High-Order Accurate Flux-Splitting Scheme for Conservation Laws with Discontinuous Flux Function in Space
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 desi...
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MDPI AG
2021-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/10/1079 |
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| author | Tingting Xiang Guodong Wang Suping Zhang |
| author_facet | Tingting Xiang Guodong Wang Suping Zhang |
| author_sort | Tingting Xiang |
| collection | DOAJ |
| description | 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. |
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| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T11:32:55Z |
| publishDate | 2021-05-01 |
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| spelling | doaj.art-9d450d067ef448d99bf5aeb845dfb3d92023-11-21T19:07:51ZengMDPI AGMathematics2227-73902021-05-01910107910.3390/math9101079High-Order Accurate Flux-Splitting Scheme for Conservation Laws with Discontinuous Flux Function in SpaceTingting Xiang0Guodong Wang1Suping Zhang2School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, ChinaSchool of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, ChinaSchool of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, ChinaA 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.https://www.mdpi.com/2227-7390/9/10/1079conservation lawsdiscontinuous fluxEngquist–Osher-type interface fluxflux-splittingWENO reconstruction |
| spellingShingle | Tingting Xiang Guodong Wang Suping Zhang High-Order Accurate Flux-Splitting Scheme for Conservation Laws with Discontinuous Flux Function in Space Mathematics conservation laws discontinuous flux Engquist–Osher-type interface flux flux-splitting WENO reconstruction |
| title | High-Order Accurate Flux-Splitting Scheme for Conservation Laws with Discontinuous Flux Function in Space |
| title_full | High-Order Accurate Flux-Splitting Scheme for Conservation Laws with Discontinuous Flux Function in Space |
| title_fullStr | High-Order Accurate Flux-Splitting Scheme for Conservation Laws with Discontinuous Flux Function in Space |
| title_full_unstemmed | High-Order Accurate Flux-Splitting Scheme for Conservation Laws with Discontinuous Flux Function in Space |
| title_short | High-Order Accurate Flux-Splitting Scheme for Conservation Laws with Discontinuous Flux Function in Space |
| title_sort | high order accurate flux splitting scheme for conservation laws with discontinuous flux function in space |
| topic | conservation laws discontinuous flux Engquist–Osher-type interface flux flux-splitting WENO reconstruction |
| url | https://www.mdpi.com/2227-7390/9/10/1079 |
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