High Order Extrapolation Techniques for WENO Finite-Difference Schemes Applied to NACA Airfoil Profiles

TL;DR

This paper introduces a high order boundary extrapolation method combined with WENO finite-difference schemes to improve the resolution of solutions around NACA airfoil profiles, achieving results comparable to unstructured mesh techniques.

Contribution

It presents a novel high order boundary extrapolation technique integrated with WENO schemes for better accuracy near complex geometries.

Findings

High order boundary extrapolation improves solution accuracy near airfoil edges.

Results are comparable to unstructured mesh methods in accuracy.

The method enhances resolution without significantly increasing computational cost.

Abstract

Finite-difference WENO schemes are capable of approximating accurately and efficiently weak solutions of hyperbolic conservation laws. In this context high order numerical boundary conditions have been proven to increase significantly the resolution of the numerical solutions. In this paper a finite-difference WENO scheme is combined with a high order boundary extrapolation technique at ghost cells to solve problems involving NACA airfoil profiles. The results obtained are comparable with those obtained through other techniques involving unstructured meshes.