Exponential approximation space reconstruction weighted essentially nonoscillatory scheme for dispersive partial differential equations
Year: 2023
Type: article
Abstract: 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‐order derivative formulation is developed directly using WENO spatial reconstruction procedure, and third‐order TVD Runge–Kutta scheme is used for the evaluation of time derivative. This exponential approximation space consists a tension parameter that may be optimized to fit the specific feature of the characteristic data, yielding better results without spurious oscillations compared to the polynomial approximation space. A detailed formulation is presented for the construction of conservative flux approximation, smoothness indicators, nonlinear weights, and verified that the proposed scheme provides the required fifth convergence order. One‐ and two‐dimensional numerical examples are presented to support the theoretical claims.
DOI: 10.1002/mma.9720
Authors: Lavanya V. Salian, Rathan Samala
Institution: Indian Institute of Petroleum and Energy
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4387813304