scholarly journals Entropy Symmetrization and High-Order Accurate Entropy Stable Numerical Schemes for Relativistic MHD Equations

2020 ◽  
Vol 42 (4) ◽  
pp. A2230-A2261 ◽  
Author(s):  
Kailiang Wu ◽  
Chi-Wang Shu
Keyword(s):  
High Order ◽  
Mhd Equations ◽  
Numerical Schemes ◽  
Entropy Stable

A high-order solver for aerodynamic flow simulations and comparison of different numerical schemes

2017 ◽  
Author(s):  
Sergey Mikhaylov ◽  
Alexander Morozov ◽  
Vladimir Podaruev ◽  
Alexey Troshin
Keyword(s):  
High Order ◽  
Numerical Schemes ◽  
Flow Simulations

scholarly journals Entropy stable essentially nonoscillatory methods based on RBF reconstruction

2019 ◽  
Vol 53 (3) ◽  
pp. 925-958 ◽  
Author(s):  
Jan S. Hesthaven ◽  
Fabian Mönkeberg
Keyword(s):  
Radial Basis Functions ◽  
Hyperbolic Conservation Laws ◽  
High Order ◽  
Basis Functions ◽  
One Dimensional ◽  
Hyperbolic Conservation ◽  
Radial Basis ◽  
Sign Property ◽  
Entropy Stable ◽  
Essentially Nonoscillatory

To solve hyperbolic conservation laws we propose to use high-order essentially nonoscillatory methods based on radial basis functions. We introduce an entropy stable arbitrary high-order finite difference method (RBF-TeCNOp) and an entropy stable second order finite volume method (RBF-EFV2) for one-dimensional problems. Thus, we show that methods based on radial basis functions are as powerful as methods based on polynomial reconstruction. The main contribution is the construction of an algorithm and a smoothness indicator that ensures an interpolation function which fulfills the sign-property on general one dimensional grids.

scholarly journals A high order immersed finite element method for parabolic interface problems

2019 ◽  
Vol 29 ◽  
pp. 01007
Author(s):  
Derrick Jones ◽  
Xu Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
High Order ◽  
Interface Problems ◽  
Numerical Schemes ◽  
Numerical Examples ◽  
Immersed Finite Element Method ◽  
Immersed Finite Element ◽  
Time Marching ◽  
Element Method

We present a high order immersed finite element (IFE) method for solving 1D parabolic interface problems. These methods allow the solution mesh to be independent of the interface. Time marching schemes including Backward-Eulerand Crank-Nicolson methods are implemented to fully discretize the system. Numerical examples are provided to test the performance of our numerical schemes.

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