Wai Sun Don

Ocean University of China

Richtmyer–Meshkov instabilityPhysicsStatistical physicsMathematical analysisMixing (physics)Nonlinear systemMach numberFinite differenceDetonationFinite difference methodInstabilitySpectral methodApplied mathematicsHigh orderMathematicsConservation lawEuler equationsMechanicsShock waveClassical mechanics

81Publications

24H-index

2,521Citations

Publications 83

Newest

#1Wai Sun Don (Ocean University of China)H-Index: 24

#2Run Li (Ocean University of China)H-Index: 1

Last. Yinghua Wang (Nanjing Tech University)H-Index: 2

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Abstract null null A novel, simple, robust, and effective modification in the nonlinear weights of the scale-invariant WENO operator is proposed that achieves an optimal order of accuracy with smooth function regardless of the critical point (Cp-property), a scale-invariant with an arbitrary scaling of a function (Si-property), an essentially non-oscillatory approximation of a discontinuous function (ENO-property), and, in some cases, a well-balanced WENO finite difference/volume scheme (WB-prop...

#1Bao-Shan WangH-Index: 4

#2Wai Sun DonH-Index: 24

Last. Yongle LiuH-Index: 4

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Sensitivity Parameter-Independent Characteristic-Wise Well-Balanced Finite Volume WENO Scheme for the Euler Equations Under Gravitational Fields

#1Peng LiH-Index: 5

#2Bao-Shan Wang (Ocean University of China)H-Index: 4

Last. Wai Sun Don (Ocean University of China)H-Index: 24

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Euler equations with a gravitational source term (PDEs) admit a hydrostatic equilibrium state where the source term exactly balances the flux gradient. The property of exact preservation of the equilibria is highly desirable when the PDEs are numerically solved. Li and Xing (J Comput Phys 316:145–163, 2016) proposed a high-order well-balanced characteristic-wise finite volume weighted essentially non-oscillatory (FV-WENO) scheme for the cases of isothermal equilibrium and polytropic equilibrium....

Fifth-Order A-WENO Finite-Difference Schemes Based on a New Adaptive Diffusion Central Numerical Flux

#1Bao-Shan WangH-Index: 4

#2Wai Sun DonH-Index: 24

Last. Alexander KurganovH-Index: 30

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A new adaptive diffusion central numerical flux within the framework of fifth-order characteristicwise alternative WENO-Z finite-difference schemes (A-WENO) with a modified local Lax--Friedrichs (L...

Entropy Stable and Well-Balanced Discontinuous Galerkin Methods for the Nonlinear Shallow Water Equations

#1Xiao Wen (Ocean University of China)H-Index: 5

#2Wai Sun Don (Ocean University of China)H-Index: 24

Last. Yulong Xing (OSU: Ohio State University)H-Index: 23

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The nonlinear shallow water equations (SWEs) are widely used to model the unsteady water flows in rivers and coastal areas, with extensive applications in ocean and hydraulic engineering. In this work, we propose entropy stable, well-balanced and positivity-preserving discontinuous Galerkin (DG) methods, under arbitrary choices of quadrature rules, for the SWEs with a non-flat bottom topography. In Chan (J Comput Phys 362:346–374, 2018), a SBP-like differentiation operator was introduced to cons...

An Edge Detector Based on Artificial Neural Network with Application to Hybrid Compact-WENO Finite Difference Scheme

#1Xiao WenH-Index: 5

#2Wai Sun DonH-Index: 24

Last. Jan S. HesthavenH-Index: 63

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A new approach is proposed to detect edges based on an artificial neural network (ANN). Some elementary continuous and discontinuous functions interpolated in the polynomial space and their continuity are used as the training sets to train a back propagation neural network containing two hidden layers. The ANN edge detector is used to detect the edges in an image and the locations of discontinuity in the hybrid fifth order Compact-WENO nonlinear (Hybrid) scheme for solving hyperbolic conservatio...

Seventh and ninth orders characteristic-wise alternative WENO finite difference schemes for hyperbolic conservation laws

#1Zhen Gao (Ocean University of China)H-Index: 11

#2Li-Li Fang (Ocean University of China)H-Index: 1

Last. Wai Sun Don (Ocean University of China)H-Index: 24

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Abstract In this work, the characteristic-wise alternative formulation of the seventh and ninth orders conservative weighted essentially non-oscillatory (AWENO) finite difference schemes are derived. The polynomial reconstruction procedure is applied to the conservative variables rather than the flux function of the classical WENO scheme. The numerical flux contains a low order term and high order derivative terms. The low order term can use arbitrary monotone fluxes that can enhance the resolut...

High order well-balanced finite difference WENO interpolation-based schemes for shallow water equations

#1Peng LiH-Index: 5

#2Wai Sun Don (Ocean University of China)H-Index: 24

Last. Zhen Gao (Ocean University of China)H-Index: 11

view all 3 authors...

Abstract A numerical framework of the generalized form of high order well-balanced finite difference weighted essentially non-oscillatory (WENO) interpolation-based schemes is proposed for the shallow water equations. It demonstrates more flexible construction process than the classical WENO reconstruction-based schemes. The weighted compact nonlinear schemes and finite difference alternative WENO schemes are two specific cases. To maintain the exact C-property, the splitting technique for the s...

A Characteristic-wise Alternative WENO-Z Finite Difference Scheme for Solving the Compressible Multicomponent Non-reactive Flows in the Overestimated Quasi-conservative Form

#1Wai Sun Don (Ocean University of China)H-Index: 24

#2Dong-Mei Li (Ocean University of China)H-Index: 1

Last. Bao-Shan Wang (Ocean University of China)H-Index: 4

view all 4 authors...

The fifth, seventh and ninth order characteristic-wise alternative weighted essentially non-oscillatory (AWENO) finite difference schemes are applied to the fully conservative (FC) form and the overestimated quasi-conservative (OQC) form of the compressible multicomponent flows. Several linear and nonlinear numerical operators such as the linear Lax–Friedrichs operator and linearized nonlinear WENO operator and their mathematical properties are defined in order to build a general mathematical (n...

Generalized Sensitivity Parameter Free Fifth Order WENO Finite Difference Scheme with Z-Type Weights

#1Yinghua Wang (Ocean University of China)H-Index: 2

#2Bao-Shan Wang (Ocean University of China)H-Index: 4

Last. Wai Sun Don (Ocean University of China)H-Index: 24

view all 3 authors...

A modified fifth order Z-type (nonlinear) weights, which consist of a linear term and a nonlinear term, in the weighted essentially non-oscillatory (WENO) polynomial reconstruction procedure for the WENO-Z finite difference scheme in solving hyperbolic conservation laws is proposed. The nonlinear term is modified by a modifier function that is based on the linear combination of the local smoothness indicators. The WENO scheme with the modified Z-type weights (WENO-D) scheme and its improved vers...

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