (2021), Iss. P.104961

    https://doi.org/10.1016/j.compfluid.2021.104961 [Citations: 36]
  54. High-order hybrid DG-FV framework for compressible multi-fluid problems on unstructured meshes

    Maltsev, Vadim | Skote, Martin | Tsoutsanis, Panagiotis

    Journal of Computational Physics, Vol. 502 (2024), Iss. P.112819

    https://doi.org/10.1016/j.jcp.2024.112819 [Citations: 4]
  55. Arbitrary-Lagrangian-Eulerian One-Step WENO Finite Volume Schemes on Unstructured Triangular Meshes

    Boscheri, Walter | Dumbser, Michael

    Communications in Computational Physics, Vol. 14 (2013), Iss. 5 P.1174

    https://doi.org/10.4208/cicp.181012.010313a [Citations: 68]
  56. Parametric Study on Formation Flying Effectiveness for a Blended-Wing UAV

    Shin, Hyo-Sang | Antoniadis, Antonis F. | Tsourdos, Antonios

    Journal of Intelligent & Robotic Systems, Vol. 93 (2019), Iss. 1-2 P.179

    https://doi.org/10.1007/s10846-018-0842-4 [Citations: 8]
  57. Parametric study on efficient formation flying for a blended-wing UAV

    Shin, Hyo-Sang | Antoniadis, Antonis F. | Tsourdos, Antonios

    2017 International Conference on Unmanned Aircraft Systems (ICUAS), (2017), P.1657

    https://doi.org/10.1109/ICUAS.2017.7991453 [Citations: 3]
  58. Handbook of Numerical Methods for Hyperbolic Problems - Basic and Fundamental Issues

    ENO and WENO Schemes

    Zhang, Y.-T. | Shu, C.-W.

    2016

    https://doi.org/10.1016/bs.hna.2016.09.009 [Citations: 17]
  59. Towards Building the OP-Mapped WENO Schemes: A General Methodology

    Li, Ruo | Zhong, Wei

    Mathematical and Computational Applications, Vol. 26 (2021), Iss. 4 P.67

    https://doi.org/10.3390/mca26040067 [Citations: 0]
  60. Hovering rotor solutions by high-order methods on unstructured grids

    Ricci, Francesco | Silva, Paulo A.S.F. | Tsoutsanis, Panagiotis | Antoniadis, Antonis F.

    Aerospace Science and Technology, Vol. 97 (2020), Iss. P.105648

    https://doi.org/10.1016/j.ast.2019.105648 [Citations: 21]
  61. Implicit Large Eddy Simulation of weakly-compressible turbulent channel flow

    Kokkinakis, I.W. | Drikakis, D.

    Computer Methods in Applied Mechanics and Engineering, Vol. 287 (2015), Iss. P.229

    https://doi.org/10.1016/j.cma.2015.01.016 [Citations: 69]
  62. ADER-WENO finite volume schemes with space–time adaptive mesh refinement

    Dumbser, Michael | Zanotti, Olindo | Hidalgo, Arturo | Balsara, Dinshaw S.

    Journal of Computational Physics, Vol. 248 (2013), Iss. P.257

    https://doi.org/10.1016/j.jcp.2013.04.017 [Citations: 151]
  63. A vertex-based reconstruction for cell-centered finite-volume discretization on unstructured grids

    Chen, Zedong | Zhang, Fan | Liu, Jun | Chen, Biaosong

    Journal of Computational Physics, Vol. 451 (2022), Iss. P.110827

    https://doi.org/10.1016/j.jcp.2021.110827 [Citations: 1]
  64. New high-resolution-preserving sliding mesh techniques for higher-order finite volume schemes

    Ramírez, Luis | Foulquié, Charles | Nogueira, Xesús | Khelladi, Sofiane | Chassaing, Jean-Camille | Colominas, Ignasi

    Computers & Fluids, Vol. 118 (2015), Iss. P.114

    https://doi.org/10.1016/j.compfluid.2015.06.008 [Citations: 37]
  65. A well-balanced and exactly divergence-free staggered semi-implicit hybrid finite volume / finite element scheme for the incompressible MHD equations

    Fambri, F. | Zampa, E. | Busto, S. | Río-Martín, L. | Hindenlang, F. | Sonnendrücker, E. | Dumbser, M.

    Journal of Computational Physics, Vol. 493 (2023), Iss. P.112493

    https://doi.org/10.1016/j.jcp.2023.112493 [Citations: 7]
  66. WENO schemes on unstructured meshes using a relaxed a posteriori MOOD limiting approach

    Farmakis, Pericles S. | Tsoutsanis, Panagiotis | Nogueira, Xesús

    Computer Methods in Applied Mechanics and Engineering, Vol. 363 (2020), Iss. P.112921

    https://doi.org/10.1016/j.cma.2020.112921 [Citations: 31]
  67. Arbitrary-order unstructured finite-volume methods for implicit large eddy simulation of turbulent flows with adaptive dissipation/dispersion adjustment (ADDA)

    Tsoutsanis, Panagiotis | Nogueira, Xesus

    Journal of Computational Physics, Vol. 523 (2025), Iss. P.113653

    https://doi.org/10.1016/j.jcp.2024.113653 [Citations: 0]
  68. High-order finite volume multi-resolution WENO schemes with adaptive linear weights on triangular meshes

    Lin, Yicheng | Zhu, Jun

    Journal of Computational Physics, Vol. 506 (2024), Iss. P.112927

    https://doi.org/10.1016/j.jcp.2024.112927 [Citations: 2]
  69. High-Order Finite-Volume TENO Schemes with Dual ENO-Like Stencil Selection for Unstructured Meshes

    Ji, Zhe | Liang, Tian | Fu, Lin

    Journal of Scientific Computing, Vol. 95 (2023), Iss. 3

    https://doi.org/10.1007/s10915-023-02199-1 [Citations: 10]
  70. New Finite Volume Weighted Essentially Nonoscillatory Schemes on Triangular Meshes

    Zhu, Jun | Qiu, Jianxian

    SIAM Journal on Scientific Computing, Vol. 40 (2018), Iss. 2 P.A903

    https://doi.org/10.1137/17M1112790 [Citations: 50]
  71. Low-Mach number treatment for Finite-Volume schemes on unstructured meshes

    Simmonds, Nicholas | Tsoutsanis, Panagiotis | Antoniadis, Antonis F. | Jenkins, Karl W. | Gaylard, Adrian

    Applied Mathematics and Computation, Vol. 336 (2018), Iss. P.368

    https://doi.org/10.1016/j.amc.2018.04.076 [Citations: 3]
  72. An efficient high order direct ALE ADER finite volume scheme with a posteriori limiting for hydrodynamics and magnetohydrodynamics

    Boscheri, Walter

    International Journal for Numerical Methods in Fluids, Vol. 84 (2017), Iss. 2 P.76

    https://doi.org/10.1002/fld.4342 [Citations: 7]
  73. High‐order ADER‐WENO ALE schemes on unstructured triangular meshes—application of several node solvers to hydrodynamics and magnetohydrodynamics

    Boscheri, W. | Dumbser, M. | Balsara, D. S.

    International Journal for Numerical Methods in Fluids, Vol. 76 (2014), Iss. 10 P.737

    https://doi.org/10.1002/fld.3947 [Citations: 63]
  74. A new class of Moving-Least-Squares WENO–SPH schemes

    Avesani, Diego | Dumbser, Michael | Bellin, Alberto

    Journal of Computational Physics, Vol. 270 (2014), Iss. P.278

    https://doi.org/10.1016/j.jcp.2014.03.041 [Citations: 67]
  75. High Order ADER Schemes for Continuum Mechanics

    Busto, Saray | Chiocchetti, Simone | Dumbser, Michael | Gaburro, Elena | Peshkov, Ilya

    Frontiers in Physics, Vol. 8 (2020), Iss.

    https://doi.org/10.3389/fphy.2020.00032 [Citations: 54]
  76. A Class of New High-order Finite-Volume TENO Schemes for Hyperbolic Conservation Laws with Unstructured Meshes

    Ji, Zhe | Liang, Tian | Fu, Lin

    Journal of Scientific Computing, Vol. 92 (2022), Iss. 2

    https://doi.org/10.1007/s10915-022-01925-5 [Citations: 21]
  77. High order parametrized maximum-principle-preserving and positivity-preserving WENO schemes on unstructured meshes

    Christlieb, Andrew J. | Liu, Yuan | Tang, Qi | Xu, Zhengfu

    Journal of Computational Physics, Vol. 281 (2015), Iss. P.334

    https://doi.org/10.1016/j.jcp.2014.10.029 [Citations: 40]
  78. Lagrangian ADER-WENO finite volume schemes on unstructured triangular meshes based on genuinely multidimensional HLL Riemann solvers

    Boscheri, Walter | Balsara, Dinshaw S. | Dumbser, Michael

    Journal of Computational Physics, Vol. 267 (2014), Iss. P.112

    https://doi.org/10.1016/j.jcp.2014.02.023 [Citations: 61]
  79. A Robust Reconstruction for Unstructured WENO Schemes

    Liu, Yuan | Zhang, Yong-Tao

    Journal of Scientific Computing, Vol. 54 (2013), Iss. 2-3 P.603

    https://doi.org/10.1007/s10915-012-9598-3 [Citations: 73]
  80. A Robust WENO Type Finite Volume Solver for Steady Euler Equations on Unstructured Grids

    Hu, Guanghui | Li, Ruo | Tang, Tao

    Communications in Computational Physics, Vol. 9 (2011), Iss. 3 P.627

    https://doi.org/10.4208/cicp.031109.080410s [Citations: 48]