[Paper Review] Raising β to 2 froze the interface at 14 cells and made a sine worse than first-order upwind — Tallois's compressive limiter
·3 min read
With a β=2 compressive limiter on the volume fraction, a slab interface stays 14 cells wide after five periods. The same limiter gives a sine wave a larger L1 error than first-order upwind.
The Same Code Gave 0.79 and 2.00 at Once — What Verification Cases Actually Measure
·8 min read
Sod's density L1 order is 0.79 on a discontinuous tube. The same MUSCL–HLLC code gives 2.001 on a smooth wave, and minmod pulls that down to 1.491.
The Fake Extrema a Second-Order Reconstruction Invents on Unstructured Grids — Barth–Jespersen and Venkatakrishnan Limiters
·7 min read
A second-order face value on an unstructured cell can leave the neighbor range. Barth–Jespersen clips that slope; Venkatakrishnan rounds the clip with K.
Advecting Without Splitting Directions — The Bell-Colella-Glaz Unsplit Upwind Scheme
·7 min read
Directional splitting twists a diagonal scalar. Bell-Colella-Glaz keeps the rotating disk's peak with a (1-CFL) slope weight plus a transverse correction.