derivatives on a curvilinear grid
 

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!

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.

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