Close Search Advanced
Journals
Resources
About Us
Open Access

A Robust WENO Type Finite Volume Solver for Steady Euler Equations on Unstructured Grids

A Robust WENO Type Finite Volume Solver for Steady Euler Equations on Unstructured Grids
Preview
Add to basket

Year:    2011

Communications in Computational Physics, Vol. 9 (2011), Iss. 3 : pp. 627–648

Abstract

A recent work of Li et al. [Numer. Math. Theor. Meth. Appl., 1(2008), pp. 92-112] proposed a finite volume solver to solve 2D steady Euler equations. Although the Venkatakrishnan limiter is used to prevent the non-physical oscillations nearby the shock region, the overshoot or undershoot phenomenon can still be observed. Moreover, the numerical accuracy is degraded by using Venkatakrishnan limiter. To fix the problems, in this paper the WENO type reconstruction is employed to gain both the accurate approximations in smooth region and non-oscillatory sharp profiles near the shock discontinuity. The numerical experiments will demonstrate the efficiency and robustness of the proposed numerical strategy.

Submit Article

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.031109.080410s

Communications in Computational Physics, Vol. 9 (2011), Iss. 3 : pp. 627–648

Published online:    2011-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:   

  1. A Fourth-Order Unstructured NURBS-Enhanced Finite Volume WENO Scheme for Steady Euler Equations in Curved Geometries

    Meng, Xucheng | Gu, Yaguang | Hu, Guanghui

    Communications on Applied Mathematics and Computation, Vol. 5 (2023), Iss. 1 P.315

    https://doi.org/10.1007/s42967-021-00163-0 [Citations: 2]

  2. Two-Grid Finite Volume Element Methods for Solving Cahn–Hilliard Equation

    Xu, Wenhan | Ge, Liang

    Bulletin of the Iranian Mathematical Society, Vol. 49 (2023), Iss. 3

    https://doi.org/10.1007/s41980-023-00774-8 [Citations: 0]

  3. 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]
  4. Theory, Numerics and Applications of Hyperbolic Problems II

    On Robust and Adaptive Finite Volume Methods for Steady Euler Equations

    Hu, Guanghui | Meng, Xucheng | Tang, Tao

    2018

    https://doi.org/10.1007/978-3-319-91548-7_2 [Citations: 0]

  5. Steady-state simulation of Euler equations by the discontinuous Galerkin method with the hybrid limiter

    Wei, Lei | Xia, Yinhua

    Journal of Computational Physics, Vol. 515 (2024), Iss. P.113288

    https://doi.org/10.1016/j.jcp.2024.113288 [Citations: 1]

  6. Constrained Interpolation Profile Conservative Semi-Lagrangian Scheme Based on Third-Order Polynomial Functions and Essentially Non-Oscillatory (CIP-CSL3ENO) Scheme

    Li, Qijie | Omar, Syazana | Deng, Xi | Yokoi, Kensuke

    Communications in Computational Physics, Vol. 22 (2017), Iss. 3 P.765

    https://doi.org/10.4208/cicp.OA-2016-0117 [Citations: 7]
  7. 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]

  8. A new type of multi-resolution WENO schemes with increasingly higher order of accuracy

    Zhu, Jun | Shu, Chi-Wang

    Journal of Computational Physics, Vol. 375 (2018), Iss. P.659

    https://doi.org/10.1016/j.jcp.2018.09.003 [Citations: 126]

  9. 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]

  10. A numerical study of 2D detonation waves with adaptive finite volume methods on unstructured grids

    Hu, Guanghui

    Journal of Computational Physics, Vol. 331 (2017), Iss. P.297

    https://doi.org/10.1016/j.jcp.2016.11.041 [Citations: 8]

  11. A New Sixth-Order Finite Difference WENO Scheme for Fractional Differential Equations

    Zhang, Yan | Deng, Weihua | Zhu, Jun

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

    https://doi.org/10.1007/s10915-021-01486-z [Citations: 8]

  12. Fast sweeping methods for hyperbolic systems of conservation laws at steady state II

    Engquist, Björn | Froese, Brittany D. | Tsai, Yen-Hsi Richard

    Journal of Computational Physics, Vol. 286 (2015), Iss. P.70

    https://doi.org/10.1016/j.jcp.2015.01.028 [Citations: 11]

  13. Multi-resolution HWENO schemes for hyperbolic conservation laws

    Li, Jiayin | Shu, Chi-Wang | Qiu, Jianxian

    Journal of Computational Physics, Vol. 446 (2021), Iss. P.110653

    https://doi.org/10.1016/j.jcp.2021.110653 [Citations: 15]

  14. A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws

    Hao, Wenrui | Hauenstein, Jonathan D. | Shu, Chi-Wang | Sommese, Andrew J. | Xu, Zhiliang | Zhang, Yong-Tao

    Journal of Computational Physics, Vol. 250 (2013), Iss. P.332

    https://doi.org/10.1016/j.jcp.2013.05.008 [Citations: 32]

  15. Simulation of Inviscid Compressible Flows Using PDE Transform

    Hu, Langhua | Yang, Siyang | Wei, Guo-Wei

    Communications in Computational Physics, Vol. 16 (2014), Iss. 5 P.1201

    https://doi.org/10.4208/cicp.031113.160514a [Citations: 0]

  16. A nonlinear multigrid steady-state solver for 1D microflow

    Hu, Zhicheng | Li, Ruo

    Computers & Fluids, Vol. 103 (2014), Iss. P.193

    https://doi.org/10.1016/j.compfluid.2014.07.022 [Citations: 4]

  17. 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: 30]

  18. A low dissipation finite difference nested multi-resolution WENO scheme for Euler/Navier-Stokes equations

    Wang, Zhenming | Zhu, Jun | Tian, Linlin | Zhao, Ning

    Journal of Computational Physics, Vol. 429 (2021), Iss. P.110006

    https://doi.org/10.1016/j.jcp.2020.110006 [Citations: 15]

  19. 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]

  20. Semi-conservative high order scheme with numerical entropy indicator for intrusive formulations of hyperbolic systems

    Gerster, Stephan | Semplice, Matteo

    Journal of Computational Physics, Vol. 489 (2023), Iss. P.112254

    https://doi.org/10.1016/j.jcp.2023.112254 [Citations: 0]

  21. New Finite Difference Mapped WENO Schemes with Increasingly High Order of Accuracy

    Zhu, Jun | Qiu, Jianxian

    Communications on Applied Mathematics and Computation, Vol. 5 (2023), Iss. 1 P.64

    https://doi.org/10.1007/s42967-021-00122-9 [Citations: 3]

  22. Adjoint-based an adaptive finite volume method for steady Euler equations with non-oscillatory k -exact reconstruction

    Hu, Guanghui | Meng, Xucheng | Yi, Nianyu

    Computers & Fluids, Vol. 139 (2016), Iss. P.174

    https://doi.org/10.1016/j.compfluid.2016.06.012 [Citations: 12]

  23. Fast sweeping methods for hyperbolic systems of conservation laws at steady state

    Engquist, Björn | Froese, Brittany D. | Tsai, Yen-Hsi Richard

    Journal of Computational Physics, Vol. 255 (2013), Iss. P.316

    https://doi.org/10.1016/j.jcp.2013.08.036 [Citations: 13]

  24. High Order Cubic-Polynomial Interpolation Schemes on Triangular Meshes

    Feng, Renzhong

    Communications in Computational Physics, Vol. 12 (2012), Iss. 5 P.1588

    https://doi.org/10.4208/cicp.201210.250212a [Citations: 2]

  25. Comparison of structured- and unstructured-grid, compressible and incompressible methods using the vortex pairing problem

    Tsoutsanis, Panagiotis | Kokkinakis, Ioannis W. | Könözsy, László | Drikakis, Dimitris | Williams, Robin J.R. | Youngs, David L.

    Computer Methods in Applied Mechanics and Engineering, Vol. 293 (2015), Iss. P.207

    https://doi.org/10.1016/j.cma.2015.04.010 [Citations: 71]

  26. A new fifth-order alternative finite difference multi-resolution WENO scheme for solving compressible flow

    Wang, Zhenming | Zhu, Jun | Yang, Yuchen | Zhao, Ning

    Computer Methods in Applied Mechanics and Engineering, Vol. 382 (2021), Iss. P.113853

    https://doi.org/10.1016/j.cma.2021.113853 [Citations: 15]

  27. An adaptive finite volume solver for steady Euler equations with non-oscillatory k-exact reconstruction

    Hu, Guanghui | Yi, Nianyu

    Journal of Computational Physics, Vol. 312 (2016), Iss. P.235

    https://doi.org/10.1016/j.jcp.2016.02.019 [Citations: 13]

  28. 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]

  29. 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: 34]

  30. High order finite difference hermite WENO schemes for the Hamilton–Jacobi equations on unstructured meshes

    Zheng, Feng | Shu, Chi-Wang | Qiu, Jianxian

    Computers & Fluids, Vol. 183 (2019), Iss. P.53

    https://doi.org/10.1016/j.compfluid.2019.02.010 [Citations: 3]

  31. a posteriori stabilized sixth-order finite volume scheme for one-dimensional steady-state hyperbolic equations

    Clain, Stéphane | Loubère, Raphaël | Machado, Gaspar J.

    Advances in Computational Mathematics, Vol. 44 (2018), Iss. 2 P.571

    https://doi.org/10.1007/s10444-017-9556-6 [Citations: 7]

  32. 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: 1]

  33. A new type of high-order multi-resolution trigonometric WENO schemes with adaptive linear weights for hyperbolic conservation laws

    Zhang, Yan | Zhu, Jun

    Computers & Fluids, Vol. 281 (2024), Iss. P.106372

    https://doi.org/10.1016/j.compfluid.2024.106372 [Citations: 0]

  34. 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: 4]

  35. 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]

  36. 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]

  37. 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: 0]

  38. A Finite Difference Mapped WENO Scheme with Unequal-Size Stencils for Hyperbolic Conservation Laws

    Zhu, Jun | Qiu, Jianxian

    Journal of Scientific Computing, Vol. 93 (2022), Iss. 3

    https://doi.org/10.1007/s10915-022-02034-z [Citations: 0]

  39. 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: 29]

  40. 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: 52]

  41. An improved fifth-order WENO scheme with symmetry-preserving smoothness indicators for hyperbolic conservation laws

    Zhong, Wei | Wang, Shufei | Qiu, Jiulu | Gao, Jiahao

    Journal of Computational Physics, Vol. 491 (2023), Iss. P.112350

    https://doi.org/10.1016/j.jcp.2023.112350 [Citations: 1]

  42. A new fifth order finite difference WENO scheme for solving hyperbolic conservation laws

    Zhu, Jun | Qiu, Jianxian

    Journal of Computational Physics, Vol. 318 (2016), Iss. P.110

    https://doi.org/10.1016/j.jcp.2016.05.010 [Citations: 198]

  43. New mapped unequal-sized trigonometric WENO scheme for hyperbolic conservation laws

    Zhang, Yan | Zhu, Jun

    Computers & Fluids, Vol. 245 (2022), Iss. P.105585

    https://doi.org/10.1016/j.compfluid.2022.105585 [Citations: 0]

  44. An adaptive finite volume method for 2D steady Euler equations with WENO reconstruction

    Hu, Guanghui

    Journal of Computational Physics, Vol. 252 (2013), Iss. P.591

    https://doi.org/10.1016/j.jcp.2013.07.006 [Citations: 18]

  45. A Third Order Adaptive ADER Scheme for One Dimensional Conservation Laws

    Gu, Yaguang | Hu, Guanghui

    Communications in Computational Physics, Vol. 22 (2017), Iss. 3 P.829

    https://doi.org/10.4208/cicp.OA-2016-0088 [Citations: 1]

  46. Assessment of high-order finite volume methods on unstructured meshes for RANS solutions of aeronautical configurations

    Antoniadis, Antonis F. | Tsoutsanis, Panagiotis | Drikakis, Dimitris

    Computers & Fluids, Vol. 146 (2017), Iss. P.86

    https://doi.org/10.1016/j.compfluid.2017.01.002 [Citations: 40]