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November 18, 2018, 12:26 |
derivatives on a curvilinear grid
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#1 |
New Member
john clyne
Join Date: Nov 2018
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Hello, can someone please shed some light on how to compute partial derivatives using finite differences on a 2D or 3D curvilinear mesh (hexahedral or quadrilateral cells)? I know only the coordinates and sample values at the mesh nodes.
thanks! |
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November 18, 2018, 19:44 |
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#2 |
Senior Member
Join Date: Jul 2009
Posts: 358
Rep Power: 19 |
Look up body-fitted grids or curvilinear grids. The equations are transformed into computational space using the grid metrics. This is for structured grids. For unstructured grids you would need to use the directional derivative, which is the gradient projected alond a coordinate direction. There are various ways to compute the gradient, including Green-Gauss and least squares.
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November 19, 2018, 03:41 |
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#3 |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,897
Rep Power: 73 |
Alternatively, you can define linear or quadratic shape functions over triangles in a FEM manner.
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Tags |
curvilinear coordinate, finite differences |
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