High-Order Numerical Schemes for Unsteady Compressible Flow on the Dissipation of Internal Energy

Various TVD(total variation diminishing) and WENO(weighted essentially non-oscillatory) methods with high-order spatial accuracy are verified and compared for three examples of one-dimensional problems: Sod's shock tube and shock-entropy wave interaction. Both limiter-based with second-order accuracy generally used in engineering society and WENO-based methods with fifth and seventh order accuracy are tested for the spatial reconstruction of Riemann problem approximated with Roe's scheme where the result is precisely verified for methods one by one for the characteristic-wise WENO as well as the original WENO flux splitting method. The instant distribution of internal energy is focused on the flow region near the contact discontinuity and the entropy wave in this study, and the full capacity of numerical schemes are presented each other for the oscillation of internal energy.