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NASA NTRS · 20210024787

F-ANG+: A 3-D Augmented-Stencil Face-Averaged Nodal-Gradient Cell-Centered Finite-Volume Method for Hypersonic Flows

Jeffery A White·Hiroaki Nishikawa·Matthew D. O’Connell
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Weighted Least-SquaresComputational Fluid DynamicsHypersonic FlowGradient LimitersUnstructured GridsAdapted Grids

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Jeffery A White, Hiroaki Nishikawa, Matthew D. O’Connell. F-ANG+: A 3-D Augmented-Stencil Face-Averaged Nodal-Gradient Cell-Centered Finite-Volume Method for Hypersonic Flows. https://ntrs.nasa.gov/citations/20210024787

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F-ANG+: A 3-D Augmented-Stencil Face-Averaged Nodal-Gradient Cell-Centered Finite-Volume Method for Hypersonic Flows

We describe the extension of a 2-D simplified face-averaged nodal-gradient (F-ANG) method to 3-D and demonstrate that the 3-D simplified F-ANG method is accomplished by augmenting the nodecentered gradient least squares stencil. This augmented stencil F-ANG method is shown to result in advection and diffusion schemes that are stable for hexahedral, prismatic, pyramidal and tetrahedral cells without having to resort to cell-averaged nodal gradients. In addition, we describe the modifications to the augmented stencil required to support the use of wall function boundary conditions. Finally we describe a consistent, face-stencil based multi-dimensional limiter procedure (MLP), and show it to be fully consistent and compatible with the linearity-preserving unstructured- MUSCL (LP-U-MUSCL) scheme for all values of kappa. These methods and schema are implemented in the cell-centered finite-volume code VULCAN-CFD, which is then used to investigate whether the robustness improvements demonstrated in 2-D carry over to 3-D by computing hypersonic flows using mixed-element grids as well as highly adapted tetrahedral grids.

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