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How Tensor Transforms Between Cartesian and Polar Coordinate Systems

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Old   February 26, 2018, 19:53
Default How Tensor Transforms Between Cartesian and Polar Coordinate Systems
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The specific problem is to calculate the viscoelastic flow around the cylinder, the value of the stress tensor at the boundary is to be set. The calculation uses Cartesian coordinates. Under the formula of the stress tensor of the cylindrical wall under the polar coordinate system, the required result needs to be calculated through three steps:
1, The speed gradient (tensor) under Cartesian coordinate system transform to the polar coordinate system.
2, Calculate the stress tensor by (Equation 18).
3, stress tensor and then transform to Cartesian coordinate system.

Is this the case? I can understand the stress tensor. My question is the speed gradient in the Cartesian coordinate system transformed directly into the polar coordinate system?

thank you all.
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