MacCormack Scheme Sod's Shock Tube Test
 

I am a beginner in CFD, and I was coding the Sod's Shock Tube Test 2 (as per this link http://www.thevisualroom.com/sods_test_problem.html) in Matlab. While using the Maccormack Scheme I am getting ridiculous overshoots, and even the damping term (using a 4th order one) is not providing enough damping to get to an acceptable solution. What should I do?

have a reading in the books

https://www.amazon.co.uk/Numerical-S.../dp/0521607930

https://www.amazon.com/Methods-Hyper.../dp/0521009243

Thank You for the suggestions!