I am new to tensor mathematics and CFD mathematics, but the following books have been quite helpful. [1-3] have great reviews of the mathematics of scalars, vectors, and tensors. [2-4] together cover the mathematics of CFD. Now, I just need better comprehension. #CFDBooks #BeginningOpenFOAM
Note that equation 10b is wrong in Mathematical Exposition 1[3]. See [5] for verification by a PhD in Fluid Dynamics from University of Texas at Austin.
References:
[1] SimCenter. National Center for Computational Engineering. An Introduction to Vectors and Tensors from a Computational Perspective. URL: https://www.utc.edu/sites/default/files/2020-06/utc-cecs-simcenter-2014-01.pdf
[2] Tobias Holzmann. Mathematics, Numerics, Derivations and OpenFOAM(R), Holzmann CFD, Leoben, fourth edition, February 2017. URL: http://www.holzmann-cfd.de
[3] Warsi, Z.U.A.. Fluid Dynamics. Taylor and Francis CRC ebook account. Kindle Edition.
[4] Hirsch, Charles. (2007). Numerical Computation of Internal and External Flows: The Fundamentals of Computational Fluid Dynamics. Elsevier
[5] https://math.stackexchange.com/questions/4266972/am-i-expanding-grad-v-which-is-in-index-notation-correctly-is-equation-10b-wr
An Experiment In Life 