Enhancement of shock-capturing methods via machine learning

B Stevens, T Colonius - Theoretical and Computational Fluid Dynamics, 2020 - Springer
In recent years, machine learning has been used to create data-driven solutions to problems
for which an algorithmic solution is intractable, as well as fine-tuning existing algorithms …

Simple smoothness indicator WENO-Z scheme for hyperbolic conservation laws

S Rathan, NR Gande, AA Bhise - Applied Numerical Mathematics, 2020 - Elsevier
The advantage of WENO-JS scheme (1996)[22] over the WENO-LOC scheme (1994)[27] is
that the WENO-LOC non-linear weights do not achieve the desired order of convergence in …

L1-type smoothness indicators based WENO scheme for nonlinear degenerate parabolic equations

S Rathan, R Kumar, AD Jagtap - Applied Mathematics and Computation, 2020 - Elsevier
In this article an efficient sixth-order finite difference weighted essentially non-oscillatory
scheme is developed to solve nonlinear degenerate parabolic equations. A new type of …

A low‐dissipation third‐order weighted essentially nonoscillatory scheme with a new reference smoothness indicator

Y Wang, Y Du, K Zhao, L Yuan - International Journal for …, 2020 - Wiley Online Library
The classical third‐order weighted essentially nonoscillatory (WENO) scheme is notoriously
dissipative as it loses the optimal order of accuracy at critical points and its two‐point finite …

[HTML][HTML] WENO scheme on characteristics for the equilibrium dispersive model of chromatography with generalized Langmuir isotherms

R Donat, MC Martí, P Mulet - Applied Numerical Mathematics, 2024 - Elsevier
Column chromatography is a laboratory and industrial technique used to separate different
substances mixed in a solution. Mathematically, it can be modeled using non-linear partial …

An efficient three-level weighted essentially non-oscillatory scheme for hyperbolic equations

AAG Neelan, RJ Chandran, MA Diaz… - Computational and Applied …, 2023 - Springer
An improved version of the three-level order-adaptive weighted essentially non-oscillatory
(WENO-OA) scheme introduced in Neelan et al.(Results Appl Math 12: 100217, 2021) is …

Exponential approximation space reconstruction weighted essentially nonoscillatory scheme for dispersive partial differential equations

LV Salian, R Samala - Mathematical Methods in the Applied …, 2024 - Wiley Online Library
In this work, we construct a fifth‐order weighted essentially non‐oscillatory (WENO) scheme
with exponential approximation space for solving dispersive equations. A conservative third …

[HTML][HTML] Three-level order-adaptive weighted essentially non-oscillatory schemes

AAG Neelan, MT Nair, R Bürger - Results in Applied Mathematics, 2021 - Elsevier
Classical fifth-order weighted essentially non-oscillatory (WENO) schemes are based on
reconstructions from three consecutive second-order polynomials. They give a third-order …

A new scale-invariant hybrid WENO scheme for steady Euler and Navier-Stokes equations

Y Wan - Applied Numerical Mathematics, 2025 - Elsevier
The steady-state convergence property of prevalent weighted essentially non-oscillatory
(WENO) schemes usually relies on the sensitivity parameter. On the one hand, it is …

A new framework to construct third‐order weighted essentially nonoscillatory weights using weight limiter functions

S Parvin, R Kumar Dubey - International Journal for Numerical …, 2021 - Wiley Online Library
A new simple and generic framework is proposed to construct nonlinear weights for third‐
order weighted essentially nonoscillatory scheme (WENO) reconstructions. It is done by …