Improved third‐order weighted essentially nonoscillatory schemes with new smoothness indicators

2020 ◽  
Vol 93 (1) ◽  
pp. 1-23
Author(s):  
Chen Li ◽  
Qilong Guo ◽  
Dong Sun ◽  
Pengxin Liu ◽  
Hanxin Zhang
Keyword(s):  
Third Order ◽  
Weighted Essentially Nonoscillatory ◽  
Smoothness Indicators ◽  
Essentially Nonoscillatory

scholarly journals Optimized Weighted Essentially Nonoscillatory Third-Order Schemes for Hyperbolic Conservation Laws

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
A. R. Appadu ◽  
A. A. I. Peer
Keyword(s):  
Hyperbolic Conservation Laws ◽  
Temporal Integration ◽  
Weno Scheme ◽  
Integration Scheme ◽  
Advection Equation ◽  
Third Order ◽  
Hyperbolic Conservation ◽  
Weighted Essentially Nonoscillatory ◽  
Linear Advection Equation ◽  
Essentially Nonoscillatory

We describe briefly how a third-order Weighted Essentially Nonoscillatory (WENO) scheme is derived by coupling a WENO spatial discretization scheme with a temporal integration scheme. The scheme is termed WENO3. We perform a spectral analysis of its dispersive and dissipative properties when used to approximate the 1D linear advection equation and use a technique of optimisation to find the optimal cfl number of the scheme. We carry out some numerical experiments dealing with wave propagation based on the 1D linear advection and 1D Burger’s equation at some different cfl numbers and show that the optimal cfl does indeed cause less dispersion, less dissipation, and lowerL1errors. Lastly, we test numerically the order of convergence of the WENO3 scheme.

scholarly journals Fifth-Order Mapped Semi-Lagrangian Weighted Essentially Nonoscillatory Methods Near Certain Smooth Extrema

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Lang Wu ◽  
Dazhi Zhang ◽  
Boying Wu ◽  
Xiong Meng
Keyword(s):  
Finite Difference ◽  
Finite Volume ◽  
Interpolation Scheme ◽  
Numerical Examples ◽  
Weighted Essentially Nonoscillatory ◽  
Accuracy Test ◽  
A Cell ◽  
Fifth Order ◽  
Cell Average ◽  
Essentially Nonoscillatory

Fifth-order mapped semi-Lagrangian weighted essentially nonoscillatory (WENO) methods at certain smooth extrema are developed in this study. The schemes contain the mapped semi-Lagrangian finite volume (M-SL-FV) WENO 5 method and the mapped compact semi-Lagrangian finite difference (M-C-SL-FD) WENO 5 method. The weights in the more common scheme lose accuracy at certain smooth extrema. We introduce mapped weighting to handle the problem. In general, a cell average is applied to construct the M-SL-FV WENO 5 reconstruction, and the M-C-SL-FD WENO 5 interpolation scheme is proposed based on an interpolation approach. An accuracy test and numerical examples are used to demonstrate that the two schemes reduce the loss of accuracy and improve the ability to capture discontinuities.

scholarly journals Weighted Essentially Nonoscillatory Method for Two-Dimensional Population Balance Equations in Crystallization

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Chunlei Ruan ◽  
Kunfeng Liang ◽  
Xianjie Chang ◽  
Ling Zhang
Keyword(s):  
Crystal Size ◽  
Hyperbolic Equations ◽  
Population Balance ◽  
Numerical Dispersion ◽  
Two Dimensional ◽  
Governing Equations ◽  
Balance Equations ◽  
Population Balance Equations ◽  
Weighted Essentially Nonoscillatory ◽  
Essentially Nonoscillatory

Population balance equations (PBEs) are the main governing equations to model the processes of crystallization. Two-dimensional PBEs refer to the crystals that grow anisotropically with the change of two internal coordinates. Since the PBEs are hyperbolic equations, it is necessary to build up high resolution schemes to avoid numerical diffusion and numerical dispersion in order to obtain the accurate crystal size distribution (CSD). In this work, a 5th order weighted essentially nonoscillatory (WENO) method is introduced to compute the two-dimensional PBEs. Several numerical benchmark examples from literatures are carried out; it is found that WENO method has higher resolution than HR method which is well established. Therefore, WENO method is recommended in crystallization simulation when the crystal size distributions are sharp and higher accuracy is needed.

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