What You Give Up the Exact Riemann Solution For — the Roe Solver and the Entropy Fix
·7 min read
When an eigenvalue crosses zero, Roe locks an expansion shock. The sqrt(rho) average and Harten's floor decide whether that sonic kink stays.
The Euler Eigensystem in an Arbitrary Direction — Three Waves, Two Repeats, One Singularity
·6 min read
At n_x=0.01 the R-1 left-eigenvector row divides by 100, and at zero it diverges. A 30 degree face keeps R-1; a face along y switches to R-2.
[Paper Review] Why Roe breaks at low Mach — Hope–Collins (2022) and three artificial-diffusion scalings
·6 min read
At Mach 0.01 the convective scaling leaves amplitude 0.018. Acoustic and mixed scalings still hold 0.974 and 0.971 after one acoustic period.