High order Godunov-type scheme for conservation laws with discontinuous flux function in space

2021 ◽  
Author(s):  
Qianqian Wei ◽  
Guodong Wang ◽  
Yanying Ma
Keyword(s):  
Conservation Laws ◽  
High Order ◽  
Flux Function ◽  
Discontinuous Flux Function ◽  
Discontinuous Flux

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

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1079
Author(s):  
Tingting Xiang ◽  
Guodong Wang ◽  
Suping Zhang
Keyword(s):  
Conservation Laws ◽  
High Order ◽  
Splitting Scheme ◽  
Scalar Conservation Laws ◽  
Flux Function ◽  
Flux Splitting ◽  
Discontinuous Flux Function ◽  
Discontinuous Flux ◽  
Scalar Conservation ◽  
Accurate Scheme

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.

scholarly journals Zero Diffusion-Dispersion-Smoothing Limits for a Scalar Conservation Law with Discontinuous Flux Function

2009 ◽  
Vol 2009 ◽  
pp. 1-33 ◽  
Author(s):  
H. Holden ◽  
K. H. Karlsen ◽  
D. Mitrovic
Keyword(s):  
Conservation Laws ◽  
Conservation Law ◽  
Flux Function ◽  
Discontinuous Flux Function ◽  
Scalar Conservation Law ◽  
Discontinuous Flux ◽  
Dispersion Terms ◽  
Scalar Conservation

We consider multidimensional conservation laws with discontinuous flux, which are regularized with vanishing diffusion and dispersion terms and with smoothing of the flux discontinuities. We use the approach ofH-measures to investigate the zero diffusion-dispersion-smoothing limit.

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