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High order weighted essentially nonoscillatory WENO-η schemes for hyperbolic conservation laws

Ping Fan
2014 Journal of Computational Physics  
Furthermore, general formulae for the global smoothness indicators are derived with which the WENO-Zη schemes can be extended to all odd-orders of accuracy.  ...  allows the extension of the WENO-η scheme to higher orders of accuracy.  ...  Introduction High-order accurate weighted essentially non-oscillatory (WENO) schemes have recently been developed to solve the hyperbolic conservation law u t + f (u) x = 0 (1) Based on the successful  ... 
doi:10.1016/j.jcp.2014.03.033 fatcat:uh3bqdh3jfekhjxvkdjjitjx5a

Weighted essentially non-oscillatory scheme on unstructured quadrilateral and triangular meshes for hyperbolic conservation laws

Fengxiang Zhao, Liang Pan, Shuanghu Wang
2018 Journal of Computational Physics  
In this paper, a third-order weighted essentially non-oscillatory (WENO) scheme is developed for hyperbolic conservation laws on unstructured quadrilateral and triangular meshes.  ...  However, in the traditional WENO scheme on unstructured meshes, the very large and negative weights may appear for the mesh with lower quality, and the very large weights make the WENO scheme unstable  ...  In this paper, a third-order WENO scheme is developed on unstructured quadrilateral and triangular meshes for the hyperbolic conservation laws.  ... 
doi:10.1016/j.jcp.2018.08.008 fatcat:o6zxzktyxjet3j4rnc5i22gqfe

A modified fifth-order WENO scheme for hyperbolic conservation laws [article]

Samala Rathan, G Naga Raju
2016 arXiv   pre-print
This paper deals with a new fifth-order weighted essentially non-oscillatory (WENO) scheme improving the WENO-NS and WENO-P methods which are introduced in Ha et al. J. Comput.  ...  In this paper, we have presented a scheme by defining a new global-smoothness indicator which shows an improved behavior over the solution to the WENO-NS and WENO-P schemes and the proposed scheme attains  ...  This is the first successful higher order spatial discretization method for the hyperbolic conservation laws that achieves the essentially non-oscillatory (ENO) property and known as ENO schemes.  ... 
arXiv:1609.07625v2 fatcat:ospc7hmubrfwnegkud42q6hy6u

A Speed-Up Strategy for Finite Volume WENO Schemes for Hyperbolic Conservation Laws

Fei Teng, Li Yuan, Tao Tang
2010 Journal of Scientific Computing  
In this paper, a speed-up strategy for finite volume WENO schemes is developed for solving hyperbolic conservation laws.  ...  The corresponding order of accuracy for the solutions is shown to be the same as obtained by original WENO schemes. The strategy is implemented with both WENO and mapped WENO schemes.  ...  Introduction The discontinuities in solutions of hyperbolic conservation laws often produce spurious oscillations in high-order accurate numerical schemes.  ... 
doi:10.1007/s10915-010-9407-9 fatcat:awz4rmn2wbbzzc3ux5r2nqemdm

High Order Finite Difference WENO Schemes for Nonlinear Degenerate Parabolic Equations

Yuanyuan Liu, Chi-Wang Shu, Mengping Zhang
2011 SIAM Journal on Scientific Computing  
High order accurate weighted essentially non-oscillatory (WENO) schemes are usually designed to solve hyperbolic conservation laws or to discretize the first derivative convection terms in convection dominated  ...  In this paper we discuss a high order WENO finite difference discretization for nonlinear degenerate parabolic equations which may contain discontinuous solutions.  ...  Introduction Weighted essentially non-oscillatory (WENO) schemes were introduced in the literature to approximate hyperbolic conservation laws and the first derivative convection terms in convection dominated  ... 
doi:10.1137/100791002 fatcat:lelpqpmgkzdwfdfzo6iiruleoi

High-order gas-kinetic scheme with three-dimensional WENO reconstruction for the Euler and Navier-Stokes solutions [article]

Liang Pan, Kun Xu
2019 arXiv   pre-print
In this paper, a simple and efficient third-order weighted essentially non-oscillatory (WENO) reconstruction is developed for three-dimensional flows, in which the idea of two-dimensional WENO-AO scheme  ...  With such WENO reconstruction, a high-order gas-kinetic scheme (HGKS) is developed for both three-dimensional inviscid and viscous flows.  ...  Pan is supported by National Science Foundation of China (11701038) and the Fundamental Research Funds for the Central Universities. The work of K.  ... 
arXiv:1909.01580v1 fatcat:7j6qv62e2vaebcq3ruo7oywnxi

Entropy stable non-oscillatory fluxes: An optimized wedding of entropy conservative flux with non-oscillatory flux [article]

Ritesh Kumar Dubey
2021 arXiv   pre-print
This simple approach is robust which does not explicitly requires the computation of costly dissipation operator and high order reconstruction of scaled entropy variable for constructing the diffusion  ...  Moreover, these entropy stable schemes maintains the formal order of accuracy of the lower order flux used in the convex combination.  ...  The aim of this work is to construct robust and efficient arbitrary high order non-oscillatory entropy stable scheme for hyperbolic conservation laws (1) .  ... 
arXiv:2108.07088v1 fatcat:2wvjsk4eo5gfpkuvrbixrylk7m

A perturbational weighted essentially non-oscillatory scheme

Fangjun Zeng, Yiqing Shen, Shengping Liu
2018 Computers & Fluids  
In this paper, based on the perturbed fluxes of all candidate fluxes used in the traditional fifthorder WENO scheme, a fifth-order accurate perturbational weighted essentially non-oscillatory (P-WENO)  ...  Thus, the new weighted scheme, which uses the same weights of the WENO-Z scheme and the perturbed fluxes, can meet the necessary and sufficient condition for fifth-order convergence even at critical points  ...  Introduction The weighted essentially non-oscillatory (WENO) schemes have been widely used in solving compressible flows due to their uniformly high order accuracy in smooth regions and essentially nonoscillatory  ... 
doi:10.1016/j.compfluid.2018.07.003 fatcat:tk6b5usambg6xjrqtdi2cjijzm

Simple smoothness indicator WENO-Z scheme for hyperbolic conservation laws [article]

Samala Rathan, G. Naga Raju, Ashlesha A. Bhise
2019 arXiv   pre-print
The advantage of WENO-JS5 scheme [ J. Comput. Phys. 1996] over the WENO-LOC scheme [J. Comput.  ...  Phys.1994] is that the WENO-LOC nonlinear weights do not achieve the desired order of convergence in smooth monotone regions and at critical points.  ...  Numerical Scheme In this section, for completeness we report the flux version of fifth-order WENO schemes presented in [6] for hyperbolic conservation laws (1.1).  ... 
arXiv:1909.13023v1 fatcat:yrfgfawvqna53ixjenpjdvkhli

High Order Well-Balanced WENO Scheme for the Gas Dynamics Equations Under Gravitational Fields

Yulong Xing, Chi-Wang Shu
2012 Journal of Scientific Computing  
In this paper we design high order well-balanced finite difference WENO schemes to this system, which can preserve the hydrostatic balance state exactly and at the same time can maintain genuine high order  ...  Numerical tests are performed to verify high order accuracy, well-balanced property, and good resolution for smooth and discontinuous solutions.  ...  maintains the original high order accuracy and essentially nonoscillatory property for general solutions.  ... 
doi:10.1007/s10915-012-9585-8 fatcat:scbalnhcarfxlk4n5bmnenqwi4

Approximation of Hyperbolic Models for Chemosensitive Movement

Francis Filbet, Chi-Wang Shu
2005 SIAM Journal on Scientific Computing  
On the other hand, a high-order finite difference weighted essentially nonoscillatory (WENO) scheme is constructed and the well-balanced reconstruction is adapted to this scheme to exactly preserve steady  ...  Numerical methods with different orders of accuracy are proposed to approximate hyperbolic models for chemosensitive movements.  ...  Our approach relies on finite volume schemes and finite difference schemes with high-order weighted essentially nonoscillatory (WENO) reconstructions and allows us to exactly preserve a particular class  ... 
doi:10.1137/040604054 fatcat:i3n3luabifgnfkjl5b2ibtb7xy

Finite Difference Hermite WENO Schemes for Hyperbolic Conservation Laws

Hongxia Liu, Jianxian Qiu
2014 Journal of Scientific Computing  
In this paper, a class of weighted essentially non-oscillatory (WENO) schemes based on Hermite polynomials, termed HWENO (Hermite WENO) schemes, for solving one and two dimensional nonlinear hyperbolic  ...  conservation law systems is presented.  ...  Introduction In this paper, we investigated the finite difference Hermite weighted essentially nonoscillatory (HWENO) schemes for solving the nonlinear hyperbolic conservation laws: u t + ∇ · F(u) = 0.  ... 
doi:10.1007/s10915-014-9905-2 fatcat:jshp77pujrha3gagjymesvxhku

Implicit Weighted ENO Schemes for the Three-Dimensional Incompressible Navier–Stokes Equations

Jaw-Yen Yang, Shih-Chang Yang, Yih-Nan Chen, Chiang-An Hsu
1998 Journal of Computational Physics  
Weighted essentially nonoscillatory spatial operators are employed for inviscid fluxes and fourth-order central differencing for viscous fluxes.  ...  A class of lower-upper approximate-factorization implicit weighted essentially nonoscillatory (ENO) schemes for solving the three-dimensional incompressible Navier-Stokes equations in a generalized coordinate  ...  INTRODUCTION The design and construction of the WENO (weighted ENO) schemes for hyperbolic conservation laws are based on ENO (essentially nonoscillatory) schemes which were first introduced by Harten  ... 
doi:10.1006/jcph.1998.6062 fatcat:vyctb7seljbovijb4dxdb3cmtq

IMPROVED TECHNIQUE FOR CONTROLLING OSCILLATION OF COASTAL MORPHOLOGICAL MODELING SYSTEM

Yun-Chih Chiang, Sung-Shan Hsiao, Ming-Chung Lin
2011 Journal of Marine Science and Technology  
The numerical scheme for the sediment conservation law and nonlinear coupling between these modules can lead to dispersions, diffusions, spurious oscillations and instability problems that are still not  ...  The coastal morphological modeling system is based on the sediment conservation law, which couples modules for waves, wave-driven currents, and sediment transport rates.  ...  Among these oscillation removal schemes, the NOC and WENO scheme are more stable finite-difference schemes than the others. 1) WENO Scheme The WENO schemes are based on the essentially nonoscillatory  ... 
doi:10.51400/2709-6998.2204 fatcat:g4wz3sjerfb7ng6qlhn5dczfuu

Gravitational waveforms from binary neutron star mergers with high-order weighted-essentially-nonoscillatory schemes in numerical relativity

Sebastiano Bernuzzi, Tim Dietrich
2016 Physical Review D  
In this work, we explore the use of high-order weighted-essentially-nonoscillatory (WENO) schemes in neutron star merger simulations and investigate the accuracy of the waveforms obtained with such methods  ...  High-order WENO schemes can be thus efficiently used for high-quality waveforms production, also in future large-scale investigations of the binary parameter space.  ...  A particularly efficient reconstruction is the fifth order weighted-essentially-nonoscillatory (WENO) interpolation scheme of [17] , which is very well known in the computational physics literature.  ... 
doi:10.1103/physrevd.94.064062 fatcat:jdernmanirebfjgzfeeqh4vunq
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