scholarly journals Entropy conservation property and entropy stabilization of high-order continuous Galerkin approximations to scalar conservation laws

2020 ◽  
Vol 213 ◽  
pp. 104742
Author(s):  
Dmitri Kuzmin ◽  
Manuel Quezada de Luna
Keyword(s):  
Conservation Laws ◽  
High Order ◽  
Scalar Conservation Laws ◽  
Conservation Property ◽  
Galerkin Approximations ◽  
Continuous Galerkin ◽  
Entropy Conservation ◽  
Scalar Conservation ◽  
Order Continuous

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 Numerical Solution of Scalar Conservation Laws with Random Flux Functions

2016 ◽  
Vol 4 (1) ◽  
pp. 552-591 ◽  
Author(s):  
Siddhartha Mishra ◽  
Nils Henrik Risebro ◽  
Christoph Schwab ◽  
Svetlana Tokareva
Keyword(s):  
Conservation Laws ◽  
Numerical Solution ◽  
Scalar Conservation Laws ◽  
Scalar Conservation
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