High-Order Accurate Flux-Splitting Scheme for Conservation Laws with Discontinuous Flux Function in Space

Tingting Xiang, Guodong Wang and Suping Zhang
Additional contact information
Tingting Xiang: School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
Guodong Wang: School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
Suping Zhang: School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China

Mathematics, 2021, vol. 9, issue 10, 1-15

Abstract: A new modified Engquist–Osher-type flux-splitting scheme is proposed to approximate the scalar conservation laws with discontinuous flux function in space. The fact that the discontinuity of the fluxes in space results in the jump of the unknown function may be the reason why it is difficult to design a high-order scheme to solve this hyperbolic conservation law. In order to implement the WENO flux reconstruction, we apply the new modified Engquist–Osher-type flux to compensate for the discontinuity of fluxes in space. Together the third-order TVD Runge–Kutta time discretization, we can obtain the high-order accurate scheme, which keeps equilibrium state across the discontinuity in space, to solve the scalar conservation laws with discontinuous flux function. Some examples are given to demonstrate the good performance of the new high-order accurate scheme.

Keywords: conservation laws; discontinuous flux; Engquist–Osher-type interface flux; flux-splitting; WENO reconstruction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/10/1079/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/10/1079/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:10:p:1079-:d:552035

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().