Fifth order AWENO finite difference scheme with adaptive numerical diffusion for Euler equations

Y Wang, WS Don, BS Wang - Computers & Fluids, 2023 - Elsevier
In solving hyperbolic conservation laws using the fifth-order characteristic-wise alternative
WENO finite-difference scheme (AWENO) with Z-type affine-invariant nonlinear Ai-weights …

Affine-invariant WENO weights and operator

BS Wang, WS Don - Applied Numerical Mathematics, 2022 - Elsevier
The novel and simple nonlinear affine-invariant weights (Ai-weights) are devised for the Ai-
WENO operator to handle the case when the function being reconstructed undergoes an …

Fifth-order well-balanced positivity-preserving finite difference AWENO scheme with hydrostatic reconstruction for hyperbolic chemotaxis models

BS Wang, WS Don, P Li - Applied Numerical Mathematics, 2023 - Elsevier
We propose a fifth-order well-balanced positivity-preserving finite difference alternative
WENO (AWENO) scheme with the affine-invariant WENO interpolation based on the Z-type …

Sixth-order perturbed WENO interpolation-based AWENO and WCNS-E schemes for hyperbolic conservation laws

Z Gao, YR Zhao, BS Wang - Applied Mathematics Letters, 2024 - Elsevier
The weighted essentially non-oscillatory (WENO) interpolation-based schemes (the
alternative WENO (AWENO) scheme and the explicit weighted compact nonlinear (WCNS …

A new family of downwind-limited, scale-invariant WENO schemes with optimal accuracy

P Jin, A Al-Rikabi, X Deng - Computers & Fluids, 2023 - Elsevier
Despite improvement over decades, there are still at least two key issues not fully solved in
Weighted Essentially Non-oscillatory (WENO) schemes. Firstly, most WENO schemes hardly …

A Well-Balanced Fifth-Order A-WENO Scheme Based on Flux Globalization

S Chu, A Kurganov, R Xin - arXiv preprint arXiv:2412.19901, 2024 - arxiv.org
We construct a new fifth-order flux globalization based well-balanced (WB) alternative
weighted essentially non-oscillatory (A-WENO) scheme for general nonconservative …

A bound-and positivity-preserving discontinuous Galerkin method for solving the γ-based model

H Wang, H Zhu, Z Gao - Journal of Computational Physics, 2024 - Elsevier
In this work, a bound-and positivity-preserving quasi-conservative discontinuous Galerkin
(DG) method is proposed for the γ-based model of compressible two-medium flows. The …

Improved well-balanced AWENO schemes with hydrostatic reconstruction for the Euler equations under gravitational fields

Q Fu, Z Gao, Y Gu, P Li, BS Wang - Mathematics and Computers in …, 2024 - Elsevier
The Euler equations under gravitational fields allow the hydrostatic equilibrium states, which
requires that the numerical scheme of the system should also have this characteristic. In our …

Affine-Invariant WENO Operator on Nonuniform Cartesian Mesh with Application to Finite Volume and Discontinuous Galerkin Methods

XS Xiang, BS Wang, Z Gao, P Li - Journal of Scientific Computing, 2025 - Springer
For solving hyperbolic conservation laws that arise frequently in computational physics, high
order finite volume WENO (FV-WENO) schemes and discontinuous Galerkin (DG) methods …

[PDF][PDF] Fifth-Order Bound-, Positivity-, and Equilibrium-Preserving Affine-Invariant AWENO Scheme for Two-Medium γ-based Model of Stiffened Gas

BS Wang, WS Don - Shock Waves, 2023 - researchgate.net
We describe a quasi-conservative finite difference AWENO scheme with the affine-invariant
Z-type nonlinear weights (Ai-AWENO) for the γ-based model. The shockcapturing scheme …