MUSCL-Hancock method with Total-Variation-Diminishing 'principle' (MINBEE slope limiter) and HLLC Riemann Solver are used to solve 1-D Euler Equations.

The following are same numerical experiments as before. As you can see, second order scheme is more accurate also more spurious. If TVD principle is not applied to MUSCL-Hancock second order method, the spurious effect will be more severe. Please compare it with the HLLC scheme ​HLLC.

When I was writing this program, I did not follow the book exactly. One will find the problem if he (she) apply the method described in book to the second test (2 strong rarefaction wave case). To be more specific, I made some modification to the slope limiter, but it become very complicated. A more attractive method is Adaptive Primitive Conservative Scheme using Characteristic Limiting Method and MUSCL-Hancock Method with Total-Variation-Diminishing 'principle' (slope limiter). I thought about how to implement it, should I do it? (It will take another week or two)

Example: Shock tube

Example: Two strong rarefaction

Example: Left rarefaction and right contact and shock wave

Example: Right half of Woodward and Colella problem. Gibbs phenomenon happens.

Example: Two shock case