IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i6p592-d514352.html
   My bibliography  Save this article

Four-Quadrant Riemann Problem for a 2×2 System II

Author

Listed:
  • Jinah Hwang

    (Division of Applied Mathematical Sciences, Korea University, Sejong 30019, Korea)

  • Suyeon Shin

    (Division of Applied Mathematical Sciences, Korea University, Sejong 30019, Korea)

  • Myoungin Shin

    (Department of Ocean Systems Engineering, Sejong University, Seoul 05006, Korea)

  • Woonjae Hwang

    (Division of Applied Mathematical Sciences, Korea University, Sejong 30019, Korea)

Abstract

In previous work, we considered a four-quadrant Riemann problem for a 2 × 2 hyperbolic system in which delta shock appears at the initial discontinuity without assuming that each jump of the initial data projects exactly one plane elementary wave. In this paper, we consider the case that does not involve a delta shock at the initial discontinuity. We classified 18 topologically distinct solutions and constructed analytic and numerical solutions for each case. The constructed analytic solutions show the rich structure of wave interactions in the Riemann problem, which coincide with the computed numerical solutions.

Suggested Citation

  • Jinah Hwang & Suyeon Shin & Myoungin Shin & Woonjae Hwang, 2021. "Four-Quadrant Riemann Problem for a 2×2 System II," Mathematics, MDPI, vol. 9(6), pages 1-25, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:592-:d:514352
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/6/592/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/6/592/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hwang, Jinah & Shin, Myoungin & Shin, Suyeon & Hwang, Woonjae, 2018. "Two dimensional Riemann problem for a 2 × 2 system of hyperbolic conservation laws involving three constant states," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 49-62.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jinah Hwang & Suyeon Shin & Myoungin Shin & Woonjae Hwang, 2021. "Four-Quadrant Riemann Problem for a 2 × 2 System Involving Delta Shock," Mathematics, MDPI, vol. 9(2), pages 1-22, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:592-:d:514352. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.