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What is the total variation of a flow variable (Φ) at a particular time step t?

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What is the total variation of a flow variable (Φ) at a particular time step t?

(a) TV^t=∏iΦi+1-Φi

(b) TV^t=∫n Φndn

(c) TV^t=∑iΦ(i+1)Φi

(d) TV^t=∑iΦ(i+1)Φi

The question was asked in an internship interview.

My question comes from High Resolution Schemes topic in section High Resolution Schemes of Computational Fluid Dynamics

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Correct option is (d) TV^t=∑iΦ(i+1)Φi

Explanation: Total variation is the summation of variations of the flow variable between two consecutive nodes. This is mathematically given as

TV^t=∑iΦi+1-Φi.

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