Towards Robust and Accurate Implicit Gradient Methods for Second- and Third-Order Nodal-Gradient Cell-Centered Finite-Volume Discretizations on Tetrahedral Grids

Hiroaki Nishikawa

NASA NTRS · 20240004368

Towards Robust and Accurate Implicit Gradient Methods for Second- and Third-Order Nodal-Gradient Cell-Centered Finite-Volume Discretizations on Tetrahedral Grids

Abstract

In this paper, we introduce implicit gradient methods as alternatives to conventional least-squares gradient methods for second- and third-order nodal-gradient cell-centered finite-volume discretizations, where solutions are stored at cells but gradients are stored at nodes. Because of the unique configuration of solutions and gradients, implicit gradient systems developed for the node-centered edge-based discretization method can be directly applied once the numerical solutions are interpolated from cells to nodes with sufficient accuracy. The resulting defect-correction solver can be loosely coupled with a flow-equation solver, and at convergence, solutions and gradients that satisfy the corresponding residual equations are obtained. Each iteration is relatively cheap compared with least-squares methods involving hundreds of neighbors. Numerical results are presented for accuracy verification studies and some simple but realistic flow problems.

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Computational Fluid Dynamics Unstructured Grids Implicit gradients Third-order scheme

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BibTeX RIS

Hiroaki Nishikawa. Towards Robust and Accurate Implicit Gradient Methods for Second- and Third-Order Nodal-Gradient Cell-Centered Finite-Volume Discretizations on Tetrahedral Grids. https://ntrs.nasa.gov/citations/20240004368

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