The answer can be done if you read the references below:
Leveque (2002) - Finite Volume Methods for Hyperbolic Problems
Toro (2009) - Riemann Solvers and Numerical Methods for Fluid Mechanics
Godlevski and Raviart (1996) - Numerical Approximation of Hyperbolic Systems of Conservation Laws. With kind regards.
Sorry, but we need to give artifcial disspaition (AD) for MacCormack scheme. The code does'nt converge otherwise. For TVD scheme, we need not give any such disspation term. The following paper uses AD.
http://www.sciencedirect.com/science/article/pii/S0045793010002641
And I am presently using AD term mentioned in the CFD by Anderson book, and it is working fine for the simple case I have teasted.
You must avoid pseudo dissipation terms because most of the time lead to "wrong" solutions
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