11 problems

A numerical method for the Euler equations is considered, with vorticity as a diagnostic of anomalous numerical solutions such as carbuncle phenomena and unphysical Mach stems. Mor…

Sweeping-limiter conjecture. The combination of the robust scaling limiter for pressure correction and the mass-redistribution technique of the sweeping limiter explains why only o…

For a numerical scheme, let the mass flux denote its mass-flux function and let the pressure term denote the pressure contribution to that flux. Liou's conjecture. Schemes with a m…

Let SEGNN denote the geometric graph neural network used to estimate three-dimensional velocity fields from arterial input meshes, and let $\mathrm{SE}(3)$ denote the group of roto…

Let $\beta_x$ and $\beta_y$ be the Fourier wave-number variables, and let the function governing the amplification factor be $|z_0|^2$, where $z_0$ is defined by the characteristic…

Efficiency-difference conjecture. The difference is due to the design domain being more compact rather than elongated, the low Reynolds number, and the dependence on the initial de…

Consider the three-dimensional Euler solution arising from the same initial data used in the comparison computations described in Cases 1 and 3. Finite-time singularity conjecture.…

In the reported hierarchical high-order CFD solver experiments, the matrix ranks vary across the computational domain, with larger test cases exhibiting relatively high maximum ran…

Cost-increment conjecture. The cost increment factor for regular triangulation refinement is conjectured to satisfy

For the present flow over a circular cylinder, the overall numerical error is conjectured to be highly sensitive to the most upstream errors. This concerns the propagation of local…

The van Leer fluxes are observed to perform well in the computations. Low-diffusion massflux conjecture. Problems arise only when a low-diffusion (non-dissipative) massflux is used…