Higher Order Gradients on Unstructured Meshes using Compact Formulation for Node-Centered Schemes
Paper in proceeding, 2022

This paper introduces a new approach for gradient computations on node-centered unstructured grids. The proposed approach is to derive a gradient algorithm from a least squares approximation, where a local system is solved to introduce connectivity between neighbouring nodes. The resulting scheme forms a globally coupled linear system of equations for the gradients which can be solved efficiently by iterative techniques. Fourth-order gradient accuracy for interior nodes can be obtained on isotropic quadrilateral and mixed elements (quadrilaterals and triangles) grids. The same accuracy is achieved on quadrilateral and mixed elements grids with high-aspect-ratio. Additionally, a different formulation to the standard distance weighted least squares node-centered gradients is proposed, which shows robust second-order accuracy on grids with high-aspect-ratio compared to the standard formulation. The paper concludes with a proposed continuation for future developments.

Author

Magnus Carlsson

Chalmers, Mechanics and Maritime Sciences (M2), Fluid Dynamics

Lars Davidson

Chalmers, Mechanics and Maritime Sciences (M2), Fluid Dynamics

Peng Shia-Hui

Chalmers, Mechanics and Maritime Sciences (M2), Fluid Dynamics

Swedish Defence Research Agency (FOI)

Sebastian Arvidson

Saab

Chalmers, Mechanics and Maritime Sciences (M2), Fluid Dynamics

AIAA AVIATION 2022 Forum

AIAA 2022-4156
9781624106354 (ISBN)

AIAA AVIATION 2022 Forum
Chicago, USA,

Subject Categories

Computational Mathematics

Control Engineering

Signal Processing

DOI

10.2514/6.2022-4156

More information

Latest update

8/16/2022