derivatives on a curvilinear grid

clyne · November 18, 2018, 12:26

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!

agd · November 18, 2018, 19:44

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.

FMDenaro · November 19, 2018, 03:41

Alternatively, you can define linear or quadratic shape functions over triangles in a FEM manner.

November 18, 2018, 12:26	derivatives on a curvilinear grid	#1
clyne New Member john clyne Join Date: Nov 2018 Posts: 1 Rep Power: 0	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		#2
agd 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.

November 19, 2018, 03:41		#3
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,882 Rep Power: 73	Alternatively, you can define linear or quadratic shape functions over triangles in a FEM manner.