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Chapter 1
Tensor mathematics

This Chapter describes tensors and their algebraic operations and how they are represented in mathematical text in this book. It then explains how tensors and tensor algebra are programmed in OpenFOAM.


 1.1 Coordinate system
 1.2 Tensors
  1.2.1 Tensor notation
 1.3 Algebraic tensor operations
  1.3.1 The inner product
  1.3.2 The double inner product of two tensors
  1.3.3 The triple inner product of two third rank tensors
  1.3.4 The outer product
  1.3.5 The cross product of two vectors
  1.3.6 Other general tensor operations
  1.3.7 Geometric transformation and the identity tensor
  1.3.8 Useful tensor identities
  1.3.9 Operations exclusive to tensors of rank 2
  1.3.10 Operations exclusive to scalars
 1.4 OpenFOAM tensor classes
  1.4.1 Algebraic tensor operations in OpenFOAM
 1.5 Dimensional units

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