Development of A Hermite Weighted Compact Nonlinear Scheme based on the Two-Stage Fourth-Order Temporal Accurate Framework

TL;DR

This paper introduces an advanced nonlinear scheme combining Hermite weighted compact nonlinear schemes with a two-stage fourth-order temporal discretization, aiming for high accuracy and low dissipation in computational fluid dynamics.

Contribution

It develops a novel Hermite WCNS that integrates a two-stage fourth-order temporal framework, enhancing accuracy and stability over existing methods.

Findings

Achieves high-order temporal accuracy with reduced numerical dissipation.

Demonstrates improved stability and accuracy in test simulations.

Provides a new approach for efficient high-fidelity simulations.

Abstract

Improved five-point low dissipation nonlinear schemes are proposed in this paper within the framework of weighted compact nonlinear schemes (WCNSs) \cite{Deng2000}. Particularly we follow the work of Li and Du \cite{Li2016} on the two-stage fourth-order temporal accurate discretization scheme, which is developed based on the Lax-Wendroff method.