A new type of increasingly high-order multi-resolution trigonometric WENO schemes for hyperbolic conservation laws and highly oscillatory problems

2020 ◽  
Vol 200 ◽  
pp. 104448 ◽  
Author(s):  
Yanmeng Wang ◽  
Jun Zhu
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
High Order ◽  
Weno Schemes ◽  
Hyperbolic Conservation ◽  
Highly Oscillatory ◽  
New Type ◽  
Highly Oscillatory Problems

High Order Fixed-Point Sweeping WENO Methods for Steady State of Hyperbolic Conservation Laws and Its Convergence Study

2016 ◽  
Vol 20 (4) ◽  
pp. 835-869 ◽  
Author(s):  
Liang Wu ◽  
Yong-Tao Zhang ◽  
Shuhai Zhang ◽  
Chi-Wang Shu
Keyword(s):  
Fixed Point ◽  
Steady State ◽  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
High Order ◽  
Efficient Computation ◽  
Weno Schemes ◽  
Hyperbolic Conservation ◽  
Time Marching ◽  
Fifth Order

AbstractFixed-point iterative sweeping methods were developed in the literature to efficiently solve static Hamilton-Jacobi equations. This class of methods utilizes the Gauss-Seidel iterations and alternating sweeping strategy to achieve fast convergence rate. They take advantage of the properties of hyperbolic partial differential equations (PDEs) and try to cover a family of characteristics of the corresponding Hamilton-Jacobi equation in a certain direction simultaneously in each sweeping order. Different from other fast sweeping methods, fixed-point iterative sweeping methods have the advantages such as that they have explicit forms and do not involve inverse operation of nonlinear local systems. In principle, it can be applied in solving very general equations using any monotone numerical fluxes and high order approximations easily. In this paper, based on the recently developed fifth order WENO schemes which improve the convergence of the classical WENO schemes by removing slight post-shock oscillations, we design fifth order fixed-point sweeping WENO methods for efficient computation of steady state solution of hyperbolic conservation laws. Especially, we show that although the methods do not have linear computational complexity, they converge to steady state solutions much faster than regular time-marching approach by stability improvement for high order schemes with a forward Euler time-marching.

scholarly journals High order explicit local time stepping methods for hyperbolic conservation laws

2020 ◽  
Vol 89 (324) ◽  
pp. 1807-1842
Author(s):  
Thi-Thao-Phuong Hoang ◽  
Lili Ju ◽  
Wei Leng ◽  
Zhu Wang
Keyword(s):  
Conservation Laws ◽  
Local Time ◽  
Hyperbolic Conservation Laws ◽  
High Order ◽  
Hyperbolic Conservation ◽  
Time Stepping ◽  
Local Time Stepping
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